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krahets
2026-03-29 05:07:03 +08:00
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commit 9466700256
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zh-hant/chapter_sorting/bubble_sort/index.html
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@@ -35,18 +35,23 @@
<link rel="icon" href="../../assets/images/favicon.png">
<meta name="generator" content="mkdocs-1.6.1, mkdocs-material-9.7.1">
<meta name="generator" content="zensical-0.0.29">
<title>11.3   泡沫排序 - Hello 演算法</title>
<title>11.3 泡沫排序 - Hello 演算法</title>
<link rel="stylesheet" href="../../assets/stylesheets/main.484c7ddc.min.css">
<link rel="stylesheet" href="../../assets/stylesheets/palette.ab4e12ef.min.css">
<link rel="stylesheet" href="../../assets/stylesheets/modern/main.6f2fbb28.min.css">
<link rel="stylesheet" href="../../assets/stylesheets/modern/palette.dfe2e883.min.css">
@@ -60,29 +65,20 @@
<link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans+SC:300,300i,400,400i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans+SC:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
<style>:root{--md-text-font:"Noto Sans SC";--md-code-font:"JetBrains Mono"}</style>
<link rel="stylesheet" href="../../stylesheets/extra.css">
<script>__md_scope=new URL("../..",location),__md_hash=e=>[...e].reduce(((e,_)=>(e<<5)-e+_.charCodeAt(0)),0),__md_get=(e,_=localStorage,t=__md_scope)=>JSON.parse(_.getItem(t.pathname+"."+e)),__md_set=(e,_,t=localStorage,a=__md_scope)=>{try{t.setItem(a.pathname+"."+e,JSON.stringify(_))}catch(e){}}</script>
<script>__md_scope=new URL("../..",location),__md_hash=e=>[...e].reduce(((e,t)=>(e<<5)-e+t.charCodeAt(0)),0),__md_get=(e,t=localStorage,a=__md_scope)=>JSON.parse(t.getItem(("__palette"===e?"/":a.pathname)+"."+e)),__md_set=(e,t,a=localStorage,_=__md_scope)=>{try{a.setItem(("__palette"===e?"/":_.pathname)+"."+e,JSON.stringify(t))}catch(e){}},document.documentElement.setAttribute("data-platform",navigator.platform)</script>
<link href="../../assets/stylesheets/glightbox.min.css" rel="stylesheet"/><style>
html.glightbox-open { overflow: initial; height: 100%; }
.gslide-title { margin-top: 0px; user-select: text; }
.gslide-desc { color: #666; user-select: text; }
.gslide-image img { background: white; }
.gscrollbar-fixer { padding-right: 15px; }
.gdesc-inner { font-size: 0.75rem; }
body[data-md-color-scheme="slate"] .gdesc-inner { background: var(--md-default-bg-color);}
body[data-md-color-scheme="slate"] .gslide-title { color: var(--md-default-fg-color);}
body[data-md-color-scheme="slate"] .gslide-desc { color: var(--md-default-fg-color);}</style> <script src="../../assets/javascripts/glightbox.min.js"></script></head>
</head>
@@ -97,7 +93,7 @@
<input class="md-toggle" data-md-toggle="drawer" type="checkbox" id="__drawer" autocomplete="off">
<input class="md-toggle" data-md-toggle="search" type="checkbox" id="__search" autocomplete="off">
<label class="md-overlay" for="__drawer"></label>
<label class="md-overlay" for="__drawer" aria-label="導航"></label>
<div data-md-component="skip">
@@ -139,12 +135,12 @@
<nav class="md-header__inner md-grid" aria-label="頁首">
<a href="../.." title="Hello 演算法" class="md-header__button md-logo" aria-label="Hello 演算法" data-md-component="logo">
<img src="../../assets/images/logo.svg" alt="logo">
<img src="../../assets/images/logo.svg" alt="Hello 演算法">
</a>
<label class="md-header__button md-icon" for="__drawer">
<label class="md-header__button md-icon" for="__drawer" aria-label="導航">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 6h18v2H3zm0 5h18v2H3zm0 5h18v2H3z"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-menu" viewBox="0 0 24 24"><path d="M4 5h16M4 12h16M4 19h16"/></svg>
</label>
<div class="md-header__title" data-md-component="header-title">
<div class="md-header__ellipsis">
@@ -169,7 +165,7 @@
<input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="teal" aria-label="深色模式" type="radio" name="__palette" id="__palette_0">
<input class="md-option" data-md-color-media="none" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="teal" aria-label="深色模式" type="radio" name="__palette" id="__palette_0">
<label class="md-header__button md-icon" title="深色模式" for="__palette_1" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07zm-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13zm-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87zM19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35zm4.33-2.7 1.15-2.77 2.2 2.54zm1.15-4.96-1.14-2.78 3.34.24zM9.63 18.93l2.77 1.15-2.53 2.19z"/></svg>
@@ -179,7 +175,7 @@
<input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="black" data-md-color-accent="teal" aria-label="淺色模式" type="radio" name="__palette" id="__palette_1">
<input class="md-option" data-md-color-media="none" data-md-color-scheme="slate" data-md-color-primary="black" data-md-color-accent="teal" aria-label="淺色模式" type="radio" name="__palette" id="__palette_1">
<label class="md-header__button md-icon" title="淺色模式" for="__palette_0" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07zm-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13zm-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87zM19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35zm4.33-2.7 1.15-2.77 2.2 2.54zm1.15-4.96-1.14-2.78 3.34.24zM9.63 18.93l2.77 1.15-2.53 2.19z"/></svg>
@@ -197,7 +193,7 @@
<div class="md-select">
<button class="md-header__button md-icon" aria-label="選擇語言">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12.87 15.07-2.54-2.51.03-.03A17.5 17.5 0 0 0 14.07 6H17V4h-7V2H8v2H1v2h11.17C11.5 7.92 10.44 9.75 9 11.35 8.07 10.32 7.3 9.19 6.69 8h-2c.73 1.63 1.73 3.17 2.98 4.56l-5.09 5.02L4 19l5-5 3.11 3.11zM18.5 10h-2L12 22h2l1.12-3h4.75L21 22h2zm-2.62 7 1.62-4.33L19.12 17z"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-languages" viewBox="0 0 24 24"><path d="m5 8 6 6M4 14l6-6 2-3M2 5h12M7 2h1M22 22l-5-10-5 10M14 18h6"/></svg>
</button>
<div class="md-select__inner">
<ul class="md-select__list">
@@ -240,64 +236,30 @@
<label class="md-header__button md-icon" for="__search">
<label class="md-header__button md-icon" for="__search" aria-label="搜尋">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.52 6.52 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-search" viewBox="0 0 24 24"><path d="m21 21-4.34-4.34"/><circle cx="11" cy="11" r="8"/></svg>
</label>
<div class="md-search" data-md-component="search" role="dialog">
<label class="md-search__overlay" for="__search"></label>
<div class="md-search__inner" role="search">
<form class="md-search__form" name="search">
<input type="text" class="md-search__input" name="query" aria-label="搜尋" placeholder="搜尋" autocapitalize="off" autocorrect="off" autocomplete="off" spellcheck="false" data-md-component="search-query" required>
<label class="md-search__icon md-icon" for="__search">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.52 6.52 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11z"/></svg>
</label>
<nav class="md-search__options" aria-label="搜尋">
<a href="javascript:void(0)" class="md-search__icon md-icon" title="分享" aria-label="分享" data-clipboard data-clipboard-text="" data-md-component="search-share" tabindex="-1">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 16.08c-.76 0-1.44.3-1.96.77L8.91 12.7c.05-.23.09-.46.09-.7s-.04-.47-.09-.7l7.05-4.11c.54.5 1.25.81 2.04.81a3 3 0 0 0 3-3 3 3 0 0 0-3-3 3 3 0 0 0-3 3c0 .24.04.47.09.7L8.04 9.81C7.5 9.31 6.79 9 6 9a3 3 0 0 0-3 3 3 3 0 0 0 3 3c.79 0 1.5-.31 2.04-.81l7.12 4.15c-.05.21-.08.43-.08.66 0 1.61 1.31 2.91 2.92 2.91s2.92-1.3 2.92-2.91A2.92 2.92 0 0 0 18 16.08"/></svg>
</a>
<button type="reset" class="md-search__icon md-icon" title="清空" aria-label="清空" tabindex="-1">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 6.41 17.59 5 12 10.59 6.41 5 5 6.41 10.59 12 5 17.59 6.41 19 12 13.41 17.59 19 19 17.59 13.41 12z"/></svg>
</button>
</nav>
<div class="md-search__suggest" data-md-component="search-suggest"></div>
</form>
<div class="md-search__output">
<div class="md-search__scrollwrap" tabindex="0" data-md-scrollfix>
<div class="md-search-result" data-md-component="search-result">
<div class="md-search-result__meta">
正在初始化搜尋引擎
</div>
<ol class="md-search-result__list" role="presentation"></ol>
</div>
</div>
</div>
</div>
<div class="md-search" data-md-component="search" role="dialog" aria-label="搜尋">
<button type="button" class="md-search__button">
搜尋
</button>
</div>
<div class="md-header__source">
<div class="md-header__source">
<a href="https://github.com/krahets/hello-algo" title="前往倉庫" class="md-source" data-md-component="source">
<div class="md-source__icon md-icon">
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</div>
<div class="md-source__repository">
krahets/hello-algo
</div>
</a>
</div>
</div>
</nav>
</header>
@@ -325,7 +287,7 @@
<label class="md-nav__title" for="__drawer">
<a href="../.." title="Hello 演算法" class="md-nav__button md-logo" aria-label="Hello 演算法" data-md-component="logo">
<img src="../../assets/images/logo.svg" alt="logo">
<img src="../../assets/images/logo.svg" alt="Hello 演算法">
</a>
Hello 演算法
@@ -335,7 +297,7 @@
<a href="https://github.com/krahets/hello-algo" title="前往倉庫" class="md-source" data-md-component="source">
<div class="md-source__icon md-icon">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path d="M173.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6m-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3m44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9M252.8 8C114.1 8 8 113.3 8 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C436.2 457.8 504 362.9 504 252 504 113.3 391.5 8 252.8 8M105.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1m-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7m32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1m-11.4-14.7c-1.6 1-1.6 3.6 0 5.9s4.3 3.3 5.6 2.3c1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path fill="currentColor" d="M173.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6m-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3m44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9M252.8 8C114.1 8 8 113.3 8 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C436.2 457.8 504 362.9 504 252 504 113.3 391.5 8 252.8 8M105.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1m-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7m32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1m-11.4-14.7c-1.6 1-1.6 3.6 0 5.9s4.3 3.3 5.6 2.3c1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2"/></svg>
</div>
<div class="md-source__repository">
krahets/hello-algo
@@ -2848,7 +2810,7 @@
<span class="md-nav__icon md-icon"></span>
</label>
<a href="./" class="md-nav__link md-nav__link--active">
<a href="././" class="md-nav__link md-nav__link--active">
@@ -2867,6 +2829,7 @@
<nav class="md-nav md-nav--secondary" aria-label="目錄">
@@ -4337,6 +4300,7 @@
<div class="md-sidebar__inner">
<nav class="md-nav md-nav--secondary" aria-label="目錄">
@@ -4411,7 +4375,7 @@
class="md-content__button md-icon"
>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0M88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24z"/></svg>
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</a>
@@ -4426,25 +4390,25 @@
<div class="tabbed-set tabbed-alternate" data-tabs="1:7"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">&lt;1&gt;</label><label for="__tabbed_1_2">&lt;2&gt;</label><label for="__tabbed_1_3">&lt;3&gt;</label><label for="__tabbed_1_4">&lt;4&gt;</label><label for="__tabbed_1_5">&lt;5&gt;</label><label for="__tabbed_1_6">&lt;6&gt;</label><label for="__tabbed_1_7">&lt;7&gt;</label></div>
<div class="tabbed-content">
<div class="tabbed-block">
<p><a class="glightbox" href="../bubble_sort.assets/bubble_operation_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="利用元素交換操作模擬冒泡" class="animation-figure" src="../bubble_sort.assets/bubble_operation_step1.png" /></a></p>
<p><img alt="利用元素交換操作模擬冒泡" class="animation-figure" src="../bubble_sort.assets/bubble_operation_step1.png" /></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../bubble_sort.assets/bubble_operation_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="bubble_operation_step2" class="animation-figure" src="../bubble_sort.assets/bubble_operation_step2.png" /></a></p>
<p><img alt="bubble_operation_step2" class="animation-figure" src="../bubble_sort.assets/bubble_operation_step2.png" /></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../bubble_sort.assets/bubble_operation_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="bubble_operation_step3" class="animation-figure" src="../bubble_sort.assets/bubble_operation_step3.png" /></a></p>
<p><img alt="bubble_operation_step3" class="animation-figure" src="../bubble_sort.assets/bubble_operation_step3.png" /></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../bubble_sort.assets/bubble_operation_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="bubble_operation_step4" class="animation-figure" src="../bubble_sort.assets/bubble_operation_step4.png" /></a></p>
<p><img alt="bubble_operation_step4" class="animation-figure" src="../bubble_sort.assets/bubble_operation_step4.png" /></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../bubble_sort.assets/bubble_operation_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="bubble_operation_step5" class="animation-figure" src="../bubble_sort.assets/bubble_operation_step5.png" /></a></p>
<p><img alt="bubble_operation_step5" class="animation-figure" src="../bubble_sort.assets/bubble_operation_step5.png" /></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../bubble_sort.assets/bubble_operation_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="bubble_operation_step6" class="animation-figure" src="../bubble_sort.assets/bubble_operation_step6.png" /></a></p>
<p><img alt="bubble_operation_step6" class="animation-figure" src="../bubble_sort.assets/bubble_operation_step6.png" /></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../bubble_sort.assets/bubble_operation_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="bubble_operation_step7" class="animation-figure" src="../bubble_sort.assets/bubble_operation_step7.png" /></a></p>
<p><img alt="bubble_operation_step7" class="animation-figure" src="../bubble_sort.assets/bubble_operation_step7.png" /></p>
</div>
</div>
</div>
@@ -4458,7 +4422,7 @@
<li>以此類推，經過 <span class="arithmatex">\(n - 1\)</span> 輪“冒泡”後，<strong>前 <span class="arithmatex">\(n - 1\)</span> 大的元素都被交換至正確位置</strong>。</li>
<li>僅剩的一個元素必定是最小元素，無須排序，因此陣列排序完成。</li>
</ol>
<p><a class="glightbox" href="../bubble_sort.assets/bubble_sort_overview.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="泡沫排序流程" class="animation-figure" src="../bubble_sort.assets/bubble_sort_overview.png" /></a></p>
<p><img alt="泡沫排序流程" class="animation-figure" src="../bubble_sort.assets/bubble_sort_overview.png" /></p>
<p align="center"> 圖 11-5 &nbsp; 泡沫排序流程 </p>
<p>示例程式碼如下：</p>
@@ -5002,7 +4966,7 @@ aria-label="頁脚"
>
<div class="md-footer__button md-icon">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11z"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-arrow-left" viewBox="0 0 24 24"><path d="m12 19-7-7 7-7M19 12H5"/></svg>
</div>
<div class="md-footer__title">
<span class="md-footer__direction">
@@ -5034,7 +4998,7 @@ aria-label="頁脚"
</div>
<div class="md-footer__button md-icon">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M4 11v2h12l-5.5 5.5 1.42 1.42L19.84 12l-7.92-7.92L10.5 5.5 16 11z"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-arrow-right" viewBox="0 0 24 24"><path d="M5 12h14M12 5l7 7-7 7"/></svg>
</div>
</a>
@@ -5112,7 +5076,7 @@ aria-label="頁脚"
<button type="button" class="md-top md-icon" data-md-component="top" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 20h-2V8l-5.5 5.5-1.42-1.42L12 4.16l7.92 7.92-1.42 1.42L13 8z"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-circle-arrow-up" viewBox="0 0 24 24"><circle cx="12" cy="12" r="10"/><path d="m16 12-4-4-4 4M12 16V8"/></svg>
回到頂部
</button>
@@ -5120,46 +5084,6 @@ aria-label="頁脚"
<footer class="md-footer">
<nav class="md-footer__inner md-grid" aria-label="頁脚" >
<a href="../selection_sort/" class="md-footer__link md-footer__link--prev" aria-label="上一頁: 11.2 &amp;nbsp; 選擇排序">
<div class="md-footer__button md-icon">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11z"/></svg>
</div>
<div class="md-footer__title">
<span class="md-footer__direction">
上一頁
</span>
<div class="md-ellipsis">
11.2 &nbsp; 選擇排序
</div>
</div>
</a>
<a href="../insertion_sort/" class="md-footer__link md-footer__link--next" aria-label="下一頁: 11.4 &amp;nbsp; 插入排序">
<div class="md-footer__title">
<span class="md-footer__direction">
下一頁
</span>
<div class="md-ellipsis">
11.4 &nbsp; 插入排序
</div>
</div>
<div class="md-footer__button md-icon">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M4 11v2h12l-5.5 5.5 1.42 1.42L19.84 12l-7.92-7.92L10.5 5.5 16 11z"/></svg>
</div>
</a>
</nav>
<div class="md-footer-meta md-typeset">
<div class="md-footer-meta__inner md-grid">
<div class="md-copyright">
@@ -5182,7 +5106,7 @@ aria-label="頁脚"
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zh-hant/chapter_sorting/bucket_sort/index.html
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krahets/hello-algo
</div>
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@@ -325,7 +287,7 @@
<label class="md-nav__title" for="__drawer">
<a href="../.." title="Hello 演算法" class="md-nav__button md-logo" aria-label="Hello 演算法" data-md-component="logo">
<img src="../../assets/images/logo.svg" alt="logo">
<img src="../../assets/images/logo.svg" alt="Hello 演算法">
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Hello 演算法
@@ -335,7 +297,7 @@
<a href="https://github.com/krahets/hello-algo" title="前往倉庫" class="md-source" data-md-component="source">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path d="M173.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6m-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3m44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9M252.8 8C114.1 8 8 113.3 8 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C436.2 457.8 504 362.9 504 252 504 113.3 391.5 8 252.8 8M105.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1m-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7m32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1m-11.4-14.7c-1.6 1-1.6 3.6 0 5.9s4.3 3.3 5.6 2.3c1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2"/></svg>
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krahets/hello-algo
@@ -2988,7 +2950,7 @@
<span class="md-nav__icon md-icon"></span>
</label>
<a href="./" class="md-nav__link md-nav__link--active">
<a href="././" class="md-nav__link md-nav__link--active">
@@ -3007,6 +2969,7 @@
<nav class="md-nav md-nav--secondary" aria-label="目錄">
@@ -4337,6 +4300,7 @@
<div class="md-sidebar__inner">
<nav class="md-nav md-nav--secondary" aria-label="目錄">
@@ -4411,7 +4375,7 @@
class="md-content__button md-icon"
>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0M88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24z"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path fill="currentColor" d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0M88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24z"/></svg>
</a>
@@ -4430,7 +4394,7 @@
<li>對每個桶分別執行排序（這裡採用程式語言的內建排序函式）。</li>
<li>按照桶從小到大的順序合併結果。</li>
</ol>
<p><a class="glightbox" href="../bucket_sort.assets/bucket_sort_overview.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="桶排序演算法流程" class="animation-figure" src="../bucket_sort.assets/bucket_sort_overview.png" /></a></p>
<p><img alt="桶排序演算法流程" class="animation-figure" src="../bucket_sort.assets/bucket_sort_overview.png" /></p>
<p align="center"> 圖 11-13 &nbsp; 桶排序演算法流程 </p>
<p>程式碼如下所示：</p>
@@ -4843,12 +4807,12 @@
<p>桶排序的時間複雜度理論上可以達到 <span class="arithmatex">\(O(n)\)</span> ，<strong>關鍵在於將元素均勻分配到各個桶中</strong>，因為實際資料往往不是均勻分佈的。例如，我們想要將淘寶上的所有商品按價格範圍平均分配到 10 個桶中，但商品價格分佈不均，低於 100 元的非常多，高於 1000 元的非常少。若將價格區間平均劃分為 10 個，各個桶中的商品數量差距會非常大。</p>
<p>為實現平均分配，我們可以先設定一條大致的分界線，將資料粗略地分到 3 個桶中。<strong>分配完畢後，再將商品較多的桶繼續劃分為 3 個桶，直至所有桶中的元素數量大致相等</strong>。</p>
<p>如圖 11-14 所示，這種方法本質上是建立一棵遞迴樹，目標是讓葉節點的值儘可能平均。當然，不一定要每輪將資料劃分為 3 個桶，具體劃分方式可根據資料特點靈活選擇。</p>
<p><a class="glightbox" href="../bucket_sort.assets/scatter_in_buckets_recursively.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="遞迴劃分桶" class="animation-figure" src="../bucket_sort.assets/scatter_in_buckets_recursively.png" /></a></p>
<p><img alt="遞迴劃分桶" class="animation-figure" src="../bucket_sort.assets/scatter_in_buckets_recursively.png" /></p>
<p align="center"> 圖 11-14 &nbsp; 遞迴劃分桶 </p>
<p>如果我們提前知道商品價格的機率分佈，<strong>則可以根據資料機率分佈設定每個桶的價格分界線</strong>。值得注意的是，資料分佈並不一定需要特意統計，也可以根據資料特點採用某種機率模型進行近似。</p>
<p>如圖 11-15 所示，我們假設商品價格服從正態分佈，這樣就可以合理地設定價格區間，從而將商品平均分配到各個桶中。</p>
<p><a class="glightbox" href="../bucket_sort.assets/scatter_in_buckets_distribution.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="根據機率分佈劃分桶" class="animation-figure" src="../bucket_sort.assets/scatter_in_buckets_distribution.png" /></a></p>
<p><img alt="根據機率分佈劃分桶" class="animation-figure" src="../bucket_sort.assets/scatter_in_buckets_distribution.png" /></p>
<p align="center"> 圖 11-15 &nbsp; 根據機率分佈劃分桶 </p>
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<label class="md-header__button md-icon" title="深色模式" for="__palette_1" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07zm-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13zm-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87zM19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35zm4.33-2.7 1.15-2.77 2.2 2.54zm1.15-4.96-1.14-2.78 3.34.24zM9.63 18.93l2.77 1.15-2.53 2.19z"/></svg>
@@ -179,7 +175,7 @@
<input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="black" data-md-color-accent="teal" aria-label="淺色模式" type="radio" name="__palette" id="__palette_1">
<input class="md-option" data-md-color-media="none" data-md-color-scheme="slate" data-md-color-primary="black" data-md-color-accent="teal" aria-label="淺色模式" type="radio" name="__palette" id="__palette_1">
<label class="md-header__button md-icon" title="淺色模式" for="__palette_0" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07zm-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13zm-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87zM19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35zm4.33-2.7 1.15-2.77 2.2 2.54zm1.15-4.96-1.14-2.78 3.34.24zM9.63 18.93l2.77 1.15-2.53 2.19z"/></svg>
@@ -197,7 +193,7 @@
<div class="md-select">
<button class="md-header__button md-icon" aria-label="選擇語言">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12.87 15.07-2.54-2.51.03-.03A17.5 17.5 0 0 0 14.07 6H17V4h-7V2H8v2H1v2h11.17C11.5 7.92 10.44 9.75 9 11.35 8.07 10.32 7.3 9.19 6.69 8h-2c.73 1.63 1.73 3.17 2.98 4.56l-5.09 5.02L4 19l5-5 3.11 3.11zM18.5 10h-2L12 22h2l1.12-3h4.75L21 22h2zm-2.62 7 1.62-4.33L19.12 17z"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-languages" viewBox="0 0 24 24"><path d="m5 8 6 6M4 14l6-6 2-3M2 5h12M7 2h1M22 22l-5-10-5 10M14 18h6"/></svg>
</button>
<div class="md-select__inner">
<ul class="md-select__list">
@@ -240,64 +236,30 @@
<label class="md-header__button md-icon" for="__search">
<label class="md-header__button md-icon" for="__search" aria-label="搜尋">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.52 6.52 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-search" viewBox="0 0 24 24"><path d="m21 21-4.34-4.34"/><circle cx="11" cy="11" r="8"/></svg>
</label>
<div class="md-search" data-md-component="search" role="dialog">
<label class="md-search__overlay" for="__search"></label>
<div class="md-search__inner" role="search">
<form class="md-search__form" name="search">
<input type="text" class="md-search__input" name="query" aria-label="搜尋" placeholder="搜尋" autocapitalize="off" autocorrect="off" autocomplete="off" spellcheck="false" data-md-component="search-query" required>
<label class="md-search__icon md-icon" for="__search">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.52 6.52 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11z"/></svg>
</label>
<nav class="md-search__options" aria-label="搜尋">
<a href="javascript:void(0)" class="md-search__icon md-icon" title="分享" aria-label="分享" data-clipboard data-clipboard-text="" data-md-component="search-share" tabindex="-1">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 16.08c-.76 0-1.44.3-1.96.77L8.91 12.7c.05-.23.09-.46.09-.7s-.04-.47-.09-.7l7.05-4.11c.54.5 1.25.81 2.04.81a3 3 0 0 0 3-3 3 3 0 0 0-3-3 3 3 0 0 0-3 3c0 .24.04.47.09.7L8.04 9.81C7.5 9.31 6.79 9 6 9a3 3 0 0 0-3 3 3 3 0 0 0 3 3c.79 0 1.5-.31 2.04-.81l7.12 4.15c-.05.21-.08.43-.08.66 0 1.61 1.31 2.91 2.92 2.91s2.92-1.3 2.92-2.91A2.92 2.92 0 0 0 18 16.08"/></svg>
</a>
<button type="reset" class="md-search__icon md-icon" title="清空" aria-label="清空" tabindex="-1">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 6.41 17.59 5 12 10.59 6.41 5 5 6.41 10.59 12 5 17.59 6.41 19 12 13.41 17.59 19 19 17.59 13.41 12z"/></svg>
</button>
</nav>
<div class="md-search__suggest" data-md-component="search-suggest"></div>
</form>
<div class="md-search__output">
<div class="md-search__scrollwrap" tabindex="0" data-md-scrollfix>
<div class="md-search-result" data-md-component="search-result">
<div class="md-search-result__meta">
正在初始化搜尋引擎
</div>
<ol class="md-search-result__list" role="presentation"></ol>
</div>
</div>
</div>
</div>
<div class="md-search" data-md-component="search" role="dialog" aria-label="搜尋">
<button type="button" class="md-search__button">
搜尋
</button>
</div>
<div class="md-header__source">
<div class="md-header__source">
<a href="https://github.com/krahets/hello-algo" title="前往倉庫" class="md-source" data-md-component="source">
<div class="md-source__icon md-icon">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path d="M173.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6m-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3m44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9M252.8 8C114.1 8 8 113.3 8 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C436.2 457.8 504 362.9 504 252 504 113.3 391.5 8 252.8 8M105.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1m-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7m32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1m-11.4-14.7c-1.6 1-1.6 3.6 0 5.9s4.3 3.3 5.6 2.3c1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path fill="currentColor" d="M173.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6m-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3m44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9M252.8 8C114.1 8 8 113.3 8 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C436.2 457.8 504 362.9 504 252 504 113.3 391.5 8 252.8 8M105.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1m-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7m32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1m-11.4-14.7c-1.6 1-1.6 3.6 0 5.9s4.3 3.3 5.6 2.3c1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2"/></svg>
</div>
<div class="md-source__repository">
krahets/hello-algo
</div>
</a>
</div>
</div>
</nav>
</header>
@@ -325,7 +287,7 @@
<label class="md-nav__title" for="__drawer">
<a href="../.." title="Hello 演算法" class="md-nav__button md-logo" aria-label="Hello 演算法" data-md-component="logo">
<img src="../../assets/images/logo.svg" alt="logo">
<img src="../../assets/images/logo.svg" alt="Hello 演算法">
</a>
Hello 演算法
@@ -335,7 +297,7 @@
<a href="https://github.com/krahets/hello-algo" title="前往倉庫" class="md-source" data-md-component="source">
<div class="md-source__icon md-icon">
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</div>
<div class="md-source__repository">
krahets/hello-algo
@@ -3016,7 +2978,7 @@
<span class="md-nav__icon md-icon"></span>
</label>
<a href="./" class="md-nav__link md-nav__link--active">
<a href="././" class="md-nav__link md-nav__link--active">
@@ -3035,6 +2997,7 @@
<nav class="md-nav md-nav--secondary" aria-label="目錄">
@@ -4348,6 +4311,7 @@
<div class="md-sidebar__inner">
<nav class="md-nav md-nav--secondary" aria-label="目錄">
@@ -4433,7 +4397,7 @@
class="md-content__button md-icon"
>
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</a>
@@ -4451,7 +4415,7 @@
<li><strong>藉助 <code>counter</code> 統計 <code>nums</code> 中各數字的出現次數</strong>，其中 <code>counter[num]</code> 對應數字 <code>num</code> 的出現次數。統計方法很簡單，只需走訪 <code>nums</code>（設當前數字為 <code>num</code>），每輪將 <code>counter[num]</code> 增加 <span class="arithmatex">\(1\)</span> 即可。</li>
<li><strong>由於 <code>counter</code> 的各個索引天然有序，因此相當於所有數字已經排序好了</strong>。接下來，我們走訪 <code>counter</code> ，根據各數字出現次數從小到大的順序填入 <code>nums</code> 即可。</li>
</ol>
<p><a class="glightbox" href="../counting_sort.assets/counting_sort_overview.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="計數排序流程" class="animation-figure" src="../counting_sort.assets/counting_sort_overview.png" /></a></p>
<p><img alt="計數排序流程" class="animation-figure" src="../counting_sort.assets/counting_sort_overview.png" /></p>
<p align="center"> 圖 11-16 &nbsp; 計數排序流程 </p>
<p>程式碼如下所示：</p>
@@ -4798,28 +4762,28 @@
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<p><a class="glightbox" href="../counting_sort.assets/counting_sort_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="計數排序步驟" class="animation-figure" src="../counting_sort.assets/counting_sort_step1.png" /></a></p>
<p><img alt="計數排序步驟" class="animation-figure" src="../counting_sort.assets/counting_sort_step1.png" /></p>
</div>
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<p><a class="glightbox" href="../counting_sort.assets/counting_sort_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="counting_sort_step2" class="animation-figure" src="../counting_sort.assets/counting_sort_step2.png" /></a></p>
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<p><img alt="counting_sort_step3" class="animation-figure" src="../counting_sort.assets/counting_sort_step3.png" /></p>
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<p><a class="glightbox" href="../counting_sort.assets/counting_sort_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="counting_sort_step5" class="animation-figure" src="../counting_sort.assets/counting_sort_step5.png" /></a></p>
<p><img alt="counting_sort_step5" class="animation-figure" src="../counting_sort.assets/counting_sort_step5.png" /></p>
</div>
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<p><a class="glightbox" href="../counting_sort.assets/counting_sort_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="counting_sort_step6" class="animation-figure" src="../counting_sort.assets/counting_sort_step6.png" /></a></p>
<p><img alt="counting_sort_step6" class="animation-figure" src="../counting_sort.assets/counting_sort_step6.png" /></p>
</div>
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<p><a class="glightbox" href="../counting_sort.assets/counting_sort_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="counting_sort_step7" class="animation-figure" src="../counting_sort.assets/counting_sort_step7.png" /></a></p>
<p><img alt="counting_sort_step7" class="animation-figure" src="../counting_sort.assets/counting_sort_step7.png" /></p>
</div>
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<p><a class="glightbox" href="../counting_sort.assets/counting_sort_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="counting_sort_step8" class="animation-figure" src="../counting_sort.assets/counting_sort_step8.png" /></a></p>
<p><img alt="counting_sort_step8" class="animation-figure" src="../counting_sort.assets/counting_sort_step8.png" /></p>
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@@ -5308,7 +5272,7 @@ aria-label="頁脚"
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zh-hant/chapter_sorting/heap_sort/index.html
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Hello 演算法
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@@ -2960,7 +2922,7 @@
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@@ -2979,6 +2941,7 @@
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@@ -4326,6 +4289,7 @@
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@@ -4389,7 +4353,7 @@
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@@ -4424,40 +4388,40 @@
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@@ -5024,7 +4988,7 @@ aria-label="頁脚"
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@@ -5056,7 +5020,7 @@ aria-label="頁脚"
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@@ -5134,7 +5098,7 @@ aria-label="頁脚"
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@@ -5142,46 +5106,6 @@ aria-label="頁脚"
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zh-hant/chapter_sorting/index.html
+60 -139
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@@ -18,7 +18,7 @@
<link rel="prev" href="../chapter_searching/summary/">
<link rel="next" href="sorting_algorithm/">
<link rel="next" href="./sorting_algorithm/">
@@ -35,18 +35,23 @@
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<meta name="generator" content="mkdocs-1.6.1, mkdocs-material-9.7.1">
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<title>第 11 章   排序 - Hello 演算法</title>
<title>第 11 章 排序 - Hello 演算法</title>
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<link rel="stylesheet" href="../assets/stylesheets/palette.ab4e12ef.min.css">
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<link rel="stylesheet" href="../assets/stylesheets/modern/palette.dfe2e883.min.css">
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<a href="./.." title="Hello 演算法" class="md-header__button md-logo" aria-label="Hello 演算法" data-md-component="logo">
<img src="../assets/images/logo.svg" alt="logo">
<img src="../assets/images/logo.svg" alt="Hello 演算法">
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<label class="md-header__button md-icon" for="__search">
<label class="md-header__button md-icon" for="__search" aria-label="搜尋">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.52 6.52 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-search" viewBox="0 0 24 24"><path d="m21 21-4.34-4.34"/><circle cx="11" cy="11" r="8"/></svg>
</label>
<div class="md-search" data-md-component="search" role="dialog">
<label class="md-search__overlay" for="__search"></label>
<div class="md-search__inner" role="search">
<form class="md-search__form" name="search">
<input type="text" class="md-search__input" name="query" aria-label="搜尋" placeholder="搜尋" autocapitalize="off" autocorrect="off" autocomplete="off" spellcheck="false" data-md-component="search-query" required>
<label class="md-search__icon md-icon" for="__search">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.52 6.52 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5"/></svg>
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</label>
<nav class="md-search__options" aria-label="搜尋">
<a href="javascript:void(0)" class="md-search__icon md-icon" title="分享" aria-label="分享" data-clipboard data-clipboard-text="" data-md-component="search-share" tabindex="-1">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 16.08c-.76 0-1.44.3-1.96.77L8.91 12.7c.05-.23.09-.46.09-.7s-.04-.47-.09-.7l7.05-4.11c.54.5 1.25.81 2.04.81a3 3 0 0 0 3-3 3 3 0 0 0-3-3 3 3 0 0 0-3 3c0 .24.04.47.09.7L8.04 9.81C7.5 9.31 6.79 9 6 9a3 3 0 0 0-3 3 3 3 0 0 0 3 3c.79 0 1.5-.31 2.04-.81l7.12 4.15c-.05.21-.08.43-.08.66 0 1.61 1.31 2.91 2.92 2.91s2.92-1.3 2.92-2.91A2.92 2.92 0 0 0 18 16.08"/></svg>
</a>
<button type="reset" class="md-search__icon md-icon" title="清空" aria-label="清空" tabindex="-1">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 6.41 17.59 5 12 10.59 6.41 5 5 6.41 10.59 12 5 17.59 6.41 19 12 13.41 17.59 19 19 17.59 13.41 12z"/></svg>
</button>
</nav>
<div class="md-search__suggest" data-md-component="search-suggest"></div>
</form>
<div class="md-search__output">
<div class="md-search__scrollwrap" tabindex="0" data-md-scrollfix>
<div class="md-search-result" data-md-component="search-result">
<div class="md-search-result__meta">
正在初始化搜尋引擎
</div>
<ol class="md-search-result__list" role="presentation"></ol>
</div>
</div>
</div>
</div>
<div class="md-search" data-md-component="search" role="dialog" aria-label="搜尋">
<button type="button" class="md-search__button">
搜尋
</button>
</div>
<div class="md-header__source">
<div class="md-header__source">
<a href="https://github.com/krahets/hello-algo" title="前往倉庫" class="md-source" data-md-component="source">
<div class="md-source__icon md-icon">
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</div>
<div class="md-source__repository">
krahets/hello-algo
</div>
</a>
</div>
</div>
</nav>
</header>
@@ -323,9 +285,9 @@
<nav class="md-nav md-nav--primary" aria-label="導航" data-md-level="0">
<label class="md-nav__title" for="__drawer">
<a href=".." title="Hello 演算法" class="md-nav__button md-logo" aria-label="Hello 演算法" data-md-component="logo">
<a href="./.." title="Hello 演算法" class="md-nav__button md-logo" aria-label="Hello 演算法" data-md-component="logo">
<img src="../assets/images/logo.svg" alt="logo">
<img src="../assets/images/logo.svg" alt="Hello 演算法">
</a>
Hello 演算法
@@ -335,7 +297,7 @@
<a href="https://github.com/krahets/hello-algo" title="前往倉庫" class="md-source" data-md-component="source">
<div class="md-source__icon md-icon">
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</div>
<div class="md-source__repository">
krahets/hello-algo
@@ -2719,7 +2681,7 @@
<div class="md-nav__link md-nav__container">
<a href="./" class="md-nav__link md-nav__link--active">
<a href="././" class="md-nav__link md-nav__link--active">
@@ -2765,7 +2727,7 @@
<li class="md-nav__item">
<a href="sorting_algorithm/" class="md-nav__link">
<a href="./sorting_algorithm/" class="md-nav__link">
@@ -2793,7 +2755,7 @@
<li class="md-nav__item">
<a href="selection_sort/" class="md-nav__link">
<a href="./selection_sort/" class="md-nav__link">
@@ -2821,7 +2783,7 @@
<li class="md-nav__item">
<a href="bubble_sort/" class="md-nav__link">
<a href="./bubble_sort/" class="md-nav__link">
@@ -2849,7 +2811,7 @@
<li class="md-nav__item">
<a href="insertion_sort/" class="md-nav__link">
<a href="./insertion_sort/" class="md-nav__link">
@@ -2877,7 +2839,7 @@
<li class="md-nav__item">
<a href="quick_sort/" class="md-nav__link">
<a href="./quick_sort/" class="md-nav__link">
@@ -2905,7 +2867,7 @@
<li class="md-nav__item">
<a href="merge_sort/" class="md-nav__link">
<a href="./merge_sort/" class="md-nav__link">
@@ -2933,7 +2895,7 @@
<li class="md-nav__item">
<a href="heap_sort/" class="md-nav__link">
<a href="./heap_sort/" class="md-nav__link">
@@ -2961,7 +2923,7 @@
<li class="md-nav__item">
<a href="bucket_sort/" class="md-nav__link">
<a href="./bucket_sort/" class="md-nav__link">
@@ -2989,7 +2951,7 @@
<li class="md-nav__item">
<a href="counting_sort/" class="md-nav__link">
<a href="./counting_sort/" class="md-nav__link">
@@ -3017,7 +2979,7 @@
<li class="md-nav__item">
<a href="radix_sort/" class="md-nav__link">
<a href="./radix_sort/" class="md-nav__link">
@@ -3045,7 +3007,7 @@
<li class="md-nav__item">
<a href="summary/" class="md-nav__link">
<a href="./summary/" class="md-nav__link">
@@ -4257,6 +4219,7 @@
<div class="md-sidebar__inner">
<nav class="md-nav md-nav--secondary" aria-label="目錄">
@@ -4309,7 +4272,7 @@
class="md-content__button md-icon"
>
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</a>
@@ -4319,7 +4282,7 @@
<!-- Page content -->
<h1 id="11">第 11 章 &nbsp; 排序<a class="headerlink" href="#11" title="Permanent link">&para;</a></h1>
<p><a class="glightbox" href="../assets/covers/chapter_sorting.jpg" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="排序" class="cover-image" src="../assets/covers/chapter_sorting.jpg" /></a></p>
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<p class="admonition-title">Abstract</p>
<p>排序猶如一把將混亂變為秩序的魔法鑰匙，使我們能以更高效的方式理解與處理資料。</p>
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07zm-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13zm-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87zM19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35zm4.33-2.7 1.15-2.77 2.2 2.54zm1.15-4.96-1.14-2.78 3.34.24zM9.63 18.93l2.77 1.15-2.53 2.19z"/></svg>
@@ -179,7 +175,7 @@
<input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="black" data-md-color-accent="teal" aria-label="淺色模式" type="radio" name="__palette" id="__palette_1">
<input class="md-option" data-md-color-media="none" data-md-color-scheme="slate" data-md-color-primary="black" data-md-color-accent="teal" aria-label="淺色模式" type="radio" name="__palette" id="__palette_1">
<label class="md-header__button md-icon" title="淺色模式" for="__palette_0" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07zm-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13zm-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87zM19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35zm4.33-2.7 1.15-2.77 2.2 2.54zm1.15-4.96-1.14-2.78 3.34.24zM9.63 18.93l2.77 1.15-2.53 2.19z"/></svg>
@@ -197,7 +193,7 @@
<div class="md-select">
<button class="md-header__button md-icon" aria-label="選擇語言">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12.87 15.07-2.54-2.51.03-.03A17.5 17.5 0 0 0 14.07 6H17V4h-7V2H8v2H1v2h11.17C11.5 7.92 10.44 9.75 9 11.35 8.07 10.32 7.3 9.19 6.69 8h-2c.73 1.63 1.73 3.17 2.98 4.56l-5.09 5.02L4 19l5-5 3.11 3.11zM18.5 10h-2L12 22h2l1.12-3h4.75L21 22h2zm-2.62 7 1.62-4.33L19.12 17z"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-languages" viewBox="0 0 24 24"><path d="m5 8 6 6M4 14l6-6 2-3M2 5h12M7 2h1M22 22l-5-10-5 10M14 18h6"/></svg>
</button>
<div class="md-select__inner">
<ul class="md-select__list">
@@ -240,64 +236,30 @@
<label class="md-header__button md-icon" for="__search">
<label class="md-header__button md-icon" for="__search" aria-label="搜尋">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.52 6.52 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-search" viewBox="0 0 24 24"><path d="m21 21-4.34-4.34"/><circle cx="11" cy="11" r="8"/></svg>
</label>
<div class="md-search" data-md-component="search" role="dialog">
<label class="md-search__overlay" for="__search"></label>
<div class="md-search__inner" role="search">
<form class="md-search__form" name="search">
<input type="text" class="md-search__input" name="query" aria-label="搜尋" placeholder="搜尋" autocapitalize="off" autocorrect="off" autocomplete="off" spellcheck="false" data-md-component="search-query" required>
<label class="md-search__icon md-icon" for="__search">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.52 6.52 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11z"/></svg>
</label>
<nav class="md-search__options" aria-label="搜尋">
<a href="javascript:void(0)" class="md-search__icon md-icon" title="分享" aria-label="分享" data-clipboard data-clipboard-text="" data-md-component="search-share" tabindex="-1">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 16.08c-.76 0-1.44.3-1.96.77L8.91 12.7c.05-.23.09-.46.09-.7s-.04-.47-.09-.7l7.05-4.11c.54.5 1.25.81 2.04.81a3 3 0 0 0 3-3 3 3 0 0 0-3-3 3 3 0 0 0-3 3c0 .24.04.47.09.7L8.04 9.81C7.5 9.31 6.79 9 6 9a3 3 0 0 0-3 3 3 3 0 0 0 3 3c.79 0 1.5-.31 2.04-.81l7.12 4.15c-.05.21-.08.43-.08.66 0 1.61 1.31 2.91 2.92 2.91s2.92-1.3 2.92-2.91A2.92 2.92 0 0 0 18 16.08"/></svg>
</a>
<button type="reset" class="md-search__icon md-icon" title="清空" aria-label="清空" tabindex="-1">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 6.41 17.59 5 12 10.59 6.41 5 5 6.41 10.59 12 5 17.59 6.41 19 12 13.41 17.59 19 19 17.59 13.41 12z"/></svg>
</button>
</nav>
<div class="md-search__suggest" data-md-component="search-suggest"></div>
</form>
<div class="md-search__output">
<div class="md-search__scrollwrap" tabindex="0" data-md-scrollfix>
<div class="md-search-result" data-md-component="search-result">
<div class="md-search-result__meta">
正在初始化搜尋引擎
</div>
<ol class="md-search-result__list" role="presentation"></ol>
</div>
</div>
</div>
</div>
<div class="md-search" data-md-component="search" role="dialog" aria-label="搜尋">
<button type="button" class="md-search__button">
搜尋
</button>
</div>
<div class="md-header__source">
<div class="md-header__source">
<a href="https://github.com/krahets/hello-algo" title="前往倉庫" class="md-source" data-md-component="source">
<div class="md-source__icon md-icon">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path d="M173.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6m-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3m44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9M252.8 8C114.1 8 8 113.3 8 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C436.2 457.8 504 362.9 504 252 504 113.3 391.5 8 252.8 8M105.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1m-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7m32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1m-11.4-14.7c-1.6 1-1.6 3.6 0 5.9s4.3 3.3 5.6 2.3c1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path fill="currentColor" d="M173.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6m-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3m44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9M252.8 8C114.1 8 8 113.3 8 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C436.2 457.8 504 362.9 504 252 504 113.3 391.5 8 252.8 8M105.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1m-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7m32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1m-11.4-14.7c-1.6 1-1.6 3.6 0 5.9s4.3 3.3 5.6 2.3c1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2"/></svg>
</div>
<div class="md-source__repository">
krahets/hello-algo
</div>
</a>
</div>
</div>
</nav>
</header>
@@ -325,7 +287,7 @@
<label class="md-nav__title" for="__drawer">
<a href="../.." title="Hello 演算法" class="md-nav__button md-logo" aria-label="Hello 演算法" data-md-component="logo">
<img src="../../assets/images/logo.svg" alt="logo">
<img src="../../assets/images/logo.svg" alt="Hello 演算法">
</a>
Hello 演算法
@@ -335,7 +297,7 @@
<a href="https://github.com/krahets/hello-algo" title="前往倉庫" class="md-source" data-md-component="source">
<div class="md-source__icon md-icon">
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</div>
<div class="md-source__repository">
krahets/hello-algo
@@ -2876,7 +2838,7 @@
<span class="md-nav__icon md-icon"></span>
</label>
<a href="./" class="md-nav__link md-nav__link--active">
<a href="././" class="md-nav__link md-nav__link--active">
@@ -2895,6 +2857,7 @@
<nav class="md-nav md-nav--secondary" aria-label="目錄">
@@ -4337,6 +4300,7 @@
<div class="md-sidebar__inner">
<nav class="md-nav md-nav--secondary" aria-label="目錄">
@@ -4411,7 +4375,7 @@
class="md-content__button md-icon"
>
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@@ -4424,7 +4388,7 @@
<p><u>插入排序（insertion sort）</u>是一種簡單的排序演算法，它的工作原理與手動整理一副牌的過程非常相似。</p>
<p>具體來說，我們在未排序區間選擇一個基準元素，將該元素與其左側已排序區間的元素逐一比較大小，並將該元素插入到正確的位置。</p>
<p>圖 11-6 展示了陣列插入元素的操作流程。設基準元素為 <code>base</code> ，我們需要將從目標索引到 <code>base</code> 之間的所有元素向右移動一位，然後將 <code>base</code> 賦值給目標索引。</p>
<p><a class="glightbox" href="../insertion_sort.assets/insertion_operation.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="單次插入操作" class="animation-figure" src="../insertion_sort.assets/insertion_operation.png" /></a></p>
<p><img alt="單次插入操作" class="animation-figure" src="../insertion_sort.assets/insertion_operation.png" /></p>
<p align="center"> 圖 11-6 &nbsp; 單次插入操作 </p>
<h2 id="1141">11.4.1 &nbsp; 演算法流程<a class="headerlink" href="#1141" title="Permanent link">&para;</a></h2>
@@ -4435,7 +4399,7 @@
<li>選取第 3 個元素作為 <code>base</code> ，將其插入到正確位置後，<strong>陣列的前 3 個元素已排序</strong>。</li>
<li>以此類推，在最後一輪中，選取最後一個元素作為 <code>base</code> ，將其插入到正確位置後，<strong>所有元素均已排序</strong>。</li>
</ol>
<p><a class="glightbox" href="../insertion_sort.assets/insertion_sort_overview.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="插入排序流程" class="animation-figure" src="../insertion_sort.assets/insertion_sort_overview.png" /></a></p>
<p><img alt="插入排序流程" class="animation-figure" src="../insertion_sort.assets/insertion_sort_overview.png" /></p>
<p align="center"> 圖 11-7 &nbsp; 插入排序流程 </p>
<p>示例程式碼如下：</p>
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<link rel="stylesheet" href="../../assets/stylesheets/modern/palette.dfe2e883.min.css">
@@ -60,29 +65,20 @@
<link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans+SC:300,300i,400,400i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans+SC:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
<style>:root{--md-text-font:"Noto Sans SC";--md-code-font:"JetBrains Mono"}</style>
<link rel="stylesheet" href="../../stylesheets/extra.css">
<script>__md_scope=new URL("../..",location),__md_hash=e=>[...e].reduce(((e,_)=>(e<<5)-e+_.charCodeAt(0)),0),__md_get=(e,_=localStorage,t=__md_scope)=>JSON.parse(_.getItem(t.pathname+"."+e)),__md_set=(e,_,t=localStorage,a=__md_scope)=>{try{t.setItem(a.pathname+"."+e,JSON.stringify(_))}catch(e){}}</script>
<script>__md_scope=new URL("../..",location),__md_hash=e=>[...e].reduce(((e,t)=>(e<<5)-e+t.charCodeAt(0)),0),__md_get=(e,t=localStorage,a=__md_scope)=>JSON.parse(t.getItem(("__palette"===e?"/":a.pathname)+"."+e)),__md_set=(e,t,a=localStorage,_=__md_scope)=>{try{a.setItem(("__palette"===e?"/":_.pathname)+"."+e,JSON.stringify(t))}catch(e){}},document.documentElement.setAttribute("data-platform",navigator.platform)</script>
<link href="../../assets/stylesheets/glightbox.min.css" rel="stylesheet"/><style>
html.glightbox-open { overflow: initial; height: 100%; }
.gslide-title { margin-top: 0px; user-select: text; }
.gslide-desc { color: #666; user-select: text; }
.gslide-image img { background: white; }
.gscrollbar-fixer { padding-right: 15px; }
.gdesc-inner { font-size: 0.75rem; }
body[data-md-color-scheme="slate"] .gdesc-inner { background: var(--md-default-bg-color);}
body[data-md-color-scheme="slate"] .gslide-title { color: var(--md-default-fg-color);}
body[data-md-color-scheme="slate"] .gslide-desc { color: var(--md-default-fg-color);}</style> <script src="../../assets/javascripts/glightbox.min.js"></script></head>
</head>
@@ -97,7 +93,7 @@
<input class="md-toggle" data-md-toggle="drawer" type="checkbox" id="__drawer" autocomplete="off">
<input class="md-toggle" data-md-toggle="search" type="checkbox" id="__search" autocomplete="off">
<label class="md-overlay" for="__drawer"></label>
<label class="md-overlay" for="__drawer" aria-label="導航"></label>
<div data-md-component="skip">
@@ -139,12 +135,12 @@
<nav class="md-header__inner md-grid" aria-label="頁首">
<a href="../.." title="Hello 演算法" class="md-header__button md-logo" aria-label="Hello 演算法" data-md-component="logo">
<img src="../../assets/images/logo.svg" alt="logo">
<img src="../../assets/images/logo.svg" alt="Hello 演算法">
</a>
<label class="md-header__button md-icon" for="__drawer">
<label class="md-header__button md-icon" for="__drawer" aria-label="導航">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 6h18v2H3zm0 5h18v2H3zm0 5h18v2H3z"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-menu" viewBox="0 0 24 24"><path d="M4 5h16M4 12h16M4 19h16"/></svg>
</label>
<div class="md-header__title" data-md-component="header-title">
<div class="md-header__ellipsis">
@@ -169,7 +165,7 @@
<input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="teal" aria-label="深色模式" type="radio" name="__palette" id="__palette_0">
<input class="md-option" data-md-color-media="none" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="teal" aria-label="深色模式" type="radio" name="__palette" id="__palette_0">
<label class="md-header__button md-icon" title="深色模式" for="__palette_1" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07zm-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13zm-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87zM19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35zm4.33-2.7 1.15-2.77 2.2 2.54zm1.15-4.96-1.14-2.78 3.34.24zM9.63 18.93l2.77 1.15-2.53 2.19z"/></svg>
@@ -179,7 +175,7 @@
<input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="black" data-md-color-accent="teal" aria-label="淺色模式" type="radio" name="__palette" id="__palette_1">
<input class="md-option" data-md-color-media="none" data-md-color-scheme="slate" data-md-color-primary="black" data-md-color-accent="teal" aria-label="淺色模式" type="radio" name="__palette" id="__palette_1">
<label class="md-header__button md-icon" title="淺色模式" for="__palette_0" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07zm-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13zm-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87zM19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35zm4.33-2.7 1.15-2.77 2.2 2.54zm1.15-4.96-1.14-2.78 3.34.24zM9.63 18.93l2.77 1.15-2.53 2.19z"/></svg>
@@ -197,7 +193,7 @@
<div class="md-select">
<button class="md-header__button md-icon" aria-label="選擇語言">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12.87 15.07-2.54-2.51.03-.03A17.5 17.5 0 0 0 14.07 6H17V4h-7V2H8v2H1v2h11.17C11.5 7.92 10.44 9.75 9 11.35 8.07 10.32 7.3 9.19 6.69 8h-2c.73 1.63 1.73 3.17 2.98 4.56l-5.09 5.02L4 19l5-5 3.11 3.11zM18.5 10h-2L12 22h2l1.12-3h4.75L21 22h2zm-2.62 7 1.62-4.33L19.12 17z"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-languages" viewBox="0 0 24 24"><path d="m5 8 6 6M4 14l6-6 2-3M2 5h12M7 2h1M22 22l-5-10-5 10M14 18h6"/></svg>
</button>
<div class="md-select__inner">
<ul class="md-select__list">
@@ -240,64 +236,30 @@
<label class="md-header__button md-icon" for="__search">
<label class="md-header__button md-icon" for="__search" aria-label="搜尋">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.52 6.52 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-search" viewBox="0 0 24 24"><path d="m21 21-4.34-4.34"/><circle cx="11" cy="11" r="8"/></svg>
</label>
<div class="md-search" data-md-component="search" role="dialog">
<label class="md-search__overlay" for="__search"></label>
<div class="md-search__inner" role="search">
<form class="md-search__form" name="search">
<input type="text" class="md-search__input" name="query" aria-label="搜尋" placeholder="搜尋" autocapitalize="off" autocorrect="off" autocomplete="off" spellcheck="false" data-md-component="search-query" required>
<label class="md-search__icon md-icon" for="__search">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.52 6.52 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11z"/></svg>
</label>
<nav class="md-search__options" aria-label="搜尋">
<a href="javascript:void(0)" class="md-search__icon md-icon" title="分享" aria-label="分享" data-clipboard data-clipboard-text="" data-md-component="search-share" tabindex="-1">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 16.08c-.76 0-1.44.3-1.96.77L8.91 12.7c.05-.23.09-.46.09-.7s-.04-.47-.09-.7l7.05-4.11c.54.5 1.25.81 2.04.81a3 3 0 0 0 3-3 3 3 0 0 0-3-3 3 3 0 0 0-3 3c0 .24.04.47.09.7L8.04 9.81C7.5 9.31 6.79 9 6 9a3 3 0 0 0-3 3 3 3 0 0 0 3 3c.79 0 1.5-.31 2.04-.81l7.12 4.15c-.05.21-.08.43-.08.66 0 1.61 1.31 2.91 2.92 2.91s2.92-1.3 2.92-2.91A2.92 2.92 0 0 0 18 16.08"/></svg>
</a>
<button type="reset" class="md-search__icon md-icon" title="清空" aria-label="清空" tabindex="-1">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 6.41 17.59 5 12 10.59 6.41 5 5 6.41 10.59 12 5 17.59 6.41 19 12 13.41 17.59 19 19 17.59 13.41 12z"/></svg>
</button>
</nav>
<div class="md-search__suggest" data-md-component="search-suggest"></div>
</form>
<div class="md-search__output">
<div class="md-search__scrollwrap" tabindex="0" data-md-scrollfix>
<div class="md-search-result" data-md-component="search-result">
<div class="md-search-result__meta">
正在初始化搜尋引擎
</div>
<ol class="md-search-result__list" role="presentation"></ol>
</div>
</div>
</div>
</div>
<div class="md-search" data-md-component="search" role="dialog" aria-label="搜尋">
<button type="button" class="md-search__button">
搜尋
</button>
</div>
<div class="md-header__source">
<div class="md-header__source">
<a href="https://github.com/krahets/hello-algo" title="前往倉庫" class="md-source" data-md-component="source">
<div class="md-source__icon md-icon">
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</div>
<div class="md-source__repository">
krahets/hello-algo
</div>
</a>
</div>
</div>
</nav>
</header>
@@ -325,7 +287,7 @@
<label class="md-nav__title" for="__drawer">
<a href="../.." title="Hello 演算法" class="md-nav__button md-logo" aria-label="Hello 演算法" data-md-component="logo">
<img src="../../assets/images/logo.svg" alt="logo">
<img src="../../assets/images/logo.svg" alt="Hello 演算法">
</a>
Hello 演算法
@@ -335,7 +297,7 @@
<a href="https://github.com/krahets/hello-algo" title="前往倉庫" class="md-source" data-md-component="source">
<div class="md-source__icon md-icon">
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krahets/hello-algo
@@ -2932,7 +2894,7 @@
<span class="md-nav__icon md-icon"></span>
</label>
<a href="./" class="md-nav__link md-nav__link--active">
<a href="././" class="md-nav__link md-nav__link--active">
@@ -2951,6 +2913,7 @@
<nav class="md-nav md-nav--secondary" aria-label="目錄">
@@ -4337,6 +4300,7 @@
<div class="md-sidebar__inner">
<nav class="md-nav md-nav--secondary" aria-label="目錄">
@@ -4411,7 +4375,7 @@
class="md-content__button md-icon"
>
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</a>
@@ -4426,7 +4390,7 @@
<li><strong>劃分階段</strong>：透過遞迴不斷地將陣列從中點處分開，將長陣列的排序問題轉換為短陣列的排序問題。</li>
<li><strong>合併階段</strong>：當子陣列長度為 1 時終止劃分，開始合併，持續地將左右兩個較短的有序陣列合併為一個較長的有序陣列，直至結束。</li>
</ol>
<p><a class="glightbox" href="../merge_sort.assets/merge_sort_overview.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="合併排序的劃分與合併階段" class="animation-figure" src="../merge_sort.assets/merge_sort_overview.png" /></a></p>
<p><img alt="合併排序的劃分與合併階段" class="animation-figure" src="../merge_sort.assets/merge_sort_overview.png" /></p>
<p align="center"> 圖 11-10 &nbsp; 合併排序的劃分與合併階段 </p>
<h2 id="1161">11.6.1 &nbsp; 演算法流程<a class="headerlink" href="#1161" title="Permanent link">&para;</a></h2>
@@ -4439,34 +4403,34 @@
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<p><a class="glightbox" href="../merge_sort.assets/merge_sort_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="合併排序步驟" class="animation-figure" src="../merge_sort.assets/merge_sort_step1.png" /></a></p>
<p><img alt="合併排序步驟" class="animation-figure" src="../merge_sort.assets/merge_sort_step1.png" /></p>
</div>
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<p><a class="glightbox" href="../merge_sort.assets/merge_sort_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="merge_sort_step2" class="animation-figure" src="../merge_sort.assets/merge_sort_step2.png" /></a></p>
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<p><img alt="merge_sort_step3" class="animation-figure" src="../merge_sort.assets/merge_sort_step3.png" /></p>
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<p><a class="glightbox" href="../merge_sort.assets/merge_sort_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="merge_sort_step4" class="animation-figure" src="../merge_sort.assets/merge_sort_step4.png" /></a></p>
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<p><a class="glightbox" href="../merge_sort.assets/merge_sort_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="merge_sort_step5" class="animation-figure" src="../merge_sort.assets/merge_sort_step5.png" /></a></p>
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<p><a class="glightbox" href="../merge_sort.assets/merge_sort_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="merge_sort_step6" class="animation-figure" src="../merge_sort.assets/merge_sort_step6.png" /></a></p>
<p><img alt="merge_sort_step6" class="animation-figure" src="../merge_sort.assets/merge_sort_step6.png" /></p>
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<p><a class="glightbox" href="../merge_sort.assets/merge_sort_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="merge_sort_step7" class="animation-figure" src="../merge_sort.assets/merge_sort_step7.png" /></a></p>
<p><img alt="merge_sort_step7" class="animation-figure" src="../merge_sort.assets/merge_sort_step7.png" /></p>
</div>
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<p><a class="glightbox" href="../merge_sort.assets/merge_sort_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="merge_sort_step8" class="animation-figure" src="../merge_sort.assets/merge_sort_step8.png" /></a></p>
<p><img alt="merge_sort_step8" class="animation-figure" src="../merge_sort.assets/merge_sort_step8.png" /></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../merge_sort.assets/merge_sort_step9.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="merge_sort_step9" class="animation-figure" src="../merge_sort.assets/merge_sort_step9.png" /></a></p>
<p><img alt="merge_sort_step9" class="animation-figure" src="../merge_sort.assets/merge_sort_step9.png" /></p>
</div>
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<p><a class="glightbox" href="../merge_sort.assets/merge_sort_step10.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="merge_sort_step10" class="animation-figure" src="../merge_sort.assets/merge_sort_step10.png" /></a></p>
<p><img alt="merge_sort_step10" class="animation-figure" src="../merge_sort.assets/merge_sort_step10.png" /></p>
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@@ -5119,7 +5083,7 @@ aria-label="頁脚"
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@@ -5229,7 +5193,7 @@ aria-label="頁脚"
<button type="button" class="md-top md-icon" data-md-component="top" hidden>
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回到頂部
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@@ -5237,46 +5201,6 @@ aria-label="頁脚"
<footer class="md-footer">
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zh-hant/chapter_sorting/quick_sort/index.html
+55 -133
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<title>11.5 快速排序 - Hello 演算法</title>
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<img src="../../assets/images/logo.svg" alt="Hello 演算法">
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<a href="https://github.com/krahets/hello-algo" title="前往倉庫" class="md-source" data-md-component="source">
<div class="md-source__icon md-icon">
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</div>
<div class="md-source__repository">
krahets/hello-algo
</div>
</a>
</div>
</div>
</nav>
</header>
@@ -325,7 +287,7 @@
<label class="md-nav__title" for="__drawer">
<a href="../.." title="Hello 演算法" class="md-nav__button md-logo" aria-label="Hello 演算法" data-md-component="logo">
<img src="../../assets/images/logo.svg" alt="logo">
<img src="../../assets/images/logo.svg" alt="Hello 演算法">
</a>
Hello 演算法
@@ -335,7 +297,7 @@
<a href="https://github.com/krahets/hello-algo" title="前往倉庫" class="md-source" data-md-component="source">
<div class="md-source__icon md-icon">
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</div>
<div class="md-source__repository">
krahets/hello-algo
@@ -2904,7 +2866,7 @@
<span class="md-nav__icon md-icon"></span>
</label>
<a href="./" class="md-nav__link md-nav__link--active">
<a href="././" class="md-nav__link md-nav__link--active">
@@ -2923,6 +2885,7 @@
<nav class="md-nav md-nav--secondary" aria-label="目錄">
@@ -4359,6 +4322,7 @@
<div class="md-sidebar__inner">
<nav class="md-nav md-nav--secondary" aria-label="目錄">
@@ -4455,7 +4419,7 @@
class="md-content__button md-icon"
>
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</a>
@@ -4475,31 +4439,31 @@
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<div class="tabbed-content">
<div class="tabbed-block">
<p><a class="glightbox" href="../quick_sort.assets/pivot_division_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="哨兵劃分步驟" class="animation-figure" src="../quick_sort.assets/pivot_division_step1.png" /></a></p>
<p><img alt="哨兵劃分步驟" class="animation-figure" src="../quick_sort.assets/pivot_division_step1.png" /></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../quick_sort.assets/pivot_division_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="pivot_division_step2" class="animation-figure" src="../quick_sort.assets/pivot_division_step2.png" /></a></p>
<p><img alt="pivot_division_step2" class="animation-figure" src="../quick_sort.assets/pivot_division_step2.png" /></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../quick_sort.assets/pivot_division_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="pivot_division_step3" class="animation-figure" src="../quick_sort.assets/pivot_division_step3.png" /></a></p>
<p><img alt="pivot_division_step3" class="animation-figure" src="../quick_sort.assets/pivot_division_step3.png" /></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../quick_sort.assets/pivot_division_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="pivot_division_step4" class="animation-figure" src="../quick_sort.assets/pivot_division_step4.png" /></a></p>
<p><img alt="pivot_division_step4" class="animation-figure" src="../quick_sort.assets/pivot_division_step4.png" /></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../quick_sort.assets/pivot_division_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="pivot_division_step5" class="animation-figure" src="../quick_sort.assets/pivot_division_step5.png" /></a></p>
<p><img alt="pivot_division_step5" class="animation-figure" src="../quick_sort.assets/pivot_division_step5.png" /></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../quick_sort.assets/pivot_division_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="pivot_division_step6" class="animation-figure" src="../quick_sort.assets/pivot_division_step6.png" /></a></p>
<p><img alt="pivot_division_step6" class="animation-figure" src="../quick_sort.assets/pivot_division_step6.png" /></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../quick_sort.assets/pivot_division_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="pivot_division_step7" class="animation-figure" src="../quick_sort.assets/pivot_division_step7.png" /></a></p>
<p><img alt="pivot_division_step7" class="animation-figure" src="../quick_sort.assets/pivot_division_step7.png" /></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../quick_sort.assets/pivot_division_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="pivot_division_step8" class="animation-figure" src="../quick_sort.assets/pivot_division_step8.png" /></a></p>
<p><img alt="pivot_division_step8" class="animation-figure" src="../quick_sort.assets/pivot_division_step8.png" /></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../quick_sort.assets/pivot_division_step9.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="pivot_division_step9" class="animation-figure" src="../quick_sort.assets/pivot_division_step9.png" /></a></p>
<p><img alt="pivot_division_step9" class="animation-figure" src="../quick_sort.assets/pivot_division_step9.png" /></p>
</div>
</div>
</div>
@@ -4819,7 +4783,7 @@
<li>然後，對左子陣列和右子陣列分別遞迴執行“哨兵劃分”。</li>
<li>持續遞迴，直至子陣列長度為 1 時終止，從而完成整個陣列的排序。</li>
</ol>
<p><a class="glightbox" href="../quick_sort.assets/quick_sort_overview.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="快速排序流程" class="animation-figure" src="../quick_sort.assets/quick_sort_overview.png" /></a></p>
<p><img alt="快速排序流程" class="animation-figure" src="../quick_sort.assets/quick_sort_overview.png" /></p>
<p align="center"> 圖 11-9 &nbsp; 快速排序流程 </p>
<div class="tabbed-set tabbed-alternate" data-tabs="3:13"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label></div>
@@ -5766,7 +5730,7 @@ aria-label="頁脚"
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@@ -5876,7 +5840,7 @@ aria-label="頁脚"
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zh-hant/chapter_sorting/radix_sort/index.html
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<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans+SC:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
<style>:root{--md-text-font:"Noto Sans SC";--md-code-font:"JetBrains Mono"}</style>
<link rel="stylesheet" href="../../stylesheets/extra.css">
<script>__md_scope=new URL("../..",location),__md_hash=e=>[...e].reduce(((e,_)=>(e<<5)-e+_.charCodeAt(0)),0),__md_get=(e,_=localStorage,t=__md_scope)=>JSON.parse(_.getItem(t.pathname+"."+e)),__md_set=(e,_,t=localStorage,a=__md_scope)=>{try{t.setItem(a.pathname+"."+e,JSON.stringify(_))}catch(e){}}</script>
<script>__md_scope=new URL("../..",location),__md_hash=e=>[...e].reduce(((e,t)=>(e<<5)-e+t.charCodeAt(0)),0),__md_get=(e,t=localStorage,a=__md_scope)=>JSON.parse(t.getItem(("__palette"===e?"/":a.pathname)+"."+e)),__md_set=(e,t,a=localStorage,_=__md_scope)=>{try{a.setItem(("__palette"===e?"/":_.pathname)+"."+e,JSON.stringify(t))}catch(e){}},document.documentElement.setAttribute("data-platform",navigator.platform)</script>
<link href="../../assets/stylesheets/glightbox.min.css" rel="stylesheet"/><style>
html.glightbox-open { overflow: initial; height: 100%; }
.gslide-title { margin-top: 0px; user-select: text; }
.gslide-desc { color: #666; user-select: text; }
.gslide-image img { background: white; }
.gscrollbar-fixer { padding-right: 15px; }
.gdesc-inner { font-size: 0.75rem; }
body[data-md-color-scheme="slate"] .gdesc-inner { background: var(--md-default-bg-color);}
body[data-md-color-scheme="slate"] .gslide-title { color: var(--md-default-fg-color);}
body[data-md-color-scheme="slate"] .gslide-desc { color: var(--md-default-fg-color);}</style> <script src="../../assets/javascripts/glightbox.min.js"></script></head>
</head>
@@ -97,7 +93,7 @@
<input class="md-toggle" data-md-toggle="drawer" type="checkbox" id="__drawer" autocomplete="off">
<input class="md-toggle" data-md-toggle="search" type="checkbox" id="__search" autocomplete="off">
<label class="md-overlay" for="__drawer"></label>
<label class="md-overlay" for="__drawer" aria-label="導航"></label>
<div data-md-component="skip">
@@ -139,12 +135,12 @@
<nav class="md-header__inner md-grid" aria-label="頁首">
<a href="../.." title="Hello 演算法" class="md-header__button md-logo" aria-label="Hello 演算法" data-md-component="logo">
<img src="../../assets/images/logo.svg" alt="logo">
<img src="../../assets/images/logo.svg" alt="Hello 演算法">
</a>
<label class="md-header__button md-icon" for="__drawer">
<label class="md-header__button md-icon" for="__drawer" aria-label="導航">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 6h18v2H3zm0 5h18v2H3zm0 5h18v2H3z"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-menu" viewBox="0 0 24 24"><path d="M4 5h16M4 12h16M4 19h16"/></svg>
</label>
<div class="md-header__title" data-md-component="header-title">
<div class="md-header__ellipsis">
@@ -169,7 +165,7 @@
<input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="teal" aria-label="深色模式" type="radio" name="__palette" id="__palette_0">
<input class="md-option" data-md-color-media="none" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="teal" aria-label="深色模式" type="radio" name="__palette" id="__palette_0">
<label class="md-header__button md-icon" title="深色模式" for="__palette_1" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07zm-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13zm-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87zM19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35zm4.33-2.7 1.15-2.77 2.2 2.54zm1.15-4.96-1.14-2.78 3.34.24zM9.63 18.93l2.77 1.15-2.53 2.19z"/></svg>
@@ -179,7 +175,7 @@
<input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="black" data-md-color-accent="teal" aria-label="淺色模式" type="radio" name="__palette" id="__palette_1">
<input class="md-option" data-md-color-media="none" data-md-color-scheme="slate" data-md-color-primary="black" data-md-color-accent="teal" aria-label="淺色模式" type="radio" name="__palette" id="__palette_1">
<label class="md-header__button md-icon" title="淺色模式" for="__palette_0" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07zm-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13zm-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87zM19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35zm4.33-2.7 1.15-2.77 2.2 2.54zm1.15-4.96-1.14-2.78 3.34.24zM9.63 18.93l2.77 1.15-2.53 2.19z"/></svg>
@@ -197,7 +193,7 @@
<div class="md-select">
<button class="md-header__button md-icon" aria-label="選擇語言">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12.87 15.07-2.54-2.51.03-.03A17.5 17.5 0 0 0 14.07 6H17V4h-7V2H8v2H1v2h11.17C11.5 7.92 10.44 9.75 9 11.35 8.07 10.32 7.3 9.19 6.69 8h-2c.73 1.63 1.73 3.17 2.98 4.56l-5.09 5.02L4 19l5-5 3.11 3.11zM18.5 10h-2L12 22h2l1.12-3h4.75L21 22h2zm-2.62 7 1.62-4.33L19.12 17z"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-languages" viewBox="0 0 24 24"><path d="m5 8 6 6M4 14l6-6 2-3M2 5h12M7 2h1M22 22l-5-10-5 10M14 18h6"/></svg>
</button>
<div class="md-select__inner">
<ul class="md-select__list">
@@ -240,64 +236,30 @@
<label class="md-header__button md-icon" for="__search">
<label class="md-header__button md-icon" for="__search" aria-label="搜尋">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.52 6.52 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-search" viewBox="0 0 24 24"><path d="m21 21-4.34-4.34"/><circle cx="11" cy="11" r="8"/></svg>
</label>
<div class="md-search" data-md-component="search" role="dialog">
<label class="md-search__overlay" for="__search"></label>
<div class="md-search__inner" role="search">
<form class="md-search__form" name="search">
<input type="text" class="md-search__input" name="query" aria-label="搜尋" placeholder="搜尋" autocapitalize="off" autocorrect="off" autocomplete="off" spellcheck="false" data-md-component="search-query" required>
<label class="md-search__icon md-icon" for="__search">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.52 6.52 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11z"/></svg>
</label>
<nav class="md-search__options" aria-label="搜尋">
<a href="javascript:void(0)" class="md-search__icon md-icon" title="分享" aria-label="分享" data-clipboard data-clipboard-text="" data-md-component="search-share" tabindex="-1">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 16.08c-.76 0-1.44.3-1.96.77L8.91 12.7c.05-.23.09-.46.09-.7s-.04-.47-.09-.7l7.05-4.11c.54.5 1.25.81 2.04.81a3 3 0 0 0 3-3 3 3 0 0 0-3-3 3 3 0 0 0-3 3c0 .24.04.47.09.7L8.04 9.81C7.5 9.31 6.79 9 6 9a3 3 0 0 0-3 3 3 3 0 0 0 3 3c.79 0 1.5-.31 2.04-.81l7.12 4.15c-.05.21-.08.43-.08.66 0 1.61 1.31 2.91 2.92 2.91s2.92-1.3 2.92-2.91A2.92 2.92 0 0 0 18 16.08"/></svg>
</a>
<button type="reset" class="md-search__icon md-icon" title="清空" aria-label="清空" tabindex="-1">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 6.41 17.59 5 12 10.59 6.41 5 5 6.41 10.59 12 5 17.59 6.41 19 12 13.41 17.59 19 19 17.59 13.41 12z"/></svg>
</button>
</nav>
<div class="md-search__suggest" data-md-component="search-suggest"></div>
</form>
<div class="md-search__output">
<div class="md-search__scrollwrap" tabindex="0" data-md-scrollfix>
<div class="md-search-result" data-md-component="search-result">
<div class="md-search-result__meta">
正在初始化搜尋引擎
</div>
<ol class="md-search-result__list" role="presentation"></ol>
</div>
</div>
</div>
</div>
<div class="md-search" data-md-component="search" role="dialog" aria-label="搜尋">
<button type="button" class="md-search__button">
搜尋
</button>
</div>
<div class="md-header__source">
<div class="md-header__source">
<a href="https://github.com/krahets/hello-algo" title="前往倉庫" class="md-source" data-md-component="source">
<div class="md-source__icon md-icon">
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</div>
<div class="md-source__repository">
krahets/hello-algo
</div>
</a>
</div>
</div>
</nav>
</header>
@@ -325,7 +287,7 @@
<label class="md-nav__title" for="__drawer">
<a href="../.." title="Hello 演算法" class="md-nav__button md-logo" aria-label="Hello 演算法" data-md-component="logo">
<img src="../../assets/images/logo.svg" alt="logo">
<img src="../../assets/images/logo.svg" alt="Hello 演算法">
</a>
Hello 演算法
@@ -335,7 +297,7 @@
<a href="https://github.com/krahets/hello-algo" title="前往倉庫" class="md-source" data-md-component="source">
<div class="md-source__icon md-icon">
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@@ -4408,7 +4372,7 @@
<li>對學號的第 <span class="arithmatex">\(k\)</span> 位執行“計數排序”。完成後，資料會根據第 <span class="arithmatex">\(k\)</span> 位從小到大排序。</li>
<li>將 <span class="arithmatex">\(k\)</span> 增加 <span class="arithmatex">\(1\)</span> ，然後返回步驟 <code>2.</code> 繼續迭代，直到所有位都排序完成後結束。</li>
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<p><a class="glightbox" href="../radix_sort.assets/radix_sort_overview.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="基數排序演算法流程" class="animation-figure" src="../radix_sort.assets/radix_sort_overview.png" /></a></p>
<p><img alt="基數排序演算法流程" class="animation-figure" src="../radix_sort.assets/radix_sort_overview.png" /></p>
<p align="center"> 圖 11-18 &nbsp; 基數排序演算法流程 </p>
<p>下面剖析程式碼實現。對於一個 <span class="arithmatex">\(d\)</span> 進位制的數字 <span class="arithmatex">\(x\)</span> ，要獲取其第 <span class="arithmatex">\(k\)</span> 位 <span class="arithmatex">\(x_k\)</span> ，可以使用以下計算公式：</p>
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zh-hant/chapter_sorting/selection_sort/index.html
+57 -135
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<title>11.2   選擇排序 - Hello 演算法</title>
<title>11.2 選擇排序 - Hello 演算法</title>
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</div>
<div class="md-source__repository">
krahets/hello-algo
</div>
</a>
</div>
</div>
</nav>
</header>
@@ -325,7 +287,7 @@
<label class="md-nav__title" for="__drawer">
<a href="../.." title="Hello 演算法" class="md-nav__button md-logo" aria-label="Hello 演算法" data-md-component="logo">
<img src="../../assets/images/logo.svg" alt="logo">
<img src="../../assets/images/logo.svg" alt="Hello 演算法">
</a>
Hello 演算法
@@ -335,7 +297,7 @@
<a href="https://github.com/krahets/hello-algo" title="前往倉庫" class="md-source" data-md-component="source">
<div class="md-source__icon md-icon">
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<div class="md-source__repository">
krahets/hello-algo
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<span class="md-nav__icon md-icon"></span>
</label>
<a href="./" class="md-nav__link md-nav__link--active">
<a href="././" class="md-nav__link md-nav__link--active">
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<nav class="md-nav md-nav--secondary" aria-label="目錄">
@@ -4315,6 +4278,7 @@
<div class="md-sidebar__inner">
<nav class="md-nav md-nav--secondary" aria-label="目錄">
@@ -4367,7 +4331,7 @@
class="md-content__button md-icon"
>
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@@ -4389,37 +4353,37 @@
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<div class="tabbed-content">
<div class="tabbed-block">
<p><a class="glightbox" href="../selection_sort.assets/selection_sort_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="選擇排序步驟" class="animation-figure" src="../selection_sort.assets/selection_sort_step1.png" /></a></p>
<p><img alt="選擇排序步驟" class="animation-figure" src="../selection_sort.assets/selection_sort_step1.png" /></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../selection_sort.assets/selection_sort_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="selection_sort_step2" class="animation-figure" src="../selection_sort.assets/selection_sort_step2.png" /></a></p>
<p><img alt="selection_sort_step2" class="animation-figure" src="../selection_sort.assets/selection_sort_step2.png" /></p>
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<div class="tabbed-block">
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<p><img alt="selection_sort_step3" class="animation-figure" src="../selection_sort.assets/selection_sort_step3.png" /></p>
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<div class="tabbed-block">
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<p><img alt="selection_sort_step4" class="animation-figure" src="../selection_sort.assets/selection_sort_step4.png" /></p>
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<p><img alt="selection_sort_step7" class="animation-figure" src="../selection_sort.assets/selection_sort_step7.png" /></p>
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<p><img alt="selection_sort_step8" class="animation-figure" src="../selection_sort.assets/selection_sort_step8.png" /></p>
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<p><img alt="selection_sort_step9" class="animation-figure" src="../selection_sort.assets/selection_sort_step9.png" /></p>
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<div class="tabbed-block">
<p><a class="glightbox" href="../selection_sort.assets/selection_sort_step10.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="selection_sort_step10" class="animation-figure" src="../selection_sort.assets/selection_sort_step10.png" /></a></p>
<p><img alt="selection_sort_step10" class="animation-figure" src="../selection_sort.assets/selection_sort_step10.png" /></p>
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<div class="tabbed-block">
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</div>
@@ -4688,7 +4652,7 @@
<li><strong>空間複雜度為 <span class="arithmatex">\(O(1)\)</span>、原地排序</strong>：指標 <span class="arithmatex">\(i\)</span> 和 <span class="arithmatex">\(j\)</span> 使用常數大小的額外空間。</li>
<li><strong>非穩定排序</strong>：如圖 11-3 所示，元素 <code>nums[i]</code> 有可能被交換至與其相等的元素的右邊，導致兩者的相對順序發生改變。</li>
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<p align="center"> 圖 11-3 &nbsp; 選擇排序非穩定示例 </p>
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<label class="md-header__button md-icon" title="深色模式" for="__palette_1" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07zm-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13zm-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87zM19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35zm4.33-2.7 1.15-2.77 2.2 2.54zm1.15-4.96-1.14-2.78 3.34.24zM9.63 18.93l2.77 1.15-2.53 2.19z"/></svg>
@@ -179,7 +175,7 @@
<input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="black" data-md-color-accent="teal" aria-label="淺色模式" type="radio" name="__palette" id="__palette_1">
<input class="md-option" data-md-color-media="none" data-md-color-scheme="slate" data-md-color-primary="black" data-md-color-accent="teal" aria-label="淺色模式" type="radio" name="__palette" id="__palette_1">
<label class="md-header__button md-icon" title="淺色模式" for="__palette_0" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07zm-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13zm-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87zM19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35zm4.33-2.7 1.15-2.77 2.2 2.54zm1.15-4.96-1.14-2.78 3.34.24zM9.63 18.93l2.77 1.15-2.53 2.19z"/></svg>
@@ -197,7 +193,7 @@
<div class="md-select">
<button class="md-header__button md-icon" aria-label="選擇語言">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12.87 15.07-2.54-2.51.03-.03A17.5 17.5 0 0 0 14.07 6H17V4h-7V2H8v2H1v2h11.17C11.5 7.92 10.44 9.75 9 11.35 8.07 10.32 7.3 9.19 6.69 8h-2c.73 1.63 1.73 3.17 2.98 4.56l-5.09 5.02L4 19l5-5 3.11 3.11zM18.5 10h-2L12 22h2l1.12-3h4.75L21 22h2zm-2.62 7 1.62-4.33L19.12 17z"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-languages" viewBox="0 0 24 24"><path d="m5 8 6 6M4 14l6-6 2-3M2 5h12M7 2h1M22 22l-5-10-5 10M14 18h6"/></svg>
</button>
<div class="md-select__inner">
<ul class="md-select__list">
@@ -240,64 +236,30 @@
<label class="md-header__button md-icon" for="__search">
<label class="md-header__button md-icon" for="__search" aria-label="搜尋">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.52 6.52 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-search" viewBox="0 0 24 24"><path d="m21 21-4.34-4.34"/><circle cx="11" cy="11" r="8"/></svg>
</label>
<div class="md-search" data-md-component="search" role="dialog">
<label class="md-search__overlay" for="__search"></label>
<div class="md-search__inner" role="search">
<form class="md-search__form" name="search">
<input type="text" class="md-search__input" name="query" aria-label="搜尋" placeholder="搜尋" autocapitalize="off" autocorrect="off" autocomplete="off" spellcheck="false" data-md-component="search-query" required>
<label class="md-search__icon md-icon" for="__search">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.52 6.52 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11z"/></svg>
</label>
<nav class="md-search__options" aria-label="搜尋">
<a href="javascript:void(0)" class="md-search__icon md-icon" title="分享" aria-label="分享" data-clipboard data-clipboard-text="" data-md-component="search-share" tabindex="-1">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 16.08c-.76 0-1.44.3-1.96.77L8.91 12.7c.05-.23.09-.46.09-.7s-.04-.47-.09-.7l7.05-4.11c.54.5 1.25.81 2.04.81a3 3 0 0 0 3-3 3 3 0 0 0-3-3 3 3 0 0 0-3 3c0 .24.04.47.09.7L8.04 9.81C7.5 9.31 6.79 9 6 9a3 3 0 0 0-3 3 3 3 0 0 0 3 3c.79 0 1.5-.31 2.04-.81l7.12 4.15c-.05.21-.08.43-.08.66 0 1.61 1.31 2.91 2.92 2.91s2.92-1.3 2.92-2.91A2.92 2.92 0 0 0 18 16.08"/></svg>
</a>
<button type="reset" class="md-search__icon md-icon" title="清空" aria-label="清空" tabindex="-1">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 6.41 17.59 5 12 10.59 6.41 5 5 6.41 10.59 12 5 17.59 6.41 19 12 13.41 17.59 19 19 17.59 13.41 12z"/></svg>
</button>
</nav>
<div class="md-search__suggest" data-md-component="search-suggest"></div>
</form>
<div class="md-search__output">
<div class="md-search__scrollwrap" tabindex="0" data-md-scrollfix>
<div class="md-search-result" data-md-component="search-result">
<div class="md-search-result__meta">
正在初始化搜尋引擎
</div>
<ol class="md-search-result__list" role="presentation"></ol>
</div>
</div>
</div>
</div>
<div class="md-search" data-md-component="search" role="dialog" aria-label="搜尋">
<button type="button" class="md-search__button">
搜尋
</button>
</div>
<div class="md-header__source">
<div class="md-header__source">
<a href="https://github.com/krahets/hello-algo" title="前往倉庫" class="md-source" data-md-component="source">
<div class="md-source__icon md-icon">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path d="M173.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6m-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3m44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9M252.8 8C114.1 8 8 113.3 8 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C436.2 457.8 504 362.9 504 252 504 113.3 391.5 8 252.8 8M105.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1m-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7m32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1m-11.4-14.7c-1.6 1-1.6 3.6 0 5.9s4.3 3.3 5.6 2.3c1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path fill="currentColor" d="M173.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6m-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3m44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9M252.8 8C114.1 8 8 113.3 8 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C436.2 457.8 504 362.9 504 252 504 113.3 391.5 8 252.8 8M105.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1m-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7m32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1m-11.4-14.7c-1.6 1-1.6 3.6 0 5.9s4.3 3.3 5.6 2.3c1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2"/></svg>
</div>
<div class="md-source__repository">
krahets/hello-algo
</div>
</a>
</div>
</div>
</nav>
</header>
@@ -325,7 +287,7 @@
<label class="md-nav__title" for="__drawer">
<a href="../.." title="Hello 演算法" class="md-nav__button md-logo" aria-label="Hello 演算法" data-md-component="logo">
<img src="../../assets/images/logo.svg" alt="logo">
<img src="../../assets/images/logo.svg" alt="Hello 演算法">
</a>
Hello 演算法
@@ -335,7 +297,7 @@
<a href="https://github.com/krahets/hello-algo" title="前往倉庫" class="md-source" data-md-component="source">
<div class="md-source__icon md-icon">
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</div>
<div class="md-source__repository">
krahets/hello-algo
@@ -2792,7 +2754,7 @@
<span class="md-nav__icon md-icon"></span>
</label>
<a href="./" class="md-nav__link md-nav__link--active">
<a href="././" class="md-nav__link md-nav__link--active">
@@ -2811,6 +2773,7 @@
<nav class="md-nav md-nav--secondary" aria-label="目錄">
@@ -4326,6 +4289,7 @@
<div class="md-sidebar__inner">
<nav class="md-nav md-nav--secondary" aria-label="目錄">
@@ -4389,7 +4353,7 @@
class="md-content__button md-icon"
>
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@@ -4401,7 +4365,7 @@
<h1 id="111">11.1 &nbsp; 排序演算法<a class="headerlink" href="#111" title="Permanent link">&para;</a></h1>
<p><u>排序演算法（sorting algorithm）</u>用於對一組資料按照特定順序進行排列。排序演算法有著廣泛的應用，因為有序資料通常能夠被更高效地查詢、分析和處理。</p>
<p>如圖 11-1 所示，排序演算法中的資料型別可以是整數、浮點數、字元或字串等。排序的判斷規則可根據需求設定，如數字大小、字元 ASCII 碼順序或自定義規則。</p>
<p><a class="glightbox" href="../sorting_algorithm.assets/sorting_examples.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="資料型別和判斷規則示例" class="animation-figure" src="../sorting_algorithm.assets/sorting_examples.png" /></a></p>
<p><img alt="資料型別和判斷規則示例" class="animation-figure" src="../sorting_algorithm.assets/sorting_examples.png" /></p>
<p align="center"> 圖 11-1 &nbsp; 資料型別和判斷規則示例 </p>
<h2 id="1111">11.1.1 &nbsp; 評價維度<a class="headerlink" href="#1111" title="Permanent link">&para;</a></h2>
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<script>__md_scope=new URL("../..",location),__md_hash=e=>[...e].reduce(((e,t)=>(e<<5)-e+t.charCodeAt(0)),0),__md_get=(e,t=localStorage,a=__md_scope)=>JSON.parse(t.getItem(("__palette"===e?"/":a.pathname)+"."+e)),__md_set=(e,t,a=localStorage,_=__md_scope)=>{try{a.setItem(("__palette"===e?"/":_.pathname)+"."+e,JSON.stringify(t))}catch(e){}},document.documentElement.setAttribute("data-platform",navigator.platform)</script>
<link href="../../assets/stylesheets/glightbox.min.css" rel="stylesheet"/><style>
html.glightbox-open { overflow: initial; height: 100%; }
.gslide-title { margin-top: 0px; user-select: text; }
.gslide-desc { color: #666; user-select: text; }
.gslide-image img { background: white; }
.gscrollbar-fixer { padding-right: 15px; }
.gdesc-inner { font-size: 0.75rem; }
body[data-md-color-scheme="slate"] .gdesc-inner { background: var(--md-default-bg-color);}
body[data-md-color-scheme="slate"] .gslide-title { color: var(--md-default-fg-color);}
body[data-md-color-scheme="slate"] .gslide-desc { color: var(--md-default-fg-color);}</style> <script src="../../assets/javascripts/glightbox.min.js"></script></head>
</head>
@@ -97,7 +93,7 @@
<input class="md-toggle" data-md-toggle="drawer" type="checkbox" id="__drawer" autocomplete="off">
<input class="md-toggle" data-md-toggle="search" type="checkbox" id="__search" autocomplete="off">
<label class="md-overlay" for="__drawer"></label>
<label class="md-overlay" for="__drawer" aria-label="導航"></label>
<div data-md-component="skip">
@@ -139,12 +135,12 @@
<nav class="md-header__inner md-grid" aria-label="頁首">
<a href="../.." title="Hello 演算法" class="md-header__button md-logo" aria-label="Hello 演算法" data-md-component="logo">
<img src="../../assets/images/logo.svg" alt="logo">
<img src="../../assets/images/logo.svg" alt="Hello 演算法">
</a>
<label class="md-header__button md-icon" for="__drawer">
<label class="md-header__button md-icon" for="__drawer" aria-label="導航">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 6h18v2H3zm0 5h18v2H3zm0 5h18v2H3z"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-menu" viewBox="0 0 24 24"><path d="M4 5h16M4 12h16M4 19h16"/></svg>
</label>
<div class="md-header__title" data-md-component="header-title">
<div class="md-header__ellipsis">
@@ -169,7 +165,7 @@
<input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="teal" aria-label="深色模式" type="radio" name="__palette" id="__palette_0">
<input class="md-option" data-md-color-media="none" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="teal" aria-label="深色模式" type="radio" name="__palette" id="__palette_0">
<label class="md-header__button md-icon" title="深色模式" for="__palette_1" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07zm-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13zm-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87zM19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35zm4.33-2.7 1.15-2.77 2.2 2.54zm1.15-4.96-1.14-2.78 3.34.24zM9.63 18.93l2.77 1.15-2.53 2.19z"/></svg>
@@ -179,7 +175,7 @@
<input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="black" data-md-color-accent="teal" aria-label="淺色模式" type="radio" name="__palette" id="__palette_1">
<input class="md-option" data-md-color-media="none" data-md-color-scheme="slate" data-md-color-primary="black" data-md-color-accent="teal" aria-label="淺色模式" type="radio" name="__palette" id="__palette_1">
<label class="md-header__button md-icon" title="淺色模式" for="__palette_0" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07zm-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13zm-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87zM19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35zm4.33-2.7 1.15-2.77 2.2 2.54zm1.15-4.96-1.14-2.78 3.34.24zM9.63 18.93l2.77 1.15-2.53 2.19z"/></svg>
@@ -197,7 +193,7 @@
<div class="md-select">
<button class="md-header__button md-icon" aria-label="選擇語言">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12.87 15.07-2.54-2.51.03-.03A17.5 17.5 0 0 0 14.07 6H17V4h-7V2H8v2H1v2h11.17C11.5 7.92 10.44 9.75 9 11.35 8.07 10.32 7.3 9.19 6.69 8h-2c.73 1.63 1.73 3.17 2.98 4.56l-5.09 5.02L4 19l5-5 3.11 3.11zM18.5 10h-2L12 22h2l1.12-3h4.75L21 22h2zm-2.62 7 1.62-4.33L19.12 17z"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-languages" viewBox="0 0 24 24"><path d="m5 8 6 6M4 14l6-6 2-3M2 5h12M7 2h1M22 22l-5-10-5 10M14 18h6"/></svg>
</button>
<div class="md-select__inner">
<ul class="md-select__list">
@@ -240,64 +236,30 @@
<label class="md-header__button md-icon" for="__search">
<label class="md-header__button md-icon" for="__search" aria-label="搜尋">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.52 6.52 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-search" viewBox="0 0 24 24"><path d="m21 21-4.34-4.34"/><circle cx="11" cy="11" r="8"/></svg>
</label>
<div class="md-search" data-md-component="search" role="dialog">
<label class="md-search__overlay" for="__search"></label>
<div class="md-search__inner" role="search">
<form class="md-search__form" name="search">
<input type="text" class="md-search__input" name="query" aria-label="搜尋" placeholder="搜尋" autocapitalize="off" autocorrect="off" autocomplete="off" spellcheck="false" data-md-component="search-query" required>
<label class="md-search__icon md-icon" for="__search">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.52 6.52 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11z"/></svg>
</label>
<nav class="md-search__options" aria-label="搜尋">
<a href="javascript:void(0)" class="md-search__icon md-icon" title="分享" aria-label="分享" data-clipboard data-clipboard-text="" data-md-component="search-share" tabindex="-1">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 16.08c-.76 0-1.44.3-1.96.77L8.91 12.7c.05-.23.09-.46.09-.7s-.04-.47-.09-.7l7.05-4.11c.54.5 1.25.81 2.04.81a3 3 0 0 0 3-3 3 3 0 0 0-3-3 3 3 0 0 0-3 3c0 .24.04.47.09.7L8.04 9.81C7.5 9.31 6.79 9 6 9a3 3 0 0 0-3 3 3 3 0 0 0 3 3c.79 0 1.5-.31 2.04-.81l7.12 4.15c-.05.21-.08.43-.08.66 0 1.61 1.31 2.91 2.92 2.91s2.92-1.3 2.92-2.91A2.92 2.92 0 0 0 18 16.08"/></svg>
</a>
<button type="reset" class="md-search__icon md-icon" title="清空" aria-label="清空" tabindex="-1">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 6.41 17.59 5 12 10.59 6.41 5 5 6.41 10.59 12 5 17.59 6.41 19 12 13.41 17.59 19 19 17.59 13.41 12z"/></svg>
</button>
</nav>
<div class="md-search__suggest" data-md-component="search-suggest"></div>
</form>
<div class="md-search__output">
<div class="md-search__scrollwrap" tabindex="0" data-md-scrollfix>
<div class="md-search-result" data-md-component="search-result">
<div class="md-search-result__meta">
正在初始化搜尋引擎
</div>
<ol class="md-search-result__list" role="presentation"></ol>
</div>
</div>
</div>
</div>
<div class="md-search" data-md-component="search" role="dialog" aria-label="搜尋">
<button type="button" class="md-search__button">
搜尋
</button>
</div>
<div class="md-header__source">
<div class="md-header__source">
<a href="https://github.com/krahets/hello-algo" title="前往倉庫" class="md-source" data-md-component="source">
<div class="md-source__icon md-icon">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path d="M173.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6m-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3m44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9M252.8 8C114.1 8 8 113.3 8 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C436.2 457.8 504 362.9 504 252 504 113.3 391.5 8 252.8 8M105.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1m-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7m32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1m-11.4-14.7c-1.6 1-1.6 3.6 0 5.9s4.3 3.3 5.6 2.3c1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2"/></svg>
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</div>
<div class="md-source__repository">
krahets/hello-algo
</div>
</a>
</div>
</div>
</nav>
</header>
@@ -325,7 +287,7 @@
<label class="md-nav__title" for="__drawer">
<a href="../.." title="Hello 演算法" class="md-nav__button md-logo" aria-label="Hello 演算法" data-md-component="logo">
<img src="../../assets/images/logo.svg" alt="logo">
<img src="../../assets/images/logo.svg" alt="Hello 演算法">
</a>
Hello 演算法
@@ -335,7 +297,7 @@
<a href="https://github.com/krahets/hello-algo" title="前往倉庫" class="md-source" data-md-component="source">
<div class="md-source__icon md-icon">
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<li>總的來說，我們希望找到一種排序演算法，具有高效率、穩定、原地以及自適應性等優點。然而，正如其他資料結構和演算法一樣，沒有一種排序演算法能夠同時滿足所有這些條件。在實際應用中，我們需要根據資料的特性來選擇合適的排序演算法。</li>
<li>圖 11-19 對比了主流排序演算法的效率、穩定性、就地性和自適應性等。</li>
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<p><a class="glightbox" href="../summary.assets/sorting_algorithms_comparison.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="排序演算法對比" class="animation-figure" src="../summary.assets/sorting_algorithms_comparison.png" /></a></p>
<p><img alt="排序演算法對比" class="animation-figure" src="../summary.assets/sorting_algorithms_comparison.png" /></p>
<p align="center"> 圖 11-19 &nbsp; 排序演算法對比 </p>
<h3 id="2-q-a">2. &nbsp; Q &amp; A<a class="headerlink" href="#2-q-a" title="Permanent link">&para;</a></h3>
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