mirror of
https://github.com/krahets/hello-algo.git
synced 2024-12-27 17:26:28 +08:00
4849 lines
No EOL
314 KiB
HTML
4849 lines
No EOL
314 KiB
HTML
|
||
<!doctype html>
|
||
<html lang="zh-Hant" class="no-js">
|
||
<head>
|
||
|
||
<meta charset="utf-8">
|
||
<meta name="viewport" content="width=device-width,initial-scale=1">
|
||
|
||
<meta name="description" content="動畫圖解、一鍵執行的資料結構與演算法教程">
|
||
|
||
|
||
<meta name="author" content="krahets">
|
||
|
||
|
||
<link rel="canonical" href="https://www.hello-algo.com/zh-hant/chapter_graph/graph_traversal/">
|
||
|
||
|
||
<link rel="prev" href="../graph_operations/">
|
||
|
||
|
||
<link rel="next" href="../summary/">
|
||
|
||
|
||
<link rel="icon" href="../../assets/images/favicon.png">
|
||
<meta name="generator" content="mkdocs-1.5.3, mkdocs-material-9.5.5">
|
||
|
||
|
||
|
||
<title>9.3 圖的走訪 - Hello 演算法</title>
|
||
|
||
|
||
|
||
<link rel="stylesheet" href="../../assets/stylesheets/main.50c56a3b.min.css">
|
||
|
||
|
||
<link rel="stylesheet" href="../../assets/stylesheets/palette.06af60db.min.css">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<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%7CFira+Code:400,400i,700,700i&display=fallback">
|
||
<style>:root{--md-text-font:"Noto Sans SC";--md-code-font:"Fira Code"}</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>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<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>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<body dir="ltr" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="teal">
|
||
|
||
|
||
<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>
|
||
<div data-md-component="skip">
|
||
|
||
|
||
<a href="#93" class="md-skip">
|
||
跳轉至
|
||
</a>
|
||
|
||
</div>
|
||
<div data-md-component="announce">
|
||
|
||
<aside class="md-banner">
|
||
<div class="md-banner__inner md-grid md-typeset">
|
||
|
||
<button class="md-banner__button md-icon" aria-label="不再顯示此訊息">
|
||
|
||
<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 12 19 6.41Z"/></svg>
|
||
</button>
|
||
|
||
|
||
|
||
|
||
|
||
<div class="banner-svg">
|
||
<svg xmlns="http://www.w3.org/2000/svg"
|
||
viewBox="0 0 512 512"><!--!Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free Copyright 2024 Fonticons, Inc.-->
|
||
<path
|
||
d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
|
||
</svg>
|
||
<span>紙質書（簡體中文版）已發行，詳情請見<a href="/chapter_paperbook/">這裡</a></span>
|
||
</div>
|
||
|
||
</div>
|
||
|
||
<script>var content,el=document.querySelector("[data-md-component=announce]");el&&(content=el.querySelector(".md-typeset"),__md_hash(content.innerHTML)===__md_get("__announce")&&(el.hidden=!0))</script>
|
||
|
||
</aside>
|
||
|
||
</div>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<header class="md-header md-header--shadow" data-md-component="header">
|
||
<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">
|
||
|
||
</a>
|
||
<label class="md-header__button md-icon" for="__drawer">
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 6h18v2H3V6m0 5h18v2H3v-2m0 5h18v2H3v-2Z"/></svg>
|
||
</label>
|
||
<div class="md-header__title" data-md-component="header-title">
|
||
<div class="md-header__ellipsis">
|
||
<div class="md-header__topic">
|
||
<span class="md-ellipsis">
|
||
Hello 演算法
|
||
</span>
|
||
</div>
|
||
<div class="md-header__topic" data-md-component="header-topic">
|
||
<span class="md-ellipsis">
|
||
|
||
9.3 圖的走訪
|
||
|
||
</span>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
|
||
<form class="md-header__option" data-md-component="palette">
|
||
|
||
|
||
|
||
|
||
<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">
|
||
|
||
<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 19.07 19.07 3.5m-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 1.13.51 1.67m-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 1.36.03-1.05.87.4 1.31M19 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 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z"/></svg>
|
||
</label>
|
||
|
||
|
||
|
||
|
||
|
||
<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">
|
||
|
||
<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 19.07 19.07 3.5m-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 1.13.51 1.67m-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 1.36.03-1.05.87.4 1.31M19 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 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z"/></svg>
|
||
</label>
|
||
|
||
|
||
</form>
|
||
|
||
|
||
|
||
<script>var media,input,key,value,palette=__md_get("__palette");if(palette&&palette.color){"(prefers-color-scheme)"===palette.color.media&&(media=matchMedia("(prefers-color-scheme: light)"),input=document.querySelector(media.matches?"[data-md-color-media='(prefers-color-scheme: light)']":"[data-md-color-media='(prefers-color-scheme: dark)']"),palette.color.media=input.getAttribute("data-md-color-media"),palette.color.scheme=input.getAttribute("data-md-color-scheme"),palette.color.primary=input.getAttribute("data-md-color-primary"),palette.color.accent=input.getAttribute("data-md-color-accent"));for([key,value]of Object.entries(palette.color))document.body.setAttribute("data-md-color-"+key,value)}</script>
|
||
|
||
|
||
<div class="md-header__option">
|
||
<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-.03A17.52 17.52 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 3.11.76-2.04M18.5 10h-2L12 22h2l1.12-3h4.75L21 22h2l-4.5-12m-2.62 7 1.62-4.33L19.12 17h-3.24Z"/></svg>
|
||
</button>
|
||
<div class="md-select__inner">
|
||
<ul class="md-select__list">
|
||
|
||
<li class="md-select__item">
|
||
<a href="/" hreflang="zh" class="md-select__link">
|
||
简体中文
|
||
</a>
|
||
</li>
|
||
|
||
<li class="md-select__item">
|
||
<a href="/zh-hant/" hreflang="zh-Hant" class="md-select__link">
|
||
繁體中文
|
||
</a>
|
||
</li>
|
||
|
||
<li class="md-select__item">
|
||
<a href="/en/" hreflang="en" class="md-select__link">
|
||
English
|
||
</a>
|
||
</li>
|
||
|
||
</ul>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
|
||
<label class="md-header__button 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-.27A6.516 6.516 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 5Z"/></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-.27A6.516 6.516 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 5Z"/></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 11h12Z"/></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-.7 0-.24-.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 2.91 1.61 0 2.92-1.3 2.92-2.91A2.92 2.92 0 0 0 18 16.08Z"/></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 12 19 6.41Z"/></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" 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>
|
||
|
||
|
||
<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 0 496 512"><!--! Font Awesome Free 6.5.1 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 2023 Fonticons, Inc.--><path d="M165.9 397.4c0 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 3.6zm-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 2.3zm44.2-1.7c-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-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 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 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-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-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-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-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg>
|
||
</div>
|
||
<div class="md-source__repository">
|
||
krahets/hello-algo
|
||
</div>
|
||
</a>
|
||
</div>
|
||
|
||
</nav>
|
||
|
||
</header>
|
||
|
||
<div class="md-container" data-md-component="container">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<main class="md-main" data-md-component="main">
|
||
<div class="md-main__inner md-grid">
|
||
|
||
|
||
|
||
<div class="md-sidebar md-sidebar--primary" data-md-component="sidebar" data-md-type="navigation" >
|
||
<div class="md-sidebar__scrollwrap">
|
||
<div class="md-sidebar__inner">
|
||
|
||
|
||
|
||
|
||
<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">
|
||
|
||
<img src="../../assets/images/logo.svg" alt="logo">
|
||
|
||
</a>
|
||
Hello 演算法
|
||
</label>
|
||
|
||
<div class="md-nav__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 0 496 512"><!--! Font Awesome Free 6.5.1 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 2023 Fonticons, Inc.--><path d="M165.9 397.4c0 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 3.6zm-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 2.3zm44.2-1.7c-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-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 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 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-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-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-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-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg>
|
||
</div>
|
||
<div class="md-source__repository">
|
||
krahets/hello-algo
|
||
</div>
|
||
</a>
|
||
</div>
|
||
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_1" >
|
||
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_hello_algo/" class="md-nav__link ">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m13.13 22.19-1.63-3.83c1.57-.58 3.04-1.36 4.4-2.27l-2.77 6.1M5.64 12.5l-3.83-1.63 6.1-2.77C7 9.46 6.22 10.93 5.64 12.5M19.22 4c.28 0 .53 0 .74.05.17 1.39-.02 4.25-3.3 7.53-1.7 1.71-3.73 3.02-6.01 3.89l-2.15-2.1c.92-2.31 2.23-4.34 3.92-6.03C15.18 4.58 17.64 4 19.22 4m0-2c-1.98 0-4.98.69-8.22 3.93-2.19 2.19-3.5 4.6-4.35 6.71-.28.75-.09 1.57.46 2.13l2.13 2.12c.38.38.89.61 1.42.61.23 0 .47-.06.7-.15A19.1 19.1 0 0 0 18.07 13c5.66-5.66 3.54-10.61 3.54-10.61S20.7 2 19.22 2m-4.68 7.46c-.78-.78-.78-2.05 0-2.83s2.05-.78 2.83 0c.77.78.78 2.05 0 2.83-.78.78-2.05.78-2.83 0m-5.66 7.07-1.41-1.41 1.41 1.41M6.24 22l3.64-3.64c-.34-.09-.67-.24-.97-.45L4.83 22h1.41M2 22h1.41l4.77-4.76-1.42-1.41L2 20.59V22m0-2.83 4.09-4.08c-.21-.3-.36-.62-.45-.97L2 17.76v1.41Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_1_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_1">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
序
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_2" >
|
||
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_preface/" class="md-nav__link ">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 0 章 前言
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
|
||
<label class="md-nav__link " for="__nav_2" id="__nav_2_label" tabindex="0">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_2">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
第 0 章 前言
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_preface/about_the_book/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
0.1 關於本書
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_preface/suggestions/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
0.2 如何使用本書
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_preface/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
0.3 小結
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
|
||
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_introduction/" class="md-nav__link ">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 1 章 初識演算法
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
|
||
<label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_3">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
第 1 章 初識演算法
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
1.1 演算法無處不在
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
1.2 演算法是什麼
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_introduction/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
1.3 小結
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
|
||
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_computational_complexity/" class="md-nav__link ">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 2 章 複雜度分析
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
|
||
<label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_4">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
第 2 章 複雜度分析
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
2.1 演算法效率評估
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
2.2 迭代與遞迴
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
2.3 時間複雜度
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
2.4 空間複雜度
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
2.5 小結
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
|
||
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_data_structure/" class="md-nav__link ">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 3 章 資料結構
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
|
||
<label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_5">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
第 3 章 資料結構
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
3.1 資料結構分類
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
3.2 基本資料型別
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
3.3 數字編碼 *
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
3.4 字元編碼 *
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_data_structure/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
3.5 小結
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
|
||
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 4 章 陣列與鏈結串列
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
|
||
<label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_6">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
第 4 章 陣列與鏈結串列
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
4.1 陣列
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
4.2 鏈結串列
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
4.3 串列
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
4.4 記憶體與快取 *
|
||
</span>
|
||
|
||
|
||
|
||
|
||
<span class="md-status md-status--new" title="最近新增">
|
||
</span>
|
||
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
4.5 小結
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
|
||
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_stack_and_queue/" class="md-nav__link ">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 5 章 堆疊與佇列
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
|
||
<label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_7">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
第 5 章 堆疊與佇列
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
5.1 堆疊
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
5.2 佇列
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
5.3 雙向佇列
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
5.4 小結
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
|
||
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_hashing/" class="md-nav__link ">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 6 章 雜湊表
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
|
||
<label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_8">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
第 6 章 雜湊表
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_hashing/hash_map/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
6.1 雜湊表
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
6.2 雜湊衝突
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
6.3 雜湊演算法
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_hashing/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
6.4 小結
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
|
||
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_tree/" class="md-nav__link ">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 7 章 樹
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
|
||
<label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_9">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
第 7 章 樹
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_tree/binary_tree/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
7.1 二元樹
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
7.2 二元樹走訪
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
7.3 二元樹陣列表示
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
7.4 二元搜尋樹
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_tree/avl_tree/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
7.5 AVL *
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_tree/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
7.6 小結
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
|
||
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_heap/" class="md-nav__link ">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 8 章 堆積
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
|
||
<label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_10">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
第 8 章 堆積
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_heap/heap/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
8.1 堆積
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_heap/build_heap/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
8.2 建堆積操作
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_heap/top_k/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
8.3 Top-k 問題
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_heap/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
8.4 小結
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--active md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" checked>
|
||
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../" class="md-nav__link ">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 9 章 圖
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
|
||
<label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="true">
|
||
<label class="md-nav__title" for="__nav_11">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
第 9 章 圖
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../graph/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
9.1 圖
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../graph_operations/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
9.2 圖基礎操作
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--active">
|
||
|
||
<input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__link md-nav__link--active" for="__toc">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
9.3 圖的走訪
|
||
</span>
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<a href="./" class="md-nav__link md-nav__link--active">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
9.3 圖的走訪
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
|
||
|
||
<nav class="md-nav md-nav--secondary" aria-label="目錄">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__title" for="__toc">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
目錄
|
||
</label>
|
||
<ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#931" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
9.3.1 廣度優先走訪
|
||
</span>
|
||
</a>
|
||
|
||
<nav class="md-nav" aria-label="9.3.1 廣度優先走訪">
|
||
<ul class="md-nav__list">
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#1" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
1. 演算法實現
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#2" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
2. 複雜度分析
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#932" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
9.3.2 深度優先走訪
|
||
</span>
|
||
</a>
|
||
|
||
<nav class="md-nav" aria-label="9.3.2 深度優先走訪">
|
||
<ul class="md-nav__list">
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#1_1" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
1. 演算法實現
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#2_1" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
2. 複雜度分析
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
9.4 小結
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
|
||
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_searching/" class="md-nav__link ">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 10 章 搜尋
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
|
||
<label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_12">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
第 10 章 搜尋
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/binary_search/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.1 二分搜尋
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.2 二分搜尋插入點
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.3 二分搜尋邊界
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.4 雜湊最佳化策略
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.5 重識搜尋演算法
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.6 小結
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
|
||
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_sorting/" class="md-nav__link ">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 11 章 排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
|
||
<label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_13">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
第 11 章 排序
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.1 排序演算法
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.2 選擇排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.3 泡沫排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.4 插入排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.5 快速排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.6 合併排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.7 堆積排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.8 桶排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.9 計數排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.10 基數排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.11 小結
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
|
||
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 12 章 分治
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
|
||
<label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_14">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
第 12 章 分治
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
12.1 分治演算法
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
12.2 分治搜尋策略
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
12.3 構建樹問題
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
12.4 河內塔問題
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
12.5 小結
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
|
||
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_backtracking/" class="md-nav__link ">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 13 章 回溯
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
|
||
<label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_15">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
第 13 章 回溯
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
13.1 回溯演算法
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
13.2 全排列問題
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
13.3 子集和問題
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
13.4 N 皇后問題
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_backtracking/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
13.5 小結
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
|
||
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_dynamic_programming/" class="md-nav__link ">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 14 章 動態規劃
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
|
||
<label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_16">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
第 14 章 動態規劃
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
14.1 初探動態規劃
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
14.2 DP 問題特性
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
14.3 DP 解題思路
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
14.4 0-1 背包問題
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
14.5 完全背包問題
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
14.6 編輯距離問題
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
14.7 小結
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
|
||
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_greedy/" class="md-nav__link ">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 15 章 貪婪
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
|
||
<label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_17">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
第 15 章 貪婪
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
15.1 貪婪演算法
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
15.2 分數背包問題
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
15.3 最大容量問題
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
15.4 最大切分乘積問題
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_greedy/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
15.5 小結
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
|
||
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_appendix/" class="md-nav__link ">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 16 章 附錄
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
|
||
<label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_18">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
第 16 章 附錄
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_appendix/installation/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
16.1 程式設計環境安裝
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_appendix/contribution/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
16.2 一起參與創作
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_appendix/terminology/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
16.3 術語表
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
|
||
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_reference/" class="md-nav__link ">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
參考文獻
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_19">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
參考文獻
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
|
||
|
||
<div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
|
||
<div class="md-sidebar__scrollwrap">
|
||
<div class="md-sidebar__inner">
|
||
|
||
|
||
<nav class="md-nav md-nav--secondary" aria-label="目錄">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__title" for="__toc">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
目錄
|
||
</label>
|
||
<ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#931" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
9.3.1 廣度優先走訪
|
||
</span>
|
||
</a>
|
||
|
||
<nav class="md-nav" aria-label="9.3.1 廣度優先走訪">
|
||
<ul class="md-nav__list">
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#1" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
1. 演算法實現
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#2" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
2. 複雜度分析
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#932" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
9.3.2 深度優先走訪
|
||
</span>
|
||
</a>
|
||
|
||
<nav class="md-nav" aria-label="9.3.2 深度優先走訪">
|
||
<ul class="md-nav__list">
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#1_1" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
1. 演算法實現
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#2_1" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
2. 複雜度分析
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
|
||
</nav>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
|
||
|
||
<div class="md-content" data-md-component="content">
|
||
<article class="md-content__inner md-typeset">
|
||
|
||
<!-- Tags -->
|
||
|
||
|
||
<!-- Actions -->
|
||
<!-- Actions -->
|
||
|
||
|
||
<!-- Edit button -->
|
||
|
||
<a
|
||
href="https://github.com/krahets/hello-algo/tree/main/zh-hant/docs/chapter_graph/graph_traversal.md"
|
||
title="編輯此頁"
|
||
class="md-content__button md-icon"
|
||
>
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 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 2023 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 0zM88 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-10.7-24-24-24H88z"/></svg>
|
||
</a>
|
||
|
||
|
||
<!-- View button -->
|
||
|
||
|
||
|
||
<!-- Page content -->
|
||
<h1 id="93">9.3 圖的走訪<a class="headerlink" href="#93" title="Permanent link">¶</a></h1>
|
||
<p>樹代表的是“一對多”的關係，而圖則具有更高的自由度，可以表示任意的“多對多”關係。因此，我們可以把樹看作圖的一種特例。顯然，<strong>樹的走訪操作也是圖的走訪操作的一種特例</strong>。</p>
|
||
<p>圖和樹都需要應用搜索演算法來實現走訪操作。圖的走訪方式也可分為兩種：<u>廣度優先走訪</u>和<u>深度優先走訪</u>。</p>
|
||
<h2 id="931">9.3.1 廣度優先走訪<a class="headerlink" href="#931" title="Permanent link">¶</a></h2>
|
||
<p><strong>廣度優先走訪是一種由近及遠的走訪方式，從某個節點出發，始終優先訪問距離最近的頂點，並一層層向外擴張</strong>。如圖 9-9 所示，從左上角頂點出發，首先走訪該頂點的所有鄰接頂點，然後走訪下一個頂點的所有鄰接頂點，以此類推，直至所有頂點訪問完畢。</p>
|
||
<p><a class="glightbox" href="../graph_traversal.assets/graph_bfs.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="圖的廣度優先走訪" class="animation-figure" src="../graph_traversal.assets/graph_bfs.png" /></a></p>
|
||
<p align="center"> 圖 9-9 圖的廣度優先走訪 </p>
|
||
|
||
<h3 id="1">1. 演算法實現<a class="headerlink" href="#1" title="Permanent link">¶</a></h3>
|
||
<p>BFS 通常藉助佇列來實現，程式碼如下所示。佇列具有“先入先出”的性質，這與 BFS 的“由近及遠”的思想異曲同工。</p>
|
||
<ol>
|
||
<li>將走訪起始頂點 <code>startVet</code> 加入列列，並開啟迴圈。</li>
|
||
<li>在迴圈的每輪迭代中，彈出佇列首頂點並記錄訪問，然後將該頂點的所有鄰接頂點加入到佇列尾部。</li>
|
||
<li>迴圈步驟 <code>2.</code> ，直到所有頂點被訪問完畢後結束。</li>
|
||
</ol>
|
||
<p>為了防止重複走訪頂點，我們需要藉助一個雜湊表 <code>visited</code> 來記錄哪些節點已被訪問。</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><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" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_bfs.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span> <span class="nf">graph_bfs</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span> <span class="n">GraphAdjList</span><span class="p">,</span> <span class="n">start_vet</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">)</span> <span class="o">-></span> <span class="nb">list</span><span class="p">[</span><span class="n">Vertex</span><span class="p">]:</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w"> </span><span class="sd">"""廣度優先走訪"""</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="c1"># 使用鄰接表來表示圖，以便獲取指定頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="c1"># 頂點走訪序列</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="c1"># 雜湊表，用於記錄已被訪問過的頂點</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="n">visited</span> <span class="o">=</span> <span class="nb">set</span><span class="p">[</span><span class="n">Vertex</span><span class="p">]([</span><span class="n">start_vet</span><span class="p">])</span>
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a> <span class="c1"># 佇列用於實現 BFS</span>
|
||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a> <span class="n">que</span> <span class="o">=</span> <span class="n">deque</span><span class="p">[</span><span class="n">Vertex</span><span class="p">]([</span><span class="n">start_vet</span><span class="p">])</span>
|
||
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a> <span class="c1"># 以頂點 vet 為起點，迴圈直至訪問完所有頂點</span>
|
||
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a> <span class="k">while</span> <span class="nb">len</span><span class="p">(</span><span class="n">que</span><span class="p">)</span> <span class="o">></span> <span class="mi">0</span><span class="p">:</span>
|
||
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a> <span class="n">vet</span> <span class="o">=</span> <span class="n">que</span><span class="o">.</span><span class="n">popleft</span><span class="p">()</span> <span class="c1"># 佇列首頂點出隊</span>
|
||
<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a> <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span> <span class="c1"># 記錄訪問頂點</span>
|
||
<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a> <span class="c1"># 走訪該頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a> <span class="k">for</span> <span class="n">adj_vet</span> <span class="ow">in</span> <span class="n">graph</span><span class="o">.</span><span class="n">adj_list</span><span class="p">[</span><span class="n">vet</span><span class="p">]:</span>
|
||
<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a> <span class="k">if</span> <span class="n">adj_vet</span> <span class="ow">in</span> <span class="n">visited</span><span class="p">:</span>
|
||
<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a> <span class="k">continue</span> <span class="c1"># 跳過已被訪問的頂點</span>
|
||
<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a> <span class="n">que</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">adj_vet</span><span class="p">)</span> <span class="c1"># 只入列未訪問的頂點</span>
|
||
<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a> <span class="n">visited</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">adj_vet</span><span class="p">)</span> <span class="c1"># 標記該頂點已被訪問</span>
|
||
<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a> <span class="c1"># 返回頂點走訪序列</span>
|
||
<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a> <span class="k">return</span> <span class="n">res</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_bfs.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 廣度優先走訪 */</span>
|
||
<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="c1">// 使用鄰接表來表示圖，以便獲取指定頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="n">vector</span><span class="o"><</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="n">graphBFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="o">&</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
|
||
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w"> </span><span class="n">unordered_set</span><span class="o"><</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="n">startVet</span><span class="p">};</span>
|
||
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w"> </span><span class="c1">// 佇列用於實現 BFS</span>
|
||
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w"> </span><span class="n">queue</span><span class="o"><</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="n">que</span><span class="p">;</span>
|
||
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w"> </span><span class="n">que</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">startVet</span><span class="p">);</span>
|
||
<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w"> </span><span class="c1">// 以頂點 vet 為起點，迴圈直至訪問完所有頂點</span>
|
||
<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">que</span><span class="p">.</span><span class="n">empty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">que</span><span class="p">.</span><span class="n">front</span><span class="p">();</span>
|
||
<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w"> </span><span class="n">que</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span><span class="w"> </span><span class="c1">// 佇列首頂點出隊</span>
|
||
<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 記錄訪問頂點</span>
|
||
<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w"> </span><span class="c1">// 走訪該頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">auto</span><span class="w"> </span><span class="n">adjVet</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">graph</span><span class="p">.</span><span class="n">adjList</span><span class="p">[</span><span class="n">vet</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">visited</span><span class="p">.</span><span class="n">count</span><span class="p">(</span><span class="n">adjVet</span><span class="p">))</span>
|
||
<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w"> </span><span class="k">continue</span><span class="p">;</span><span class="w"> </span><span class="c1">// 跳過已被訪問的頂點</span>
|
||
<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w"> </span><span class="n">que</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">adjVet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 只入列未訪問的頂點</span>
|
||
<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w"> </span><span class="n">visited</span><span class="p">.</span><span class="n">emplace</span><span class="p">(</span><span class="n">adjVet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 標記該頂點已被訪問</span>
|
||
<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="w"> </span><span class="c1">// 返回頂點走訪序列</span>
|
||
<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
|
||
<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_bfs.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 廣度優先走訪 */</span>
|
||
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="c1">// 使用鄰接表來表示圖，以便獲取指定頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="n">List</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="nf">graphBFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o"><></span><span class="p">();</span>
|
||
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w"> </span><span class="n">Set</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">HashSet</span><span class="o"><></span><span class="p">();</span>
|
||
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w"> </span><span class="n">visited</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">startVet</span><span class="p">);</span>
|
||
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w"> </span><span class="c1">// 佇列用於實現 BFS</span>
|
||
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w"> </span><span class="n">Queue</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">que</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">LinkedList</span><span class="o"><></span><span class="p">();</span>
|
||
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w"> </span><span class="n">que</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="n">startVet</span><span class="p">);</span>
|
||
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w"> </span><span class="c1">// 以頂點 vet 為起點，迴圈直至訪問完所有頂點</span>
|
||
<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">que</span><span class="p">.</span><span class="na">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">que</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span><span class="w"> </span><span class="c1">// 佇列首頂點出隊</span>
|
||
<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 記錄訪問頂點</span>
|
||
<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w"> </span><span class="c1">// 走訪該頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">adjVet</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">graph</span><span class="p">.</span><span class="na">adjList</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">vet</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">visited</span><span class="p">.</span><span class="na">contains</span><span class="p">(</span><span class="n">adjVet</span><span class="p">))</span>
|
||
<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w"> </span><span class="k">continue</span><span class="p">;</span><span class="w"> </span><span class="c1">// 跳過已被訪問的頂點</span>
|
||
<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w"> </span><span class="n">que</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="n">adjVet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 只入列未訪問的頂點</span>
|
||
<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w"> </span><span class="n">visited</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">adjVet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 標記該頂點已被訪問</span>
|
||
<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="w"> </span><span class="c1">// 返回頂點走訪序列</span>
|
||
<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
|
||
<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_bfs.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 廣度優先走訪 */</span>
|
||
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="c1">// 使用鄰接表來表示圖，以便獲取指定頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="n">List</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">GraphBFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
|
||
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w"> </span><span class="n">HashSet</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="n">startVet</span><span class="p">];</span>
|
||
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w"> </span><span class="c1">// 佇列用於實現 BFS</span>
|
||
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w"> </span><span class="n">Queue</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">que</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">();</span>
|
||
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w"> </span><span class="n">que</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="n">startVet</span><span class="p">);</span>
|
||
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w"> </span><span class="c1">// 以頂點 vet 為起點，迴圈直至訪問完所有頂點</span>
|
||
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">que</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">que</span><span class="p">.</span><span class="n">Dequeue</span><span class="p">();</span><span class="w"> </span><span class="c1">// 佇列首頂點出隊</span>
|
||
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 記錄訪問頂點</span>
|
||
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w"> </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">adjVet</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">graph</span><span class="p">.</span><span class="n">adjList</span><span class="p">[</span><span class="n">vet</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">visited</span><span class="p">.</span><span class="n">Contains</span><span class="p">(</span><span class="n">adjVet</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w"> </span><span class="k">continue</span><span class="p">;</span><span class="w"> </span><span class="c1">// 跳過已被訪問的頂點</span>
|
||
<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w"> </span><span class="n">que</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="n">adjVet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 只入列未訪問的頂點</span>
|
||
<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="w"> </span><span class="n">visited</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">adjVet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 標記該頂點已被訪問</span>
|
||
<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a>
|
||
<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a><span class="w"> </span><span class="c1">// 返回頂點走訪序列</span>
|
||
<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
|
||
<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_bfs.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 廣度優先走訪 */</span>
|
||
<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="c1">// 使用鄰接表來表示圖，以便獲取指定頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="kd">func</span><span class="w"> </span><span class="nx">graphBFS</span><span class="p">(</span><span class="nx">g</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjList</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="w"> </span><span class="nx">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">[]</span><span class="nx">Vertex</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="nx">Vertex</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||
<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w"> </span><span class="nx">visited</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">(</span><span class="kd">map</span><span class="p">[</span><span class="nx">Vertex</span><span class="p">]</span><span class="kd">struct</span><span class="p">{})</span>
|
||
<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w"> </span><span class="nx">visited</span><span class="p">[</span><span class="nx">startVet</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kd">struct</span><span class="p">{}{}</span>
|
||
<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w"> </span><span class="c1">// 佇列用於實現 BFS, 使用切片模擬佇列</span>
|
||
<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w"> </span><span class="nx">queue</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="nx">Vertex</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w"> </span><span class="nx">queue</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">queue</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="p">)</span>
|
||
<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w"> </span><span class="c1">// 以頂點 vet 為起點，迴圈直至訪問完所有頂點</span>
|
||
<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">queue</span><span class="p">)</span><span class="w"> </span><span class="p">></span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w"> </span><span class="c1">// 佇列首頂點出隊</span>
|
||
<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w"> </span><span class="nx">vet</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">queue</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
|
||
<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w"> </span><span class="nx">queue</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">queue</span><span class="p">[</span><span class="mi">1</span><span class="p">:]</span>
|
||
<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w"> </span><span class="c1">// 記錄訪問頂點</span>
|
||
<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">vet</span><span class="p">)</span>
|
||
<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w"> </span><span class="c1">// 走訪該頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">adjVet</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">[</span><span class="nx">vet</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">isExist</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">visited</span><span class="p">[</span><span class="nx">adjVet</span><span class="p">]</span>
|
||
<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w"> </span><span class="c1">// 只入列未訪問的頂點</span>
|
||
<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">!</span><span class="nx">isExist</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a><span class="w"> </span><span class="nx">queue</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">queue</span><span class="p">,</span><span class="w"> </span><span class="nx">adjVet</span><span class="p">)</span>
|
||
<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></a><span class="w"> </span><span class="nx">visited</span><span class="p">[</span><span class="nx">adjVet</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kd">struct</span><span class="p">{}{}</span>
|
||
<a id="__codelineno-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-4-27" name="__codelineno-4-27" href="#__codelineno-4-27"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-4-28" name="__codelineno-4-28" href="#__codelineno-4-28"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-4-29" name="__codelineno-4-29" href="#__codelineno-4-29"></a><span class="w"> </span><span class="c1">// 返回頂點走訪序列</span>
|
||
<a id="__codelineno-4-30" name="__codelineno-4-30" href="#__codelineno-4-30"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span>
|
||
<a id="__codelineno-4-31" name="__codelineno-4-31" href="#__codelineno-4-31"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_bfs.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 廣度優先走訪 */</span>
|
||
<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="c1">// 使用鄰接表來表示圖，以便獲取指定頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="kd">func</span> <span class="nf">graphBFS</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span> <span class="n">GraphAdjList</span><span class="p">,</span> <span class="n">startVet</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">)</span> <span class="p">-></span> <span class="p">[</span><span class="n">Vertex</span><span class="p">]</span> <span class="p">{</span>
|
||
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a> <span class="c1">// 頂點走訪序列</span>
|
||
<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a> <span class="kd">var</span> <span class="nv">res</span><span class="p">:</span> <span class="p">[</span><span class="n">Vertex</span><span class="p">]</span> <span class="p">=</span> <span class="p">[]</span>
|
||
<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a> <span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||
<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a> <span class="kd">var</span> <span class="nv">visited</span><span class="p">:</span> <span class="n">Set</span><span class="p"><</span><span class="n">Vertex</span><span class="p">></span> <span class="p">=</span> <span class="p">[</span><span class="n">startVet</span><span class="p">]</span>
|
||
<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a> <span class="c1">// 佇列用於實現 BFS</span>
|
||
<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a> <span class="kd">var</span> <span class="nv">que</span><span class="p">:</span> <span class="p">[</span><span class="n">Vertex</span><span class="p">]</span> <span class="p">=</span> <span class="p">[</span><span class="n">startVet</span><span class="p">]</span>
|
||
<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a> <span class="c1">// 以頂點 vet 為起點，迴圈直至訪問完所有頂點</span>
|
||
<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a> <span class="k">while</span> <span class="o">!</span><span class="n">que</span><span class="p">.</span><span class="bp">isEmpty</span> <span class="p">{</span>
|
||
<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a> <span class="kd">let</span> <span class="nv">vet</span> <span class="p">=</span> <span class="n">que</span><span class="p">.</span><span class="n">removeFirst</span><span class="p">()</span> <span class="c1">// 佇列首頂點出隊</span>
|
||
<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a> <span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span> <span class="c1">// 記錄訪問頂點</span>
|
||
<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a> <span class="c1">// 走訪該頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a> <span class="k">for</span> <span class="n">adjVet</span> <span class="k">in</span> <span class="n">graph</span><span class="p">.</span><span class="n">adjList</span><span class="p">[</span><span class="n">vet</span><span class="p">]</span> <span class="p">??</span> <span class="p">[]</span> <span class="p">{</span>
|
||
<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a> <span class="k">if</span> <span class="n">visited</span><span class="p">.</span><span class="bp">contains</span><span class="p">(</span><span class="n">adjVet</span><span class="p">)</span> <span class="p">{</span>
|
||
<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a> <span class="k">continue</span> <span class="c1">// 跳過已被訪問的頂點</span>
|
||
<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a> <span class="p">}</span>
|
||
<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a> <span class="n">que</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">adjVet</span><span class="p">)</span> <span class="c1">// 只入列未訪問的頂點</span>
|
||
<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a> <span class="n">visited</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="n">adjVet</span><span class="p">)</span> <span class="c1">// 標記該頂點已被訪問</span>
|
||
<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a> <span class="p">}</span>
|
||
<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a> <span class="p">}</span>
|
||
<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a> <span class="c1">// 返回頂點走訪序列</span>
|
||
<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a> <span class="k">return</span> <span class="n">res</span>
|
||
<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_bfs.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 廣度優先走訪 */</span>
|
||
<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="c1">// 使用鄰接表來表示圖，以便獲取指定頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="kd">function</span><span class="w"> </span><span class="nx">graphBFS</span><span class="p">(</span><span class="nx">graph</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||
<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
|
||
<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||
<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Set</span><span class="p">();</span>
|
||
<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w"> </span><span class="nx">visited</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">startVet</span><span class="p">);</span>
|
||
<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w"> </span><span class="c1">// 佇列用於實現 BFS</span>
|
||
<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">que</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nx">startVet</span><span class="p">];</span>
|
||
<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w"> </span><span class="c1">// 以頂點 vet 為起點，迴圈直至訪問完所有頂點</span>
|
||
<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">que</span><span class="p">.</span><span class="nx">length</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">vet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">que</span><span class="p">.</span><span class="nx">shift</span><span class="p">();</span><span class="w"> </span><span class="c1">// 佇列首頂點出隊</span>
|
||
<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 記錄訪問頂點</span>
|
||
<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w"> </span><span class="c1">// 走訪該頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">adjVet</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">graph</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">vet</span><span class="p">)</span><span class="w"> </span><span class="o">??</span><span class="w"> </span><span class="p">[])</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">visited</span><span class="p">.</span><span class="nx">has</span><span class="p">(</span><span class="nx">adjVet</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w"> </span><span class="k">continue</span><span class="p">;</span><span class="w"> </span><span class="c1">// 跳過已被訪問的頂點</span>
|
||
<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="w"> </span><span class="nx">que</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">adjVet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 只入列未訪問的頂點</span>
|
||
<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="w"> </span><span class="nx">visited</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">adjVet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 標記該頂點已被訪問</span>
|
||
<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-6-24" name="__codelineno-6-24" href="#__codelineno-6-24"></a><span class="w"> </span><span class="c1">// 返回頂點走訪序列</span>
|
||
<a id="__codelineno-6-25" name="__codelineno-6-25" href="#__codelineno-6-25"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
|
||
<a id="__codelineno-6-26" name="__codelineno-6-26" href="#__codelineno-6-26"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_bfs.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 廣度優先走訪 */</span>
|
||
<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="c1">// 使用鄰接表來表示圖，以便獲取指定頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="kd">function</span><span class="w"> </span><span class="nx">graphBFS</span><span class="p">(</span><span class="nx">graph</span><span class="o">:</span><span class="w"> </span><span class="kt">GraphAdjList</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="o">:</span><span class="w"> </span><span class="kt">Vertex</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="nx">Vertex</span><span class="p">[]</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||
<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">Vertex</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
|
||
<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||
<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">visited</span><span class="o">:</span><span class="w"> </span><span class="kt">Set</span><span class="o"><</span><span class="nx">Vertex</span><span class="o">></span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Set</span><span class="p">();</span>
|
||
<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w"> </span><span class="nx">visited</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">startVet</span><span class="p">);</span>
|
||
<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w"> </span><span class="c1">// 佇列用於實現 BFS</span>
|
||
<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">que</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nx">startVet</span><span class="p">];</span>
|
||
<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w"> </span><span class="c1">// 以頂點 vet 為起點，迴圈直至訪問完所有頂點</span>
|
||
<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">que</span><span class="p">.</span><span class="nx">length</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">vet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">que</span><span class="p">.</span><span class="nx">shift</span><span class="p">();</span><span class="w"> </span><span class="c1">// 佇列首頂點出隊</span>
|
||
<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 記錄訪問頂點</span>
|
||
<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w"> </span><span class="c1">// 走訪該頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">adjVet</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">graph</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">vet</span><span class="p">)</span><span class="w"> </span><span class="o">??</span><span class="w"> </span><span class="p">[])</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">visited</span><span class="p">.</span><span class="nx">has</span><span class="p">(</span><span class="nx">adjVet</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w"> </span><span class="k">continue</span><span class="p">;</span><span class="w"> </span><span class="c1">// 跳過已被訪問的頂點</span>
|
||
<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="w"> </span><span class="nx">que</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">adjVet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 只入列未訪問</span>
|
||
<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="w"> </span><span class="nx">visited</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">adjVet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 標記該頂點已被訪問</span>
|
||
<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></a><span class="w"> </span><span class="c1">// 返回頂點走訪序列</span>
|
||
<a id="__codelineno-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
|
||
<a id="__codelineno-7-26" name="__codelineno-7-26" href="#__codelineno-7-26"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_bfs.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 廣度優先走訪 */</span>
|
||
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="n">List</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">graphBFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w"> </span><span class="c1">// 使用鄰接表來表示圖，以便獲取指定頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
|
||
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w"> </span><span class="n">Set</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{};</span>
|
||
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w"> </span><span class="n">visited</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">startVet</span><span class="p">);</span>
|
||
<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w"> </span><span class="c1">// 佇列用於實現 BFS</span>
|
||
<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w"> </span><span class="n">Queue</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">que</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Queue</span><span class="p">();</span>
|
||
<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w"> </span><span class="n">que</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">startVet</span><span class="p">);</span>
|
||
<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w"> </span><span class="c1">// 以頂點 vet 為起點，迴圈直至訪問完所有頂點</span>
|
||
<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">que</span><span class="p">.</span><span class="n">isNotEmpty</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">que</span><span class="p">.</span><span class="n">removeFirst</span><span class="p">();</span><span class="w"> </span><span class="c1">// 佇列首頂點出隊</span>
|
||
<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 記錄訪問頂點</span>
|
||
<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w"> </span><span class="c1">// 走訪該頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">adjVet</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">graph</span><span class="p">.</span><span class="n">adjList</span><span class="p">[</span><span class="n">vet</span><span class="p">]</span><span class="o">!</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">visited</span><span class="p">.</span><span class="n">contains</span><span class="p">(</span><span class="n">adjVet</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="w"> </span><span class="k">continue</span><span class="p">;</span><span class="w"> </span><span class="c1">// 跳過已被訪問的頂點</span>
|
||
<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="w"> </span><span class="n">que</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">adjVet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 只入列未訪問的頂點</span>
|
||
<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a><span class="w"> </span><span class="n">visited</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">adjVet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 標記該頂點已被訪問</span>
|
||
<a id="__codelineno-8-23" name="__codelineno-8-23" href="#__codelineno-8-23"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-8-24" name="__codelineno-8-24" href="#__codelineno-8-24"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-8-25" name="__codelineno-8-25" href="#__codelineno-8-25"></a><span class="w"> </span><span class="c1">// 返回頂點走訪序列</span>
|
||
<a id="__codelineno-8-26" name="__codelineno-8-26" href="#__codelineno-8-26"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
|
||
<a id="__codelineno-8-27" name="__codelineno-8-27" href="#__codelineno-8-27"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_bfs.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 廣度優先走訪 */</span>
|
||
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="c1">// 使用鄰接表來表示圖，以便獲取指定頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="k">fn</span> <span class="nf">graph_bfs</span><span class="p">(</span><span class="n">graph</span>: <span class="nc">GraphAdjList</span><span class="p">,</span><span class="w"> </span><span class="n">start_vet</span>: <span class="nc">Vertex</span><span class="p">)</span><span class="w"> </span>-> <span class="nb">Vec</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||
<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[];</span>
|
||
<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||
<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashSet</span>::<span class="n">new</span><span class="p">();</span>
|
||
<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w"> </span><span class="n">visited</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="n">start_vet</span><span class="p">);</span>
|
||
<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w"> </span><span class="c1">// 佇列用於實現 BFS</span>
|
||
<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">que</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">VecDeque</span>::<span class="n">new</span><span class="p">();</span>
|
||
<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w"> </span><span class="n">que</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">start_vet</span><span class="p">);</span>
|
||
<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w"> </span><span class="c1">// 以頂點 vet 為起點，迴圈直至訪問完所有頂點</span>
|
||
<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="o">!</span><span class="n">que</span><span class="p">.</span><span class="n">is_empty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">vet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">que</span><span class="p">.</span><span class="n">pop_front</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span><span class="w"> </span><span class="c1">// 佇列首頂點出隊</span>
|
||
<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 記錄訪問頂點</span>
|
||
<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a>
|
||
<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w"> </span><span class="c1">// 走訪該頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">adj_vets</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">graph</span><span class="p">.</span><span class="n">adj_list</span><span class="p">.</span><span class="n">get</span><span class="p">(</span><span class="o">&</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="o">&</span><span class="n">adj_vet</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">adj_vets</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">visited</span><span class="p">.</span><span class="n">contains</span><span class="p">(</span><span class="o">&</span><span class="n">adj_vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="w"> </span><span class="k">continue</span><span class="p">;</span><span class="w"> </span><span class="c1">// 跳過已被訪問的頂點</span>
|
||
<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="w"> </span><span class="n">que</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">adj_vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 只入列未訪問的頂點</span>
|
||
<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a><span class="w"> </span><span class="n">visited</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="n">adj_vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 標記該頂點已被訪問</span>
|
||
<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-9-27" name="__codelineno-9-27" href="#__codelineno-9-27"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-9-28" name="__codelineno-9-28" href="#__codelineno-9-28"></a><span class="w"> </span><span class="c1">// 返回頂點走訪序列</span>
|
||
<a id="__codelineno-9-29" name="__codelineno-9-29" href="#__codelineno-9-29"></a><span class="w"> </span><span class="n">res</span>
|
||
<a id="__codelineno-9-30" name="__codelineno-9-30" href="#__codelineno-9-30"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_bfs.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 節點佇列結構體 */</span>
|
||
<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vertices</span><span class="p">[</span><span class="n">MAX_SIZE</span><span class="p">];</span>
|
||
<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">front</span><span class="p">,</span><span class="w"> </span><span class="n">rear</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="p">;</span>
|
||
<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="p">}</span><span class="w"> </span><span class="n">Queue</span><span class="p">;</span>
|
||
<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a>
|
||
<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="cm">/* 建構子 */</span>
|
||
<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="n">Queue</span><span class="w"> </span><span class="o">*</span><span class="nf">newQueue</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w"> </span><span class="n">Queue</span><span class="w"> </span><span class="o">*</span><span class="n">q</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">Queue</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">Queue</span><span class="p">));</span>
|
||
<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w"> </span><span class="n">q</span><span class="o">-></span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">q</span><span class="o">-></span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">q</span><span class="o">-></span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">q</span><span class="p">;</span>
|
||
<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="p">}</span>
|
||
<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a>
|
||
<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="cm">/* 判斷佇列是否為空 */</span>
|
||
<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="kt">int</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">(</span><span class="n">Queue</span><span class="w"> </span><span class="o">*</span><span class="n">q</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">q</span><span class="o">-></span><span class="n">size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="p">}</span>
|
||
<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a>
|
||
<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="cm">/* 入列操作 */</span>
|
||
<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a><span class="kt">void</span><span class="w"> </span><span class="nf">enqueue</span><span class="p">(</span><span class="n">Queue</span><span class="w"> </span><span class="o">*</span><span class="n">q</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a><span class="w"> </span><span class="n">q</span><span class="o">-></span><span class="n">vertices</span><span class="p">[</span><span class="n">q</span><span class="o">-></span><span class="n">rear</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vet</span><span class="p">;</span>
|
||
<a id="__codelineno-10-22" name="__codelineno-10-22" href="#__codelineno-10-22"></a><span class="w"> </span><span class="n">q</span><span class="o">-></span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">q</span><span class="o">-></span><span class="n">rear</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="p">;</span>
|
||
<a id="__codelineno-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="w"> </span><span class="n">q</span><span class="o">-></span><span class="n">size</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a><span class="p">}</span>
|
||
<a id="__codelineno-10-25" name="__codelineno-10-25" href="#__codelineno-10-25"></a>
|
||
<a id="__codelineno-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></a><span class="cm">/* 出列操作 */</span>
|
||
<a id="__codelineno-10-27" name="__codelineno-10-27" href="#__codelineno-10-27"></a><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="nf">dequeue</span><span class="p">(</span><span class="n">Queue</span><span class="w"> </span><span class="o">*</span><span class="n">q</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-10-28" name="__codelineno-10-28" href="#__codelineno-10-28"></a><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">q</span><span class="o">-></span><span class="n">vertices</span><span class="p">[</span><span class="n">q</span><span class="o">-></span><span class="n">front</span><span class="p">];</span>
|
||
<a id="__codelineno-10-29" name="__codelineno-10-29" href="#__codelineno-10-29"></a><span class="w"> </span><span class="n">q</span><span class="o">-></span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">q</span><span class="o">-></span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="p">;</span>
|
||
<a id="__codelineno-10-30" name="__codelineno-10-30" href="#__codelineno-10-30"></a><span class="w"> </span><span class="n">q</span><span class="o">-></span><span class="n">size</span><span class="o">--</span><span class="p">;</span>
|
||
<a id="__codelineno-10-31" name="__codelineno-10-31" href="#__codelineno-10-31"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">vet</span><span class="p">;</span>
|
||
<a id="__codelineno-10-32" name="__codelineno-10-32" href="#__codelineno-10-32"></a><span class="p">}</span>
|
||
<a id="__codelineno-10-33" name="__codelineno-10-33" href="#__codelineno-10-33"></a>
|
||
<a id="__codelineno-10-34" name="__codelineno-10-34" href="#__codelineno-10-34"></a><span class="cm">/* 檢查頂點是否已被訪問 */</span>
|
||
<a id="__codelineno-10-35" name="__codelineno-10-35" href="#__codelineno-10-35"></a><span class="kt">int</span><span class="w"> </span><span class="nf">isVisited</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="o">**</span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-10-36" name="__codelineno-10-36" href="#__codelineno-10-36"></a><span class="w"> </span><span class="c1">// 走訪查詢節點，使用 O(n) 時間</span>
|
||
<a id="__codelineno-10-37" name="__codelineno-10-37" href="#__codelineno-10-37"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-10-38" name="__codelineno-10-38" href="#__codelineno-10-38"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">visited</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">vet</span><span class="p">)</span>
|
||
<a id="__codelineno-10-39" name="__codelineno-10-39" href="#__codelineno-10-39"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-10-40" name="__codelineno-10-40" href="#__codelineno-10-40"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-10-41" name="__codelineno-10-41" href="#__codelineno-10-41"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-10-42" name="__codelineno-10-42" href="#__codelineno-10-42"></a><span class="p">}</span>
|
||
<a id="__codelineno-10-43" name="__codelineno-10-43" href="#__codelineno-10-43"></a>
|
||
<a id="__codelineno-10-44" name="__codelineno-10-44" href="#__codelineno-10-44"></a><span class="cm">/* 廣度優先走訪 */</span>
|
||
<a id="__codelineno-10-45" name="__codelineno-10-45" href="#__codelineno-10-45"></a><span class="c1">// 使用鄰接表來表示圖，以便獲取指定頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-10-46" name="__codelineno-10-46" href="#__codelineno-10-46"></a><span class="kt">void</span><span class="w"> </span><span class="nf">graphBFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="o">*</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">startVet</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">**</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">resSize</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">**</span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">visitedSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-10-47" name="__codelineno-10-47" href="#__codelineno-10-47"></a><span class="w"> </span><span class="c1">// 佇列用於實現 BFS</span>
|
||
<a id="__codelineno-10-48" name="__codelineno-10-48" href="#__codelineno-10-48"></a><span class="w"> </span><span class="n">Queue</span><span class="w"> </span><span class="o">*</span><span class="n">queue</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newQueue</span><span class="p">();</span>
|
||
<a id="__codelineno-10-49" name="__codelineno-10-49" href="#__codelineno-10-49"></a><span class="w"> </span><span class="n">enqueue</span><span class="p">(</span><span class="n">queue</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">);</span>
|
||
<a id="__codelineno-10-50" name="__codelineno-10-50" href="#__codelineno-10-50"></a><span class="w"> </span><span class="n">visited</span><span class="p">[(</span><span class="o">*</span><span class="n">visitedSize</span><span class="p">)</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">startVet</span><span class="p">;</span>
|
||
<a id="__codelineno-10-51" name="__codelineno-10-51" href="#__codelineno-10-51"></a><span class="w"> </span><span class="c1">// 以頂點 vet 為起點，迴圈直至訪問完所有頂點</span>
|
||
<a id="__codelineno-10-52" name="__codelineno-10-52" href="#__codelineno-10-52"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">isEmpty</span><span class="p">(</span><span class="n">queue</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-10-53" name="__codelineno-10-53" href="#__codelineno-10-53"></a><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dequeue</span><span class="p">(</span><span class="n">queue</span><span class="p">);</span><span class="w"> </span><span class="c1">// 佇列首頂點出隊</span>
|
||
<a id="__codelineno-10-54" name="__codelineno-10-54" href="#__codelineno-10-54"></a><span class="w"> </span><span class="n">res</span><span class="p">[(</span><span class="o">*</span><span class="n">resSize</span><span class="p">)</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vet</span><span class="p">;</span><span class="w"> </span><span class="c1">// 記錄訪問頂點</span>
|
||
<a id="__codelineno-10-55" name="__codelineno-10-55" href="#__codelineno-10-55"></a><span class="w"> </span><span class="c1">// 走訪該頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-10-56" name="__codelineno-10-56" href="#__codelineno-10-56"></a><span class="w"> </span><span class="n">AdjListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findNode</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">vet</span><span class="p">);</span>
|
||
<a id="__codelineno-10-57" name="__codelineno-10-57" href="#__codelineno-10-57"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-10-58" name="__codelineno-10-58" href="#__codelineno-10-58"></a><span class="w"> </span><span class="c1">// 跳過已被訪問的頂點</span>
|
||
<a id="__codelineno-10-59" name="__codelineno-10-59" href="#__codelineno-10-59"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">isVisited</span><span class="p">(</span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">visitedSize</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">vertex</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-10-60" name="__codelineno-10-60" href="#__codelineno-10-60"></a><span class="w"> </span><span class="n">enqueue</span><span class="p">(</span><span class="n">queue</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">vertex</span><span class="p">);</span><span class="w"> </span><span class="c1">// 只入列未訪問的頂點</span>
|
||
<a id="__codelineno-10-61" name="__codelineno-10-61" href="#__codelineno-10-61"></a><span class="w"> </span><span class="n">visited</span><span class="p">[(</span><span class="o">*</span><span class="n">visitedSize</span><span class="p">)</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">vertex</span><span class="p">;</span><span class="w"> </span><span class="c1">// 標記該頂點已被訪問</span>
|
||
<a id="__codelineno-10-62" name="__codelineno-10-62" href="#__codelineno-10-62"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-10-63" name="__codelineno-10-63" href="#__codelineno-10-63"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">next</span><span class="p">;</span>
|
||
<a id="__codelineno-10-64" name="__codelineno-10-64" href="#__codelineno-10-64"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-10-65" name="__codelineno-10-65" href="#__codelineno-10-65"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-10-66" name="__codelineno-10-66" href="#__codelineno-10-66"></a><span class="w"> </span><span class="c1">// 釋放記憶體</span>
|
||
<a id="__codelineno-10-67" name="__codelineno-10-67" href="#__codelineno-10-67"></a><span class="w"> </span><span class="n">free</span><span class="p">(</span><span class="n">queue</span><span class="p">);</span>
|
||
<a id="__codelineno-10-68" name="__codelineno-10-68" href="#__codelineno-10-68"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_bfs.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 廣度優先走訪 */</span>
|
||
<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="c1">// 使用鄰接表來表示圖，以便獲取指定頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">graphBFS</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span><span class="w"> </span><span class="n">GraphAdjList</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">:</span><span class="w"> </span><span class="n">Vertex</span><span class="p">):</span><span class="w"> </span><span class="n">MutableList</span><span class="o"><</span><span class="n">Vertex?></span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||
<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o"><</span><span class="n">Vertex?></span><span class="p">()</span>
|
||
<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||
<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashSet</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="p">()</span>
|
||
<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w"> </span><span class="n">visited</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">startVet</span><span class="p">)</span>
|
||
<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w"> </span><span class="c1">// 佇列用於實現 BFS</span>
|
||
<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">que</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">LinkedList</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="p">()</span>
|
||
<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w"> </span><span class="n">que</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="n">startVet</span><span class="p">)</span>
|
||
<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w"> </span><span class="c1">// 以頂點 vet 為起點，迴圈直至訪問完所有頂點</span>
|
||
<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">que</span><span class="p">.</span><span class="na">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">vet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">que</span><span class="p">.</span><span class="na">poll</span><span class="p">()</span><span class="w"> </span><span class="c1">// 佇列首頂點出隊</span>
|
||
<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="c1">// 記錄訪問頂點</span>
|
||
<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w"> </span><span class="c1">// 走訪該頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">adjVet</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">graph</span><span class="p">.</span><span class="na">adjList</span><span class="o">[</span><span class="n">vet</span><span class="o">]!!</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">visited</span><span class="p">.</span><span class="na">contains</span><span class="p">(</span><span class="n">adjVet</span><span class="p">))</span>
|
||
<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="w"> </span><span class="k">continue</span><span class="w"> </span><span class="c1">// 跳過已被訪問的頂點</span>
|
||
<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="w"> </span><span class="n">que</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="n">adjVet</span><span class="p">)</span><span class="w"> </span><span class="c1">// 只入列未訪問的頂點</span>
|
||
<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="w"> </span><span class="n">visited</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">adjVet</span><span class="p">)</span><span class="w"> </span><span class="c1">// 標記該頂點已被訪問</span>
|
||
<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a><span class="w"> </span><span class="c1">// 返回頂點走訪序列</span>
|
||
<a id="__codelineno-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
|
||
<a id="__codelineno-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_bfs.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">graph_bfs</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_bfs.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">graphBFS</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<details class="pythontutor">
|
||
<summary>視覺化執行</summary>
|
||
<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=from%20collections%20import%20deque%0A%0Aclass%20Vertex%3A%0A%20%20%20%20%22%22%22%E9%A0%82%E9%BB%9E%E9%A1%9E%E5%88%A5%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%20%3D%20val%0A%0Adef%20vals_to_vets%28vals%3A%20list%5Bint%5D%29%20-%3E%20list%5B%22Vertex%22%5D%3A%0A%20%20%20%20%22%22%22%E8%BC%B8%E5%85%A5%E5%80%BC%E4%B8%B2%E5%88%97%20vals%20%EF%BC%8C%E8%BF%94%E5%9B%9E%E9%A0%82%E9%BB%9E%E4%B8%B2%E5%88%97%20vets%22%22%22%0A%20%20%20%20return%20%5BVertex%28val%29%20for%20val%20in%20vals%5D%0A%0Aclass%20GraphAdjList%3A%0A%20%20%20%20%22%22%22%E5%9F%BA%E6%96%BC%E9%84%B0%E6%8E%A5%E8%A1%A8%E5%AF%A6%E7%8F%BE%E7%9A%84%E7%84%A1%E5%90%91%E5%9C%96%E9%A1%9E%E5%88%A5%22%22%22%0A%0A%20%20%20%20def%20__init__%28self%2C%20edges%3A%20list%5Blist%5BVertex%5D%5D%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%BB%BA%E6%A7%8B%E5%AD%90%22%22%22%0A%20%20%20%20%20%20%20%20self.adj_list%20%3D%20dict%5BVertex%2C%20list%5BVertex%5D%5D%28%29%0A%20%20%20%20%20%20%20%20for%20edge%20in%20edges%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self.add_vertex%28edge%5B0%5D%29%0A%20%20%20%20%20%20%20%20%20%20%20%20self.add_vertex%28edge%5B1%5D%29%0A%20%20%20%20%20%20%20%20%20%20%20%20self.add_edge%28edge%5B0%5D%2C%20edge%5B1%5D%29%0A%0A%20%20%20%20def%20add_edge%28self%2C%20vet1%3A%20Vertex%2C%20vet2%3A%20Vertex%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E6%96%B0%E5%A2%9E%E9%82%8A%22%22%22%0A%20%20%20%20%20%20%20%20if%20vet1%20not%20in%20self.adj_list%20or%20vet2%20not%20in%20self.adj_list%20or%20vet1%20%3D%3D%20vet2%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20ValueError%28%29%0A%20%20%20%20%20%20%20%20self.adj_list%5Bvet1%5D.append%28vet2%29%0A%20%20%20%20%20%20%20%20self.adj_list%5Bvet2%5D.append%28vet1%29%0A%0A%20%20%20%20def%20add_vertex%28self%2C%20vet%3A%20Vertex%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E6%96%B0%E5%A2%9E%E9%A0%82%E9%BB%9E%22%22%22%0A%20%20%20%20%20%20%20%20if%20vet%20in%20self.adj_list%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%0A%20%20%20%20%20%20%20%20self.adj_list%5Bvet%5D%20%3D%20%5B%5D%0A%0A%0Adef%20graph_bfs%28graph%3A%20GraphAdjList%2C%20start_vet%3A%20Vertex%29%20-%3E%20list%5BVertex%5D%3A%0A%20%20%20%20%22%22%22%E5%BB%A3%E5%BA%A6%E5%84%AA%E5%85%88%E8%B5%B0%E8%A8%AA%22%22%22%0A%20%20%20%20%23%20%E9%A0%82%E9%BB%9E%E8%B5%B0%E8%A8%AA%E5%BA%8F%E5%88%97%0A%20%20%20%20res%20%3D%20%5B%5D%0A%20%20%20%20%23%20%E9%9B%9C%E6%B9%8A%E8%A1%A8%EF%BC%8C%E7%94%A8%E6%96%BC%E8%A8%98%E9%8C%84%E5%B7%B2%E8%A2%AB%E8%A8%AA%E5%95%8F%E9%81%8E%E7%9A%84%E9%A0%82%E9%BB%9E%0A%20%20%20%20visited%20%3D%20set%5BVertex%5D%28%5Bstart_vet%5D%29%0A%20%20%20%20%23%20%E4%BD%87%E5%88%97%E7%94%A8%E6%96%BC%E5%AF%A6%E7%8F%BE%20BFS%0A%20%20%20%20que%20%3D%20deque%5BVertex%5D%28%5Bstart_vet%5D%29%0A%20%20%20%20%23%20%E4%BB%A5%E9%A0%82%E9%BB%9E%20vet%20%E7%82%BA%E8%B5%B7%E9%BB%9E%EF%BC%8C%E8%BF%B4%E5%9C%88%E7%9B%B4%E8%87%B3%E8%A8%AA%E5%95%8F%E5%AE%8C%E6%89%80%E6%9C%89%E9%A0%82%E9%BB%9E%0A%20%20%20%20while%20len%28que%29%20%3E%200%3A%0A%20%20%20%20%20%20%20%20vet%20%3D%20que.popleft%28%29%20%20%23%20%E4%BD%87%E5%88%97%E9%A6%96%E9%A0%82%E9%BB%9E%E5%87%BA%E9%9A%8A%0A%20%20%20%20%20%20%20%20res.append%28vet%29%20%20%23%20%E8%A8%98%E9%8C%84%E8%A8%AA%E5%95%8F%E9%A0%82%E9%BB%9E%0A%20%20%20%20%20%20%20%20%23%20%E8%B5%B0%E8%A8%AA%E8%A9%B2%E9%A0%82%E9%BB%9E%E7%9A%84%E6%89%80%E6%9C%89%E9%84%B0%E6%8E%A5%E9%A0%82%E9%BB%9E%0A%20%20%20%20%20%20%20%20for%20adj_vet%20in%20graph.adj_list%5Bvet%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20adj_vet%20in%20visited%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20continue%20%20%23%20%E8%B7%B3%E9%81%8E%E5%B7%B2%E8%A2%AB%E8%A8%AA%E5%95%8F%E7%9A%84%E9%A0%82%E9%BB%9E%0A%20%20%20%20%20%20%20%20%20%20%20%20que.append%28adj_vet%29%20%20%23%20%E5%8F%AA%E5%85%A5%E5%88%97%E6%9C%AA%E8%A8%AA%E5%95%8F%E7%9A%84%E9%A0%82%E9%BB%9E%0A%20%20%20%20%20%20%20%20%20%20%20%20visited.add%28adj_vet%29%20%20%23%20%E6%A8%99%E8%A8%98%E8%A9%B2%E9%A0%82%E9%BB%9E%E5%B7%B2%E8%A2%AB%E8%A8%AA%E5%95%8F%0A%20%20%20%20%23%20%E8%BF%94%E5%9B%9E%E9%A0%82%E9%BB%9E%E8%B5%B0%E8%A8%AA%E5%BA%8F%E5%88%97%0A%20%20%20%20return%20res%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E7%84%A1%E5%90%91%E5%9C%96%0A%20%20%20%20v%20%3D%20vals_to_vets%28%5B0%2C%201%2C%202%2C%203%2C%204%5D%29%0A%20%20%20%20edges%20%3D%20%5B%0A%20%20%20%20%20%20%20%20%5Bv%5B0%5D%2C%20v%5B1%5D%5D%2C%0A%20%20%20%20%20%20%20%20%5Bv%5B0%5D%2C%20v%5B3%5D%5D%2C%0A%20%20%20%20%20%20%20%20%5Bv%5B1%5D%2C%20v%5B2%5D%5D%2C%0A%20%20%20%20%20%20%20%20%5Bv%5B1%5D%2C%20v%5B4%5D%5D%2C%0A%20%20%20%20%20%20%20%20%5Bv%5B3%5D%2C%20v%5B4%5D%5D%2C%0A%20%20%20%20%5D%0A%20%20%20%20graph%20%3D%20GraphAdjList%28edges%29%0A%20%20%20%20del%20edges%0A%0A%20%20%20%20%23%20%E5%BB%A3%E5%BA%A6%E5%84%AA%E5%85%88%E8%B5%B0%E8%A8%AA%0A%20%20%20%20res%20%3D%20graph_bfs%28graph%2C%20v%5B0%5D%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=131&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
|
||
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=from%20collections%20import%20deque%0A%0Aclass%20Vertex%3A%0A%20%20%20%20%22%22%22%E9%A0%82%E9%BB%9E%E9%A1%9E%E5%88%A5%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%20%3D%20val%0A%0Adef%20vals_to_vets%28vals%3A%20list%5Bint%5D%29%20-%3E%20list%5B%22Vertex%22%5D%3A%0A%20%20%20%20%22%22%22%E8%BC%B8%E5%85%A5%E5%80%BC%E4%B8%B2%E5%88%97%20vals%20%EF%BC%8C%E8%BF%94%E5%9B%9E%E9%A0%82%E9%BB%9E%E4%B8%B2%E5%88%97%20vets%22%22%22%0A%20%20%20%20return%20%5BVertex%28val%29%20for%20val%20in%20vals%5D%0A%0Aclass%20GraphAdjList%3A%0A%20%20%20%20%22%22%22%E5%9F%BA%E6%96%BC%E9%84%B0%E6%8E%A5%E8%A1%A8%E5%AF%A6%E7%8F%BE%E7%9A%84%E7%84%A1%E5%90%91%E5%9C%96%E9%A1%9E%E5%88%A5%22%22%22%0A%0A%20%20%20%20def%20__init__%28self%2C%20edges%3A%20list%5Blist%5BVertex%5D%5D%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%BB%BA%E6%A7%8B%E5%AD%90%22%22%22%0A%20%20%20%20%20%20%20%20self.adj_list%20%3D%20dict%5BVertex%2C%20list%5BVertex%5D%5D%28%29%0A%20%20%20%20%20%20%20%20for%20edge%20in%20edges%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self.add_vertex%28edge%5B0%5D%29%0A%20%20%20%20%20%20%20%20%20%20%20%20self.add_vertex%28edge%5B1%5D%29%0A%20%20%20%20%20%20%20%20%20%20%20%20self.add_edge%28edge%5B0%5D%2C%20edge%5B1%5D%29%0A%0A%20%20%20%20def%20add_edge%28self%2C%20vet1%3A%20Vertex%2C%20vet2%3A%20Vertex%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E6%96%B0%E5%A2%9E%E9%82%8A%22%22%22%0A%20%20%20%20%20%20%20%20if%20vet1%20not%20in%20self.adj_list%20or%20vet2%20not%20in%20self.adj_list%20or%20vet1%20%3D%3D%20vet2%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20ValueError%28%29%0A%20%20%20%20%20%20%20%20self.adj_list%5Bvet1%5D.append%28vet2%29%0A%20%20%20%20%20%20%20%20self.adj_list%5Bvet2%5D.append%28vet1%29%0A%0A%20%20%20%20def%20add_vertex%28self%2C%20vet%3A%20Vertex%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E6%96%B0%E5%A2%9E%E9%A0%82%E9%BB%9E%22%22%22%0A%20%20%20%20%20%20%20%20if%20vet%20in%20self.adj_list%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%0A%20%20%20%20%20%20%20%20self.adj_list%5Bvet%5D%20%3D%20%5B%5D%0A%0A%0Adef%20graph_bfs%28graph%3A%20GraphAdjList%2C%20start_vet%3A%20Vertex%29%20-%3E%20list%5BVertex%5D%3A%0A%20%20%20%20%22%22%22%E5%BB%A3%E5%BA%A6%E5%84%AA%E5%85%88%E8%B5%B0%E8%A8%AA%22%22%22%0A%20%20%20%20%23%20%E9%A0%82%E9%BB%9E%E8%B5%B0%E8%A8%AA%E5%BA%8F%E5%88%97%0A%20%20%20%20res%20%3D%20%5B%5D%0A%20%20%20%20%23%20%E9%9B%9C%E6%B9%8A%E8%A1%A8%EF%BC%8C%E7%94%A8%E6%96%BC%E8%A8%98%E9%8C%84%E5%B7%B2%E8%A2%AB%E8%A8%AA%E5%95%8F%E9%81%8E%E7%9A%84%E9%A0%82%E9%BB%9E%0A%20%20%20%20visited%20%3D%20set%5BVertex%5D%28%5Bstart_vet%5D%29%0A%20%20%20%20%23%20%E4%BD%87%E5%88%97%E7%94%A8%E6%96%BC%E5%AF%A6%E7%8F%BE%20BFS%0A%20%20%20%20que%20%3D%20deque%5BVertex%5D%28%5Bstart_vet%5D%29%0A%20%20%20%20%23%20%E4%BB%A5%E9%A0%82%E9%BB%9E%20vet%20%E7%82%BA%E8%B5%B7%E9%BB%9E%EF%BC%8C%E8%BF%B4%E5%9C%88%E7%9B%B4%E8%87%B3%E8%A8%AA%E5%95%8F%E5%AE%8C%E6%89%80%E6%9C%89%E9%A0%82%E9%BB%9E%0A%20%20%20%20while%20len%28que%29%20%3E%200%3A%0A%20%20%20%20%20%20%20%20vet%20%3D%20que.popleft%28%29%20%20%23%20%E4%BD%87%E5%88%97%E9%A6%96%E9%A0%82%E9%BB%9E%E5%87%BA%E9%9A%8A%0A%20%20%20%20%20%20%20%20res.append%28vet%29%20%20%23%20%E8%A8%98%E9%8C%84%E8%A8%AA%E5%95%8F%E9%A0%82%E9%BB%9E%0A%20%20%20%20%20%20%20%20%23%20%E8%B5%B0%E8%A8%AA%E8%A9%B2%E9%A0%82%E9%BB%9E%E7%9A%84%E6%89%80%E6%9C%89%E9%84%B0%E6%8E%A5%E9%A0%82%E9%BB%9E%0A%20%20%20%20%20%20%20%20for%20adj_vet%20in%20graph.adj_list%5Bvet%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20adj_vet%20in%20visited%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20continue%20%20%23%20%E8%B7%B3%E9%81%8E%E5%B7%B2%E8%A2%AB%E8%A8%AA%E5%95%8F%E7%9A%84%E9%A0%82%E9%BB%9E%0A%20%20%20%20%20%20%20%20%20%20%20%20que.append%28adj_vet%29%20%20%23%20%E5%8F%AA%E5%85%A5%E5%88%97%E6%9C%AA%E8%A8%AA%E5%95%8F%E7%9A%84%E9%A0%82%E9%BB%9E%0A%20%20%20%20%20%20%20%20%20%20%20%20visited.add%28adj_vet%29%20%20%23%20%E6%A8%99%E8%A8%98%E8%A9%B2%E9%A0%82%E9%BB%9E%E5%B7%B2%E8%A2%AB%E8%A8%AA%E5%95%8F%0A%20%20%20%20%23%20%E8%BF%94%E5%9B%9E%E9%A0%82%E9%BB%9E%E8%B5%B0%E8%A8%AA%E5%BA%8F%E5%88%97%0A%20%20%20%20return%20res%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E7%84%A1%E5%90%91%E5%9C%96%0A%20%20%20%20v%20%3D%20vals_to_vets%28%5B0%2C%201%2C%202%2C%203%2C%204%5D%29%0A%20%20%20%20edges%20%3D%20%5B%0A%20%20%20%20%20%20%20%20%5Bv%5B0%5D%2C%20v%5B1%5D%5D%2C%0A%20%20%20%20%20%20%20%20%5Bv%5B0%5D%2C%20v%5B3%5D%5D%2C%0A%20%20%20%20%20%20%20%20%5Bv%5B1%5D%2C%20v%5B2%5D%5D%2C%0A%20%20%20%20%20%20%20%20%5Bv%5B1%5D%2C%20v%5B4%5D%5D%2C%0A%20%20%20%20%20%20%20%20%5Bv%5B3%5D%2C%20v%5B4%5D%5D%2C%0A%20%20%20%20%5D%0A%20%20%20%20graph%20%3D%20GraphAdjList%28edges%29%0A%20%20%20%20del%20edges%0A%0A%20%20%20%20%23%20%E5%BB%A3%E5%BA%A6%E5%84%AA%E5%85%88%E8%B5%B0%E8%A8%AA%0A%20%20%20%20res%20%3D%20graph_bfs%28graph%2C%20v%5B0%5D%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=131&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全螢幕觀看 ></a></div></p>
|
||
</details>
|
||
<p>程式碼相對抽象，建議對照圖 9-10 來加深理解。</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="2:11"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1"><1></label><label for="__tabbed_2_2"><2></label><label for="__tabbed_2_3"><3></label><label for="__tabbed_2_4"><4></label><label for="__tabbed_2_5"><5></label><label for="__tabbed_2_6"><6></label><label for="__tabbed_2_7"><7></label><label for="__tabbed_2_8"><8></label><label for="__tabbed_2_9"><9></label><label for="__tabbed_2_10"><10></label><label for="__tabbed_2_11"><11></label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../graph_traversal.assets/graph_bfs_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="圖的廣度優先走訪步驟" class="animation-figure" src="../graph_traversal.assets/graph_bfs_step1.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../graph_traversal.assets/graph_bfs_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_bfs_step2" class="animation-figure" src="../graph_traversal.assets/graph_bfs_step2.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../graph_traversal.assets/graph_bfs_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_bfs_step3" class="animation-figure" src="../graph_traversal.assets/graph_bfs_step3.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../graph_traversal.assets/graph_bfs_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_bfs_step4" class="animation-figure" src="../graph_traversal.assets/graph_bfs_step4.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../graph_traversal.assets/graph_bfs_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_bfs_step5" class="animation-figure" src="../graph_traversal.assets/graph_bfs_step5.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../graph_traversal.assets/graph_bfs_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_bfs_step6" class="animation-figure" src="../graph_traversal.assets/graph_bfs_step6.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../graph_traversal.assets/graph_bfs_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_bfs_step7" class="animation-figure" src="../graph_traversal.assets/graph_bfs_step7.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../graph_traversal.assets/graph_bfs_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_bfs_step8" class="animation-figure" src="../graph_traversal.assets/graph_bfs_step8.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../graph_traversal.assets/graph_bfs_step9.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_bfs_step9" class="animation-figure" src="../graph_traversal.assets/graph_bfs_step9.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../graph_traversal.assets/graph_bfs_step10.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_bfs_step10" class="animation-figure" src="../graph_traversal.assets/graph_bfs_step10.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../graph_traversal.assets/graph_bfs_step11.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_bfs_step11" class="animation-figure" src="../graph_traversal.assets/graph_bfs_step11.png" /></a></p>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p align="center"> 圖 9-10 圖的廣度優先走訪步驟 </p>
|
||
|
||
<div class="admonition question">
|
||
<p class="admonition-title">廣度優先走訪的序列是否唯一？</p>
|
||
<p>不唯一。廣度優先走訪只要求按“由近及遠”的順序走訪，<strong>而多個相同距離的頂點的走訪順序允許被任意打亂</strong>。以圖 9-10 為例，頂點 <span class="arithmatex">\(1\)</span>、<span class="arithmatex">\(3\)</span> 的訪問順序可以交換，頂點 <span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(4\)</span>、<span class="arithmatex">\(6\)</span> 的訪問順序也可以任意交換。</p>
|
||
</div>
|
||
<h3 id="2">2. 複雜度分析<a class="headerlink" href="#2" title="Permanent link">¶</a></h3>
|
||
<p><strong>時間複雜度</strong>：所有頂點都會入列並出隊一次，使用 <span class="arithmatex">\(O(|V|)\)</span> 時間；在走訪鄰接頂點的過程中，由於是無向圖，因此所有邊都會被訪問 <span class="arithmatex">\(2\)</span> 次，使用 <span class="arithmatex">\(O(2|E|)\)</span> 時間；總體使用 <span class="arithmatex">\(O(|V| + |E|)\)</span> 時間。</p>
|
||
<p><strong>空間複雜度</strong>：串列 <code>res</code> ，雜湊表 <code>visited</code> ，佇列 <code>que</code> 中的頂點數量最多為 <span class="arithmatex">\(|V|\)</span> ，使用 <span class="arithmatex">\(O(|V|)\)</span> 空間。</p>
|
||
<h2 id="932">9.3.2 深度優先走訪<a class="headerlink" href="#932" title="Permanent link">¶</a></h2>
|
||
<p><strong>深度優先走訪是一種優先走到底、無路可走再回頭的走訪方式</strong>。如圖 9-11 所示，從左上角頂點出發，訪問當前頂點的某個鄰接頂點，直到走到盡頭時返回，再繼續走到盡頭並返回，以此類推，直至所有頂點走訪完成。</p>
|
||
<p><a class="glightbox" href="../graph_traversal.assets/graph_dfs.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="圖的深度優先走訪" class="animation-figure" src="../graph_traversal.assets/graph_dfs.png" /></a></p>
|
||
<p align="center"> 圖 9-11 圖的深度優先走訪 </p>
|
||
|
||
<h3 id="1_1">1. 演算法實現<a class="headerlink" href="#1_1" title="Permanent link">¶</a></h3>
|
||
<p>這種“走到盡頭再返回”的演算法範式通常基於遞迴來實現。與廣度優先走訪類似，在深度優先走訪中，我們也需要藉助一個雜湊表 <code>visited</code> 來記錄已被訪問的頂點，以避免重複訪問頂點。</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="3:14"><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" /><input id="__tabbed_3_14" 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><label for="__tabbed_3_14">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_dfs.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="k">def</span> <span class="nf">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span> <span class="n">GraphAdjList</span><span class="p">,</span> <span class="n">visited</span><span class="p">:</span> <span class="nb">set</span><span class="p">[</span><span class="n">Vertex</span><span class="p">],</span> <span class="n">res</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">Vertex</span><span class="p">],</span> <span class="n">vet</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">):</span>
|
||
<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="w"> </span><span class="sd">"""深度優先走訪輔助函式"""</span>
|
||
<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a> <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span> <span class="c1"># 記錄訪問頂點</span>
|
||
<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a> <span class="n">visited</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span> <span class="c1"># 標記該頂點已被訪問</span>
|
||
<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a> <span class="c1"># 走訪該頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a> <span class="k">for</span> <span class="n">adjVet</span> <span class="ow">in</span> <span class="n">graph</span><span class="o">.</span><span class="n">adj_list</span><span class="p">[</span><span class="n">vet</span><span class="p">]:</span>
|
||
<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a> <span class="k">if</span> <span class="n">adjVet</span> <span class="ow">in</span> <span class="n">visited</span><span class="p">:</span>
|
||
<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a> <span class="k">continue</span> <span class="c1"># 跳過已被訪問的頂點</span>
|
||
<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a> <span class="c1"># 遞迴訪問鄰接頂點</span>
|
||
<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a> <span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span> <span class="n">visited</span><span class="p">,</span> <span class="n">res</span><span class="p">,</span> <span class="n">adjVet</span><span class="p">)</span>
|
||
<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a>
|
||
<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="k">def</span> <span class="nf">graph_dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span> <span class="n">GraphAdjList</span><span class="p">,</span> <span class="n">start_vet</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">)</span> <span class="o">-></span> <span class="nb">list</span><span class="p">[</span><span class="n">Vertex</span><span class="p">]:</span>
|
||
<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w"> </span><span class="sd">"""深度優先走訪"""</span>
|
||
<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a> <span class="c1"># 使用鄰接表來表示圖，以便獲取指定頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a> <span class="c1"># 頂點走訪序列</span>
|
||
<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a> <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
|
||
<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a> <span class="c1"># 雜湊表，用於記錄已被訪問過的頂點</span>
|
||
<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a> <span class="n">visited</span> <span class="o">=</span> <span class="nb">set</span><span class="p">[</span><span class="n">Vertex</span><span class="p">]()</span>
|
||
<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a> <span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span> <span class="n">visited</span><span class="p">,</span> <span class="n">res</span><span class="p">,</span> <span class="n">start_vet</span><span class="p">)</span>
|
||
<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a> <span class="k">return</span> <span class="n">res</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_dfs.cpp</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 深度優先走訪輔助函式 */</span>
|
||
<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="o">&</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">unordered_set</span><span class="o"><</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="o">&</span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="o">&</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 記錄訪問頂點</span>
|
||
<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w"> </span><span class="n">visited</span><span class="p">.</span><span class="n">emplace</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 標記該頂點已被訪問</span>
|
||
<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w"> </span><span class="c1">// 走訪該頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">adjVet</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">graph</span><span class="p">.</span><span class="n">adjList</span><span class="p">[</span><span class="n">vet</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">visited</span><span class="p">.</span><span class="n">count</span><span class="p">(</span><span class="n">adjVet</span><span class="p">))</span>
|
||
<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w"> </span><span class="k">continue</span><span class="p">;</span><span class="w"> </span><span class="c1">// 跳過已被訪問的頂點</span>
|
||
<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w"> </span><span class="c1">// 遞迴訪問鄰接頂點</span>
|
||
<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">adjVet</span><span class="p">);</span>
|
||
<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="p">}</span>
|
||
<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a>
|
||
<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="cm">/* 深度優先走訪 */</span>
|
||
<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="c1">// 使用鄰接表來表示圖，以便獲取指定頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="n">vector</span><span class="o"><</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="n">graphDFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="o">&</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||
<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
|
||
<a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||
<a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a><span class="w"> </span><span class="n">unordered_set</span><span class="o"><</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="n">visited</span><span class="p">;</span>
|
||
<a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">);</span>
|
||
<a id="__codelineno-15-22" name="__codelineno-15-22" href="#__codelineno-15-22"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
|
||
<a id="__codelineno-15-23" name="__codelineno-15-23" href="#__codelineno-15-23"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_dfs.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 深度優先走訪輔助函式 */</span>
|
||
<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Set</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 記錄訪問頂點</span>
|
||
<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w"> </span><span class="n">visited</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 標記該頂點已被訪問</span>
|
||
<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w"> </span><span class="c1">// 走訪該頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">adjVet</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">graph</span><span class="p">.</span><span class="na">adjList</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">vet</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">visited</span><span class="p">.</span><span class="na">contains</span><span class="p">(</span><span class="n">adjVet</span><span class="p">))</span>
|
||
<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w"> </span><span class="k">continue</span><span class="p">;</span><span class="w"> </span><span class="c1">// 跳過已被訪問的頂點</span>
|
||
<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w"> </span><span class="c1">// 遞迴訪問鄰接頂點</span>
|
||
<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">adjVet</span><span class="p">);</span>
|
||
<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="p">}</span>
|
||
<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a>
|
||
<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="cm">/* 深度優先走訪 */</span>
|
||
<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="c1">// 使用鄰接表來表示圖，以便獲取指定頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="n">List</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="nf">graphDFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||
<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o"><></span><span class="p">();</span>
|
||
<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||
<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a><span class="w"> </span><span class="n">Set</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">HashSet</span><span class="o"><></span><span class="p">();</span>
|
||
<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">);</span>
|
||
<a id="__codelineno-16-22" name="__codelineno-16-22" href="#__codelineno-16-22"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
|
||
<a id="__codelineno-16-23" name="__codelineno-16-23" href="#__codelineno-16-23"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_dfs.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 深度優先走訪輔助函式 */</span>
|
||
<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">DFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">HashSet</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 記錄訪問頂點</span>
|
||
<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w"> </span><span class="n">visited</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 標記該頂點已被訪問</span>
|
||
<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w"> </span><span class="c1">// 走訪該頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w"> </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">adjVet</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">graph</span><span class="p">.</span><span class="n">adjList</span><span class="p">[</span><span class="n">vet</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">visited</span><span class="p">.</span><span class="n">Contains</span><span class="p">(</span><span class="n">adjVet</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w"> </span><span class="k">continue</span><span class="p">;</span><span class="w"> </span><span class="c1">// 跳過已被訪問的頂點 </span>
|
||
<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w"> </span><span class="c1">// 遞迴訪問鄰接頂點</span>
|
||
<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="w"> </span><span class="n">DFS</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">adjVet</span><span class="p">);</span>
|
||
<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="p">}</span>
|
||
<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a>
|
||
<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="cm">/* 深度優先走訪 */</span>
|
||
<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="c1">// 使用鄰接表來表示圖，以便獲取指定頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><span class="n">List</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">GraphDFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||
<a id="__codelineno-17-19" name="__codelineno-17-19" href="#__codelineno-17-19"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
|
||
<a id="__codelineno-17-20" name="__codelineno-17-20" href="#__codelineno-17-20"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||
<a id="__codelineno-17-21" name="__codelineno-17-21" href="#__codelineno-17-21"></a><span class="w"> </span><span class="n">HashSet</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
|
||
<a id="__codelineno-17-22" name="__codelineno-17-22" href="#__codelineno-17-22"></a><span class="w"> </span><span class="n">DFS</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">);</span>
|
||
<a id="__codelineno-17-23" name="__codelineno-17-23" href="#__codelineno-17-23"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
|
||
<a id="__codelineno-17-24" name="__codelineno-17-24" href="#__codelineno-17-24"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_dfs.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 深度優先走訪輔助函式 */</span>
|
||
<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">g</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjList</span><span class="p">,</span><span class="w"> </span><span class="nx">visited</span><span class="w"> </span><span class="kd">map</span><span class="p">[</span><span class="nx">Vertex</span><span class="p">]</span><span class="kd">struct</span><span class="p">{},</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="nx">Vertex</span><span class="p">,</span><span class="w"> </span><span class="nx">vet</span><span class="w"> </span><span class="nx">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w"> </span><span class="c1">// append 操作會返回新的的引用，必須讓原引用重新賦值為新slice的引用</span>
|
||
<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w"> </span><span class="o">*</span><span class="nx">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">vet</span><span class="p">)</span>
|
||
<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="w"> </span><span class="nx">visited</span><span class="p">[</span><span class="nx">vet</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kd">struct</span><span class="p">{}{}</span>
|
||
<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="w"> </span><span class="c1">// 走訪該頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">adjVet</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">[</span><span class="nx">vet</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">isExist</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">visited</span><span class="p">[</span><span class="nx">adjVet</span><span class="p">]</span>
|
||
<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w"> </span><span class="c1">// 遞迴訪問鄰接頂點</span>
|
||
<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">!</span><span class="nx">isExist</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">g</span><span class="p">,</span><span class="w"> </span><span class="nx">visited</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">adjVet</span><span class="p">)</span>
|
||
<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="p">}</span>
|
||
<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a>
|
||
<a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></a><span class="cm">/* 深度優先走訪 */</span>
|
||
<a id="__codelineno-18-17" name="__codelineno-18-17" href="#__codelineno-18-17"></a><span class="c1">// 使用鄰接表來表示圖，以便獲取指定頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-18-18" name="__codelineno-18-18" href="#__codelineno-18-18"></a><span class="kd">func</span><span class="w"> </span><span class="nx">graphDFS</span><span class="p">(</span><span class="nx">g</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjList</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="w"> </span><span class="nx">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">[]</span><span class="nx">Vertex</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-18-19" name="__codelineno-18-19" href="#__codelineno-18-19"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||
<a id="__codelineno-18-20" name="__codelineno-18-20" href="#__codelineno-18-20"></a><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="nx">Vertex</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-18-21" name="__codelineno-18-21" href="#__codelineno-18-21"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||
<a id="__codelineno-18-22" name="__codelineno-18-22" href="#__codelineno-18-22"></a><span class="w"> </span><span class="nx">visited</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">(</span><span class="kd">map</span><span class="p">[</span><span class="nx">Vertex</span><span class="p">]</span><span class="kd">struct</span><span class="p">{})</span>
|
||
<a id="__codelineno-18-23" name="__codelineno-18-23" href="#__codelineno-18-23"></a><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">g</span><span class="p">,</span><span class="w"> </span><span class="nx">visited</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="p">)</span>
|
||
<a id="__codelineno-18-24" name="__codelineno-18-24" href="#__codelineno-18-24"></a><span class="w"> </span><span class="c1">// 返回頂點走訪序列</span>
|
||
<a id="__codelineno-18-25" name="__codelineno-18-25" href="#__codelineno-18-25"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span>
|
||
<a id="__codelineno-18-26" name="__codelineno-18-26" href="#__codelineno-18-26"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_dfs.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 深度優先走訪輔助函式 */</span>
|
||
<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">func</span> <span class="nf">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span> <span class="n">GraphAdjList</span><span class="p">,</span> <span class="n">visited</span><span class="p">:</span> <span class="kr">inout</span> <span class="n">Set</span><span class="p"><</span><span class="n">Vertex</span><span class="p">>,</span> <span class="n">res</span><span class="p">:</span> <span class="kr">inout</span> <span class="p">[</span><span class="n">Vertex</span><span class="p">],</span> <span class="n">vet</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">)</span> <span class="p">{</span>
|
||
<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a> <span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span> <span class="c1">// 記錄訪問頂點</span>
|
||
<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a> <span class="n">visited</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span> <span class="c1">// 標記該頂點已被訪問</span>
|
||
<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a> <span class="c1">// 走訪該頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a> <span class="k">for</span> <span class="n">adjVet</span> <span class="k">in</span> <span class="n">graph</span><span class="p">.</span><span class="n">adjList</span><span class="p">[</span><span class="n">vet</span><span class="p">]</span> <span class="p">??</span> <span class="p">[]</span> <span class="p">{</span>
|
||
<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a> <span class="k">if</span> <span class="n">visited</span><span class="p">.</span><span class="bp">contains</span><span class="p">(</span><span class="n">adjVet</span><span class="p">)</span> <span class="p">{</span>
|
||
<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a> <span class="k">continue</span> <span class="c1">// 跳過已被訪問的頂點</span>
|
||
<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a> <span class="p">}</span>
|
||
<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a> <span class="c1">// 遞迴訪問鄰接頂點</span>
|
||
<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a> <span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span> <span class="n">graph</span><span class="p">,</span> <span class="n">visited</span><span class="p">:</span> <span class="p">&</span><span class="n">visited</span><span class="p">,</span> <span class="n">res</span><span class="p">:</span> <span class="p">&</span><span class="n">res</span><span class="p">,</span> <span class="n">vet</span><span class="p">:</span> <span class="n">adjVet</span><span class="p">)</span>
|
||
<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a> <span class="p">}</span>
|
||
<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="p">}</span>
|
||
<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a>
|
||
<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a><span class="cm">/* 深度優先走訪 */</span>
|
||
<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a><span class="c1">// 使用鄰接表來表示圖，以便獲取指定頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a><span class="kd">func</span> <span class="nf">graphDFS</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span> <span class="n">GraphAdjList</span><span class="p">,</span> <span class="n">startVet</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">)</span> <span class="p">-></span> <span class="p">[</span><span class="n">Vertex</span><span class="p">]</span> <span class="p">{</span>
|
||
<a id="__codelineno-19-18" name="__codelineno-19-18" href="#__codelineno-19-18"></a> <span class="c1">// 頂點走訪序列</span>
|
||
<a id="__codelineno-19-19" name="__codelineno-19-19" href="#__codelineno-19-19"></a> <span class="kd">var</span> <span class="nv">res</span><span class="p">:</span> <span class="p">[</span><span class="n">Vertex</span><span class="p">]</span> <span class="p">=</span> <span class="p">[]</span>
|
||
<a id="__codelineno-19-20" name="__codelineno-19-20" href="#__codelineno-19-20"></a> <span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||
<a id="__codelineno-19-21" name="__codelineno-19-21" href="#__codelineno-19-21"></a> <span class="kd">var</span> <span class="nv">visited</span><span class="p">:</span> <span class="n">Set</span><span class="p"><</span><span class="n">Vertex</span><span class="p">></span> <span class="p">=</span> <span class="p">[]</span>
|
||
<a id="__codelineno-19-22" name="__codelineno-19-22" href="#__codelineno-19-22"></a> <span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span> <span class="n">graph</span><span class="p">,</span> <span class="n">visited</span><span class="p">:</span> <span class="p">&</span><span class="n">visited</span><span class="p">,</span> <span class="n">res</span><span class="p">:</span> <span class="p">&</span><span class="n">res</span><span class="p">,</span> <span class="n">vet</span><span class="p">:</span> <span class="n">startVet</span><span class="p">)</span>
|
||
<a id="__codelineno-19-23" name="__codelineno-19-23" href="#__codelineno-19-23"></a> <span class="k">return</span> <span class="n">res</span>
|
||
<a id="__codelineno-19-24" name="__codelineno-19-24" href="#__codelineno-19-24"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_dfs.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 深度優先走訪 */</span>
|
||
<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="c1">// 使用鄰接表來表示圖，以便獲取指定頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="kd">function</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">graph</span><span class="p">,</span><span class="w"> </span><span class="nx">visited</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 記錄訪問頂點</span>
|
||
<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w"> </span><span class="nx">visited</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 標記該頂點已被訪問</span>
|
||
<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="w"> </span><span class="c1">// 走訪該頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">adjVet</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">graph</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">vet</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">visited</span><span class="p">.</span><span class="nx">has</span><span class="p">(</span><span class="nx">adjVet</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w"> </span><span class="k">continue</span><span class="p">;</span><span class="w"> </span><span class="c1">// 跳過已被訪問的頂點</span>
|
||
<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="w"> </span><span class="c1">// 遞迴訪問鄰接頂點</span>
|
||
<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">graph</span><span class="p">,</span><span class="w"> </span><span class="nx">visited</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">adjVet</span><span class="p">);</span>
|
||
<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="p">}</span>
|
||
<a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a>
|
||
<a id="__codelineno-20-16" name="__codelineno-20-16" href="#__codelineno-20-16"></a><span class="cm">/* 深度優先走訪 */</span>
|
||
<a id="__codelineno-20-17" name="__codelineno-20-17" href="#__codelineno-20-17"></a><span class="c1">// 使用鄰接表來表示圖，以便獲取指定頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-20-18" name="__codelineno-20-18" href="#__codelineno-20-18"></a><span class="kd">function</span><span class="w"> </span><span class="nx">graphDFS</span><span class="p">(</span><span class="nx">graph</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-20-19" name="__codelineno-20-19" href="#__codelineno-20-19"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||
<a id="__codelineno-20-20" name="__codelineno-20-20" href="#__codelineno-20-20"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
|
||
<a id="__codelineno-20-21" name="__codelineno-20-21" href="#__codelineno-20-21"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||
<a id="__codelineno-20-22" name="__codelineno-20-22" href="#__codelineno-20-22"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Set</span><span class="p">();</span>
|
||
<a id="__codelineno-20-23" name="__codelineno-20-23" href="#__codelineno-20-23"></a><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">graph</span><span class="p">,</span><span class="w"> </span><span class="nx">visited</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="p">);</span>
|
||
<a id="__codelineno-20-24" name="__codelineno-20-24" href="#__codelineno-20-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
|
||
<a id="__codelineno-20-25" name="__codelineno-20-25" href="#__codelineno-20-25"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_dfs.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 深度優先走訪輔助函式 */</span>
|
||
<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span>
|
||
<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w"> </span><span class="nx">graph</span><span class="o">:</span><span class="w"> </span><span class="kt">GraphAdjList</span><span class="p">,</span>
|
||
<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w"> </span><span class="nx">visited</span><span class="o">:</span><span class="w"> </span><span class="kt">Set</span><span class="o"><</span><span class="nx">Vertex</span><span class="o">></span><span class="p">,</span>
|
||
<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w"> </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">Vertex</span><span class="p">[],</span>
|
||
<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="w"> </span><span class="nx">vet</span><span class="o">:</span><span class="w"> </span><span class="kt">Vertex</span>
|
||
<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 記錄訪問頂點</span>
|
||
<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w"> </span><span class="nx">visited</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 標記該頂點已被訪問</span>
|
||
<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="w"> </span><span class="c1">// 走訪該頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">adjVet</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">graph</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">vet</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">visited</span><span class="p">.</span><span class="nx">has</span><span class="p">(</span><span class="nx">adjVet</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w"> </span><span class="k">continue</span><span class="p">;</span><span class="w"> </span><span class="c1">// 跳過已被訪問的頂點</span>
|
||
<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a><span class="w"> </span><span class="c1">// 遞迴訪問鄰接頂點</span>
|
||
<a id="__codelineno-21-16" name="__codelineno-21-16" href="#__codelineno-21-16"></a><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">graph</span><span class="p">,</span><span class="w"> </span><span class="nx">visited</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">adjVet</span><span class="p">);</span>
|
||
<a id="__codelineno-21-17" name="__codelineno-21-17" href="#__codelineno-21-17"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-21-18" name="__codelineno-21-18" href="#__codelineno-21-18"></a><span class="p">}</span>
|
||
<a id="__codelineno-21-19" name="__codelineno-21-19" href="#__codelineno-21-19"></a>
|
||
<a id="__codelineno-21-20" name="__codelineno-21-20" href="#__codelineno-21-20"></a><span class="cm">/* 深度優先走訪 */</span>
|
||
<a id="__codelineno-21-21" name="__codelineno-21-21" href="#__codelineno-21-21"></a><span class="c1">// 使用鄰接表來表示圖，以便獲取指定頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-21-22" name="__codelineno-21-22" href="#__codelineno-21-22"></a><span class="kd">function</span><span class="w"> </span><span class="nx">graphDFS</span><span class="p">(</span><span class="nx">graph</span><span class="o">:</span><span class="w"> </span><span class="kt">GraphAdjList</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="o">:</span><span class="w"> </span><span class="kt">Vertex</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="nx">Vertex</span><span class="p">[]</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-21-23" name="__codelineno-21-23" href="#__codelineno-21-23"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||
<a id="__codelineno-21-24" name="__codelineno-21-24" href="#__codelineno-21-24"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">Vertex</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
|
||
<a id="__codelineno-21-25" name="__codelineno-21-25" href="#__codelineno-21-25"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||
<a id="__codelineno-21-26" name="__codelineno-21-26" href="#__codelineno-21-26"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">visited</span><span class="o">:</span><span class="w"> </span><span class="kt">Set</span><span class="o"><</span><span class="nx">Vertex</span><span class="o">></span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Set</span><span class="p">();</span>
|
||
<a id="__codelineno-21-27" name="__codelineno-21-27" href="#__codelineno-21-27"></a><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">graph</span><span class="p">,</span><span class="w"> </span><span class="nx">visited</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="p">);</span>
|
||
<a id="__codelineno-21-28" name="__codelineno-21-28" href="#__codelineno-21-28"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
|
||
<a id="__codelineno-21-29" name="__codelineno-21-29" href="#__codelineno-21-29"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_dfs.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 深度優先走訪輔助函式 */</span>
|
||
<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span>
|
||
<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w"> </span><span class="n">GraphAdjList</span><span class="w"> </span><span class="n">graph</span><span class="p">,</span>
|
||
<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w"> </span><span class="n">Set</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">visited</span><span class="p">,</span>
|
||
<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">res</span><span class="p">,</span>
|
||
<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet</span><span class="p">,</span>
|
||
<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 記錄訪問頂點</span>
|
||
<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w"> </span><span class="n">visited</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 標記該頂點已被訪問</span>
|
||
<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="w"> </span><span class="c1">// 走訪該頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">adjVet</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">graph</span><span class="p">.</span><span class="n">adjList</span><span class="p">[</span><span class="n">vet</span><span class="p">]</span><span class="o">!</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">visited</span><span class="p">.</span><span class="n">contains</span><span class="p">(</span><span class="n">adjVet</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w"> </span><span class="k">continue</span><span class="p">;</span><span class="w"> </span><span class="c1">// 跳過已被訪問的頂點</span>
|
||
<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a><span class="w"> </span><span class="c1">// 遞迴訪問鄰接頂點</span>
|
||
<a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">adjVet</span><span class="p">);</span>
|
||
<a id="__codelineno-22-17" name="__codelineno-22-17" href="#__codelineno-22-17"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-22-18" name="__codelineno-22-18" href="#__codelineno-22-18"></a><span class="p">}</span>
|
||
<a id="__codelineno-22-19" name="__codelineno-22-19" href="#__codelineno-22-19"></a>
|
||
<a id="__codelineno-22-20" name="__codelineno-22-20" href="#__codelineno-22-20"></a><span class="cm">/* 深度優先走訪 */</span>
|
||
<a id="__codelineno-22-21" name="__codelineno-22-21" href="#__codelineno-22-21"></a><span class="n">List</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">graphDFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-22-22" name="__codelineno-22-22" href="#__codelineno-22-22"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||
<a id="__codelineno-22-23" name="__codelineno-22-23" href="#__codelineno-22-23"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
|
||
<a id="__codelineno-22-24" name="__codelineno-22-24" href="#__codelineno-22-24"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||
<a id="__codelineno-22-25" name="__codelineno-22-25" href="#__codelineno-22-25"></a><span class="w"> </span><span class="n">Set</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{};</span>
|
||
<a id="__codelineno-22-26" name="__codelineno-22-26" href="#__codelineno-22-26"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">);</span>
|
||
<a id="__codelineno-22-27" name="__codelineno-22-27" href="#__codelineno-22-27"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
|
||
<a id="__codelineno-22-28" name="__codelineno-22-28" href="#__codelineno-22-28"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_dfs.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* 深度優先走訪輔助函式 */</span>
|
||
<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="k">fn</span> <span class="nf">dfs</span><span class="p">(</span><span class="n">graph</span>: <span class="kp">&</span><span class="nc">GraphAdjList</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span>: <span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="n">HashSet</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="p">,</span><span class="w"> </span><span class="n">res</span>: <span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="p">,</span><span class="w"> </span><span class="n">vet</span>: <span class="nc">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 記錄訪問頂點</span>
|
||
<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w"> </span><span class="n">visited</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 標記該頂點已被訪問</span>
|
||
<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w"> </span><span class="c1">// 走訪該頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">adj_vets</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">graph</span><span class="p">.</span><span class="n">adj_list</span><span class="p">.</span><span class="n">get</span><span class="p">(</span><span class="o">&</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="o">&</span><span class="n">adj_vet</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">adj_vets</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">visited</span><span class="p">.</span><span class="n">contains</span><span class="p">(</span><span class="o">&</span><span class="n">adj_vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="w"> </span><span class="k">continue</span><span class="p">;</span><span class="w"> </span><span class="c1">// 跳過已被訪問的頂點</span>
|
||
<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="w"> </span><span class="c1">// 遞迴訪問鄰接頂點</span>
|
||
<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">adj_vet</span><span class="p">);</span>
|
||
<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="p">}</span>
|
||
<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a>
|
||
<a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="cm">/* 深度優先走訪 */</span>
|
||
<a id="__codelineno-23-18" name="__codelineno-23-18" href="#__codelineno-23-18"></a><span class="c1">// 使用鄰接表來表示圖，以便獲取指定頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-23-19" name="__codelineno-23-19" href="#__codelineno-23-19"></a><span class="k">fn</span> <span class="nf">graph_dfs</span><span class="p">(</span><span class="n">graph</span>: <span class="nc">GraphAdjList</span><span class="p">,</span><span class="w"> </span><span class="n">start_vet</span>: <span class="nc">Vertex</span><span class="p">)</span><span class="w"> </span>-> <span class="nb">Vec</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-23-20" name="__codelineno-23-20" href="#__codelineno-23-20"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||
<a id="__codelineno-23-21" name="__codelineno-23-21" href="#__codelineno-23-21"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[];</span>
|
||
<a id="__codelineno-23-22" name="__codelineno-23-22" href="#__codelineno-23-22"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||
<a id="__codelineno-23-23" name="__codelineno-23-23" href="#__codelineno-23-23"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashSet</span>::<span class="n">new</span><span class="p">();</span>
|
||
<a id="__codelineno-23-24" name="__codelineno-23-24" href="#__codelineno-23-24"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="o">&</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="k">mut</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">start_vet</span><span class="p">);</span>
|
||
<a id="__codelineno-23-25" name="__codelineno-23-25" href="#__codelineno-23-25"></a>
|
||
<a id="__codelineno-23-26" name="__codelineno-23-26" href="#__codelineno-23-26"></a><span class="w"> </span><span class="n">res</span>
|
||
<a id="__codelineno-23-27" name="__codelineno-23-27" href="#__codelineno-23-27"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_dfs.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* 檢查頂點是否已被訪問 */</span>
|
||
<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">isVisited</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="o">**</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w"> </span><span class="c1">// 走訪查詢節點，使用 O(n) 時間</span>
|
||
<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="p">}</span>
|
||
<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a>
|
||
<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="cm">/* 深度優先走訪輔助函式 */</span>
|
||
<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="kt">void</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="o">*</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">**</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">resSize</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a><span class="w"> </span><span class="c1">// 記錄訪問頂點</span>
|
||
<a id="__codelineno-24-15" name="__codelineno-24-15" href="#__codelineno-24-15"></a><span class="w"> </span><span class="n">res</span><span class="p">[(</span><span class="o">*</span><span class="n">resSize</span><span class="p">)</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vet</span><span class="p">;</span>
|
||
<a id="__codelineno-24-16" name="__codelineno-24-16" href="#__codelineno-24-16"></a><span class="w"> </span><span class="c1">// 走訪該頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-24-17" name="__codelineno-24-17" href="#__codelineno-24-17"></a><span class="w"> </span><span class="n">AdjListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findNode</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">vet</span><span class="p">);</span>
|
||
<a id="__codelineno-24-18" name="__codelineno-24-18" href="#__codelineno-24-18"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-24-19" name="__codelineno-24-19" href="#__codelineno-24-19"></a><span class="w"> </span><span class="c1">// 跳過已被訪問的頂點</span>
|
||
<a id="__codelineno-24-20" name="__codelineno-24-20" href="#__codelineno-24-20"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">isVisited</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">resSize</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">vertex</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-24-21" name="__codelineno-24-21" href="#__codelineno-24-21"></a><span class="w"> </span><span class="c1">// 遞迴訪問鄰接頂點</span>
|
||
<a id="__codelineno-24-22" name="__codelineno-24-22" href="#__codelineno-24-22"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">resSize</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">vertex</span><span class="p">);</span>
|
||
<a id="__codelineno-24-23" name="__codelineno-24-23" href="#__codelineno-24-23"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-24-24" name="__codelineno-24-24" href="#__codelineno-24-24"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">next</span><span class="p">;</span>
|
||
<a id="__codelineno-24-25" name="__codelineno-24-25" href="#__codelineno-24-25"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-24-26" name="__codelineno-24-26" href="#__codelineno-24-26"></a><span class="p">}</span>
|
||
<a id="__codelineno-24-27" name="__codelineno-24-27" href="#__codelineno-24-27"></a>
|
||
<a id="__codelineno-24-28" name="__codelineno-24-28" href="#__codelineno-24-28"></a><span class="cm">/* 深度優先走訪 */</span>
|
||
<a id="__codelineno-24-29" name="__codelineno-24-29" href="#__codelineno-24-29"></a><span class="c1">// 使用鄰接表來表示圖，以便獲取指定頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-24-30" name="__codelineno-24-30" href="#__codelineno-24-30"></a><span class="kt">void</span><span class="w"> </span><span class="nf">graphDFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="o">*</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">startVet</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">**</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">resSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-24-31" name="__codelineno-24-31" href="#__codelineno-24-31"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">resSize</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">);</span>
|
||
<a id="__codelineno-24-32" name="__codelineno-24-32" href="#__codelineno-24-32"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_dfs.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="cm">/* 深度優先走訪輔助函式 */</span>
|
||
<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span>
|
||
<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w"> </span><span class="n">graph</span><span class="p">:</span><span class="w"> </span><span class="n">GraphAdjList</span><span class="p">,</span>
|
||
<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w"> </span><span class="n">visited</span><span class="p">:</span><span class="w"> </span><span class="n">MutableSet</span><span class="o"><</span><span class="n">Vertex?></span><span class="p">,</span>
|
||
<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o"><</span><span class="n">Vertex?></span><span class="p">,</span>
|
||
<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w"> </span><span class="n">vet</span><span class="p">:</span><span class="w"> </span><span class="n">Vertex?</span>
|
||
<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="c1">// 記錄訪問頂點</span>
|
||
<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w"> </span><span class="n">visited</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="c1">// 標記該頂點已被訪問</span>
|
||
<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="w"> </span><span class="c1">// 走訪該頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">adjVet</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">graph</span><span class="p">.</span><span class="na">adjList</span><span class="o">[</span><span class="n">vet</span><span class="o">]!!</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">visited</span><span class="p">.</span><span class="na">contains</span><span class="p">(</span><span class="n">adjVet</span><span class="p">))</span>
|
||
<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w"> </span><span class="k">continue</span><span class="w"> </span><span class="c1">// 跳過已被訪問的頂點</span>
|
||
<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="w"> </span><span class="c1">// 遞迴訪問鄰接頂點</span>
|
||
<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">adjVet</span><span class="p">)</span>
|
||
<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a><span class="p">}</span>
|
||
<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a>
|
||
<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a><span class="cm">/* 深度優先走訪 */</span>
|
||
<a id="__codelineno-25-20" name="__codelineno-25-20" href="#__codelineno-25-20"></a><span class="c1">// 使用鄰接表來表示圖，以便獲取指定頂點的所有鄰接頂點</span>
|
||
<a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">graphDFS</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span><span class="w"> </span><span class="n">GraphAdjList</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">:</span><span class="w"> </span><span class="n">Vertex?)</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o"><</span><span class="n">Vertex?></span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-25-22" name="__codelineno-25-22" href="#__codelineno-25-22"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||
<a id="__codelineno-25-23" name="__codelineno-25-23" href="#__codelineno-25-23"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o"><</span><span class="n">Vertex?></span><span class="p">()</span>
|
||
<a id="__codelineno-25-24" name="__codelineno-25-24" href="#__codelineno-25-24"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||
<a id="__codelineno-25-25" name="__codelineno-25-25" href="#__codelineno-25-25"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashSet</span><span class="o"><</span><span class="n">Vertex?></span><span class="p">()</span>
|
||
<a id="__codelineno-25-26" name="__codelineno-25-26" href="#__codelineno-25-26"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">)</span>
|
||
<a id="__codelineno-25-27" name="__codelineno-25-27" href="#__codelineno-25-27"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
|
||
<a id="__codelineno-25-28" name="__codelineno-25-28" href="#__codelineno-25-28"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_dfs.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
|
||
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a>
|
||
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">graph_dfs</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_dfs.zig</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
|
||
<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a>
|
||
<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">graphDFS</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<details class="pythontutor">
|
||
<summary>視覺化執行</summary>
|
||
<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20Vertex%3A%0A%20%20%20%20%22%22%22%E9%A0%82%E9%BB%9E%E9%A1%9E%E5%88%A5%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%20%3D%20val%0A%0Adef%20vals_to_vets%28vals%3A%20list%5Bint%5D%29%20-%3E%20list%5B%22Vertex%22%5D%3A%0A%20%20%20%20%22%22%22%E8%BC%B8%E5%85%A5%E5%80%BC%E4%B8%B2%E5%88%97%20vals%20%EF%BC%8C%E8%BF%94%E5%9B%9E%E9%A0%82%E9%BB%9E%E4%B8%B2%E5%88%97%20vets%22%22%22%0A%20%20%20%20return%20%5BVertex%28val%29%20for%20val%20in%20vals%5D%0A%0Aclass%20GraphAdjList%3A%0A%20%20%20%20%22%22%22%E5%9F%BA%E6%96%BC%E9%84%B0%E6%8E%A5%E8%A1%A8%E5%AF%A6%E7%8F%BE%E7%9A%84%E7%84%A1%E5%90%91%E5%9C%96%E9%A1%9E%E5%88%A5%22%22%22%0A%0A%20%20%20%20def%20__init__%28self%2C%20edges%3A%20list%5Blist%5BVertex%5D%5D%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%BB%BA%E6%A7%8B%E5%AD%90%22%22%22%0A%20%20%20%20%20%20%20%20self.adj_list%20%3D%20dict%5BVertex%2C%20list%5BVertex%5D%5D%28%29%0A%20%20%20%20%20%20%20%20for%20edge%20in%20edges%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self.add_vertex%28edge%5B0%5D%29%0A%20%20%20%20%20%20%20%20%20%20%20%20self.add_vertex%28edge%5B1%5D%29%0A%20%20%20%20%20%20%20%20%20%20%20%20self.add_edge%28edge%5B0%5D%2C%20edge%5B1%5D%29%0A%0A%20%20%20%20def%20add_edge%28self%2C%20vet1%3A%20Vertex%2C%20vet2%3A%20Vertex%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E6%96%B0%E5%A2%9E%E9%82%8A%22%22%22%0A%20%20%20%20%20%20%20%20if%20vet1%20not%20in%20self.adj_list%20or%20vet2%20not%20in%20self.adj_list%20or%20vet1%20%3D%3D%20vet2%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20ValueError%28%29%0A%20%20%20%20%20%20%20%20self.adj_list%5Bvet1%5D.append%28vet2%29%0A%20%20%20%20%20%20%20%20self.adj_list%5Bvet2%5D.append%28vet1%29%0A%0A%20%20%20%20def%20add_vertex%28self%2C%20vet%3A%20Vertex%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E6%96%B0%E5%A2%9E%E9%A0%82%E9%BB%9E%22%22%22%0A%20%20%20%20%20%20%20%20if%20vet%20in%20self.adj_list%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%0A%20%20%20%20%20%20%20%20self.adj_list%5Bvet%5D%20%3D%20%5B%5D%0A%0A%0Adef%20dfs%28graph%3A%20GraphAdjList%2C%20visited%3A%20set%5BVertex%5D%2C%20res%3A%20list%5BVertex%5D%2C%20vet%3A%20Vertex%29%3A%0A%20%20%20%20%22%22%22%E6%B7%B1%E5%BA%A6%E5%84%AA%E5%85%88%E8%B5%B0%E8%A8%AA%E8%BC%94%E5%8A%A9%E5%87%BD%E5%BC%8F%22%22%22%0A%20%20%20%20res.append%28vet%29%20%20%23%20%E8%A8%98%E9%8C%84%E8%A8%AA%E5%95%8F%E9%A0%82%E9%BB%9E%0A%20%20%20%20visited.add%28vet%29%20%20%23%20%E6%A8%99%E8%A8%98%E8%A9%B2%E9%A0%82%E9%BB%9E%E5%B7%B2%E8%A2%AB%E8%A8%AA%E5%95%8F%0A%20%20%20%20%23%20%E8%B5%B0%E8%A8%AA%E8%A9%B2%E9%A0%82%E9%BB%9E%E7%9A%84%E6%89%80%E6%9C%89%E9%84%B0%E6%8E%A5%E9%A0%82%E9%BB%9E%0A%20%20%20%20for%20adjVet%20in%20graph.adj_list%5Bvet%5D%3A%0A%20%20%20%20%20%20%20%20if%20adjVet%20in%20visited%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20continue%20%20%23%20%E8%B7%B3%E9%81%8E%E5%B7%B2%E8%A2%AB%E8%A8%AA%E5%95%8F%E7%9A%84%E9%A0%82%E9%BB%9E%0A%20%20%20%20%20%20%20%20%23%20%E9%81%9E%E8%BF%B4%E8%A8%AA%E5%95%8F%E9%84%B0%E6%8E%A5%E9%A0%82%E9%BB%9E%0A%20%20%20%20%20%20%20%20dfs%28graph%2C%20visited%2C%20res%2C%20adjVet%29%0A%0A%0Adef%20graph_dfs%28graph%3A%20GraphAdjList%2C%20start_vet%3A%20Vertex%29%20-%3E%20list%5BVertex%5D%3A%0A%20%20%20%20%22%22%22%E6%B7%B1%E5%BA%A6%E5%84%AA%E5%85%88%E8%B5%B0%E8%A8%AA%22%22%22%0A%20%20%20%20%23%20%E4%BD%BF%E7%94%A8%E9%84%B0%E6%8E%A5%E8%A1%A8%E4%BE%86%E8%A1%A8%E7%A4%BA%E5%9C%96%EF%BC%8C%E4%BB%A5%E4%BE%BF%E7%8D%B2%E5%8F%96%E6%8C%87%E5%AE%9A%E9%A0%82%E9%BB%9E%E7%9A%84%E6%89%80%E6%9C%89%E9%84%B0%E6%8E%A5%E9%A0%82%E9%BB%9E%0A%20%20%20%20%23%20%E9%A0%82%E9%BB%9E%E8%B5%B0%E8%A8%AA%E5%BA%8F%E5%88%97%0A%20%20%20%20res%20%3D%20%5B%5D%0A%20%20%20%20%23%20%E9%9B%9C%E6%B9%8A%E8%A1%A8%EF%BC%8C%E7%94%A8%E6%96%BC%E8%A8%98%E9%8C%84%E5%B7%B2%E8%A2%AB%E8%A8%AA%E5%95%8F%E9%81%8E%E7%9A%84%E9%A0%82%E9%BB%9E%0A%20%20%20%20visited%20%3D%20set%5BVertex%5D%28%29%0A%20%20%20%20dfs%28graph%2C%20visited%2C%20res%2C%20start_vet%29%0A%20%20%20%20return%20res%0A%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E7%84%A1%E5%90%91%E5%9C%96%0A%20%20%20%20v%20%3D%20vals_to_vets%28%5B0%2C%201%2C%202%2C%203%2C%204%5D%29%0A%20%20%20%20edges%20%3D%20%5B%0A%20%20%20%20%20%20%20%20%5Bv%5B0%5D%2C%20v%5B1%5D%5D%2C%0A%20%20%20%20%20%20%20%20%5Bv%5B0%5D%2C%20v%5B3%5D%5D%2C%0A%20%20%20%20%20%20%20%20%5Bv%5B1%5D%2C%20v%5B2%5D%5D%2C%0A%20%20%20%20%20%20%20%20%5Bv%5B1%5D%2C%20v%5B4%5D%5D%2C%0A%20%20%20%20%20%20%20%20%5Bv%5B3%5D%2C%20v%5B4%5D%5D%2C%0A%20%20%20%20%5D%0A%20%20%20%20graph%20%3D%20GraphAdjList%28edges%29%0A%0A%20%20%20%20%23%20%E6%B7%B1%E5%BA%A6%E5%84%AA%E5%85%88%E8%B5%B0%E8%A8%AA%0A%20%20%20%20res%20%3D%20graph_dfs%28graph%2C%20v%5B0%5D%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=130&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
|
||
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20Vertex%3A%0A%20%20%20%20%22%22%22%E9%A0%82%E9%BB%9E%E9%A1%9E%E5%88%A5%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%20%3D%20val%0A%0Adef%20vals_to_vets%28vals%3A%20list%5Bint%5D%29%20-%3E%20list%5B%22Vertex%22%5D%3A%0A%20%20%20%20%22%22%22%E8%BC%B8%E5%85%A5%E5%80%BC%E4%B8%B2%E5%88%97%20vals%20%EF%BC%8C%E8%BF%94%E5%9B%9E%E9%A0%82%E9%BB%9E%E4%B8%B2%E5%88%97%20vets%22%22%22%0A%20%20%20%20return%20%5BVertex%28val%29%20for%20val%20in%20vals%5D%0A%0Aclass%20GraphAdjList%3A%0A%20%20%20%20%22%22%22%E5%9F%BA%E6%96%BC%E9%84%B0%E6%8E%A5%E8%A1%A8%E5%AF%A6%E7%8F%BE%E7%9A%84%E7%84%A1%E5%90%91%E5%9C%96%E9%A1%9E%E5%88%A5%22%22%22%0A%0A%20%20%20%20def%20__init__%28self%2C%20edges%3A%20list%5Blist%5BVertex%5D%5D%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%BB%BA%E6%A7%8B%E5%AD%90%22%22%22%0A%20%20%20%20%20%20%20%20self.adj_list%20%3D%20dict%5BVertex%2C%20list%5BVertex%5D%5D%28%29%0A%20%20%20%20%20%20%20%20for%20edge%20in%20edges%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self.add_vertex%28edge%5B0%5D%29%0A%20%20%20%20%20%20%20%20%20%20%20%20self.add_vertex%28edge%5B1%5D%29%0A%20%20%20%20%20%20%20%20%20%20%20%20self.add_edge%28edge%5B0%5D%2C%20edge%5B1%5D%29%0A%0A%20%20%20%20def%20add_edge%28self%2C%20vet1%3A%20Vertex%2C%20vet2%3A%20Vertex%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E6%96%B0%E5%A2%9E%E9%82%8A%22%22%22%0A%20%20%20%20%20%20%20%20if%20vet1%20not%20in%20self.adj_list%20or%20vet2%20not%20in%20self.adj_list%20or%20vet1%20%3D%3D%20vet2%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20ValueError%28%29%0A%20%20%20%20%20%20%20%20self.adj_list%5Bvet1%5D.append%28vet2%29%0A%20%20%20%20%20%20%20%20self.adj_list%5Bvet2%5D.append%28vet1%29%0A%0A%20%20%20%20def%20add_vertex%28self%2C%20vet%3A%20Vertex%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E6%96%B0%E5%A2%9E%E9%A0%82%E9%BB%9E%22%22%22%0A%20%20%20%20%20%20%20%20if%20vet%20in%20self.adj_list%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%0A%20%20%20%20%20%20%20%20self.adj_list%5Bvet%5D%20%3D%20%5B%5D%0A%0A%0Adef%20dfs%28graph%3A%20GraphAdjList%2C%20visited%3A%20set%5BVertex%5D%2C%20res%3A%20list%5BVertex%5D%2C%20vet%3A%20Vertex%29%3A%0A%20%20%20%20%22%22%22%E6%B7%B1%E5%BA%A6%E5%84%AA%E5%85%88%E8%B5%B0%E8%A8%AA%E8%BC%94%E5%8A%A9%E5%87%BD%E5%BC%8F%22%22%22%0A%20%20%20%20res.append%28vet%29%20%20%23%20%E8%A8%98%E9%8C%84%E8%A8%AA%E5%95%8F%E9%A0%82%E9%BB%9E%0A%20%20%20%20visited.add%28vet%29%20%20%23%20%E6%A8%99%E8%A8%98%E8%A9%B2%E9%A0%82%E9%BB%9E%E5%B7%B2%E8%A2%AB%E8%A8%AA%E5%95%8F%0A%20%20%20%20%23%20%E8%B5%B0%E8%A8%AA%E8%A9%B2%E9%A0%82%E9%BB%9E%E7%9A%84%E6%89%80%E6%9C%89%E9%84%B0%E6%8E%A5%E9%A0%82%E9%BB%9E%0A%20%20%20%20for%20adjVet%20in%20graph.adj_list%5Bvet%5D%3A%0A%20%20%20%20%20%20%20%20if%20adjVet%20in%20visited%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20continue%20%20%23%20%E8%B7%B3%E9%81%8E%E5%B7%B2%E8%A2%AB%E8%A8%AA%E5%95%8F%E7%9A%84%E9%A0%82%E9%BB%9E%0A%20%20%20%20%20%20%20%20%23%20%E9%81%9E%E8%BF%B4%E8%A8%AA%E5%95%8F%E9%84%B0%E6%8E%A5%E9%A0%82%E9%BB%9E%0A%20%20%20%20%20%20%20%20dfs%28graph%2C%20visited%2C%20res%2C%20adjVet%29%0A%0A%0Adef%20graph_dfs%28graph%3A%20GraphAdjList%2C%20start_vet%3A%20Vertex%29%20-%3E%20list%5BVertex%5D%3A%0A%20%20%20%20%22%22%22%E6%B7%B1%E5%BA%A6%E5%84%AA%E5%85%88%E8%B5%B0%E8%A8%AA%22%22%22%0A%20%20%20%20%23%20%E4%BD%BF%E7%94%A8%E9%84%B0%E6%8E%A5%E8%A1%A8%E4%BE%86%E8%A1%A8%E7%A4%BA%E5%9C%96%EF%BC%8C%E4%BB%A5%E4%BE%BF%E7%8D%B2%E5%8F%96%E6%8C%87%E5%AE%9A%E9%A0%82%E9%BB%9E%E7%9A%84%E6%89%80%E6%9C%89%E9%84%B0%E6%8E%A5%E9%A0%82%E9%BB%9E%0A%20%20%20%20%23%20%E9%A0%82%E9%BB%9E%E8%B5%B0%E8%A8%AA%E5%BA%8F%E5%88%97%0A%20%20%20%20res%20%3D%20%5B%5D%0A%20%20%20%20%23%20%E9%9B%9C%E6%B9%8A%E8%A1%A8%EF%BC%8C%E7%94%A8%E6%96%BC%E8%A8%98%E9%8C%84%E5%B7%B2%E8%A2%AB%E8%A8%AA%E5%95%8F%E9%81%8E%E7%9A%84%E9%A0%82%E9%BB%9E%0A%20%20%20%20visited%20%3D%20set%5BVertex%5D%28%29%0A%20%20%20%20dfs%28graph%2C%20visited%2C%20res%2C%20start_vet%29%0A%20%20%20%20return%20res%0A%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E7%84%A1%E5%90%91%E5%9C%96%0A%20%20%20%20v%20%3D%20vals_to_vets%28%5B0%2C%201%2C%202%2C%203%2C%204%5D%29%0A%20%20%20%20edges%20%3D%20%5B%0A%20%20%20%20%20%20%20%20%5Bv%5B0%5D%2C%20v%5B1%5D%5D%2C%0A%20%20%20%20%20%20%20%20%5Bv%5B0%5D%2C%20v%5B3%5D%5D%2C%0A%20%20%20%20%20%20%20%20%5Bv%5B1%5D%2C%20v%5B2%5D%5D%2C%0A%20%20%20%20%20%20%20%20%5Bv%5B1%5D%2C%20v%5B4%5D%5D%2C%0A%20%20%20%20%20%20%20%20%5Bv%5B3%5D%2C%20v%5B4%5D%5D%2C%0A%20%20%20%20%5D%0A%20%20%20%20graph%20%3D%20GraphAdjList%28edges%29%0A%0A%20%20%20%20%23%20%E6%B7%B1%E5%BA%A6%E5%84%AA%E5%85%88%E8%B5%B0%E8%A8%AA%0A%20%20%20%20res%20%3D%20graph_dfs%28graph%2C%20v%5B0%5D%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=130&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全螢幕觀看 ></a></div></p>
|
||
</details>
|
||
<p>深度優先走訪的演算法流程如圖 9-12 所示。</p>
|
||
<ul>
|
||
<li><strong>直虛線代表向下遞推</strong>，表示開啟了一個新的遞迴方法來訪問新頂點。</li>
|
||
<li><strong>曲虛線代表向上回溯</strong>，表示此遞迴方法已經返回，回溯到了開啟此方法的位置。</li>
|
||
</ul>
|
||
<p>為了加深理解，建議將圖 9-12 與程式碼結合起來，在腦中模擬（或者用筆畫下來）整個 DFS 過程，包括每個遞迴方法何時開啟、何時返回。</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="4:11"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1"><1></label><label for="__tabbed_4_2"><2></label><label for="__tabbed_4_3"><3></label><label for="__tabbed_4_4"><4></label><label for="__tabbed_4_5"><5></label><label for="__tabbed_4_6"><6></label><label for="__tabbed_4_7"><7></label><label for="__tabbed_4_8"><8></label><label for="__tabbed_4_9"><9></label><label for="__tabbed_4_10"><10></label><label for="__tabbed_4_11"><11></label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../graph_traversal.assets/graph_dfs_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="圖的深度優先走訪步驟" class="animation-figure" src="../graph_traversal.assets/graph_dfs_step1.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../graph_traversal.assets/graph_dfs_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_dfs_step2" class="animation-figure" src="../graph_traversal.assets/graph_dfs_step2.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../graph_traversal.assets/graph_dfs_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_dfs_step3" class="animation-figure" src="../graph_traversal.assets/graph_dfs_step3.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../graph_traversal.assets/graph_dfs_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_dfs_step4" class="animation-figure" src="../graph_traversal.assets/graph_dfs_step4.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../graph_traversal.assets/graph_dfs_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_dfs_step5" class="animation-figure" src="../graph_traversal.assets/graph_dfs_step5.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../graph_traversal.assets/graph_dfs_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_dfs_step6" class="animation-figure" src="../graph_traversal.assets/graph_dfs_step6.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../graph_traversal.assets/graph_dfs_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_dfs_step7" class="animation-figure" src="../graph_traversal.assets/graph_dfs_step7.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../graph_traversal.assets/graph_dfs_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_dfs_step8" class="animation-figure" src="../graph_traversal.assets/graph_dfs_step8.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../graph_traversal.assets/graph_dfs_step9.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_dfs_step9" class="animation-figure" src="../graph_traversal.assets/graph_dfs_step9.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../graph_traversal.assets/graph_dfs_step10.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_dfs_step10" class="animation-figure" src="../graph_traversal.assets/graph_dfs_step10.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../graph_traversal.assets/graph_dfs_step11.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_dfs_step11" class="animation-figure" src="../graph_traversal.assets/graph_dfs_step11.png" /></a></p>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p align="center"> 圖 9-12 圖的深度優先走訪步驟 </p>
|
||
|
||
<div class="admonition question">
|
||
<p class="admonition-title">深度優先走訪的序列是否唯一？</p>
|
||
<p>與廣度優先走訪類似，深度優先走訪序列的順序也不是唯一的。給定某頂點，先往哪個方向探索都可以，即鄰接頂點的順序可以任意打亂，都是深度優先走訪。</p>
|
||
<p>以樹的走訪為例，“根 <span class="arithmatex">\(\rightarrow\)</span> 左 <span class="arithmatex">\(\rightarrow\)</span> 右”“左 <span class="arithmatex">\(\rightarrow\)</span> 根 <span class="arithmatex">\(\rightarrow\)</span> 右”“左 <span class="arithmatex">\(\rightarrow\)</span> 右 <span class="arithmatex">\(\rightarrow\)</span> 根”分別對應前序、中序、後序走訪，它們展示了三種走訪優先順序，然而這三者都屬於深度優先走訪。</p>
|
||
</div>
|
||
<h3 id="2_1">2. 複雜度分析<a class="headerlink" href="#2_1" title="Permanent link">¶</a></h3>
|
||
<p><strong>時間複雜度</strong>：所有頂點都會被訪問 <span class="arithmatex">\(1\)</span> 次，使用 <span class="arithmatex">\(O(|V|)\)</span> 時間；所有邊都會被訪問 <span class="arithmatex">\(2\)</span> 次，使用 <span class="arithmatex">\(O(2|E|)\)</span> 時間；總體使用 <span class="arithmatex">\(O(|V| + |E|)\)</span> 時間。</p>
|
||
<p><strong>空間複雜度</strong>：串列 <code>res</code> ，雜湊表 <code>visited</code> 頂點數量最多為 <span class="arithmatex">\(|V|\)</span> ，遞迴深度最大為 <span class="arithmatex">\(|V|\)</span> ，因此使用 <span class="arithmatex">\(O(|V|)\)</span> 空間。</p>
|
||
|
||
<!-- Source file information -->
|
||
|
||
|
||
<!-- Was this page helpful? -->
|
||
|
||
|
||
|
||
|
||
<!-- Previous and next pages link -->
|
||
<nav
|
||
class="md-footer__inner md-grid"
|
||
aria-label="頁脚"
|
||
|
||
>
|
||
|
||
<!-- Link to previous page -->
|
||
|
||
|
||
<a
|
||
href="../graph_operations/"
|
||
class="md-footer__link md-footer__link--prev"
|
||
aria-label="上一頁: 9.2 &nbsp; 圖基礎操作"
|
||
rel="prev"
|
||
>
|
||
<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 11h12Z"/></svg>
|
||
</div>
|
||
<div class="md-footer__title">
|
||
<span class="md-footer__direction">
|
||
上一頁
|
||
</span>
|
||
<div class="md-ellipsis">
|
||
9.2 圖基礎操作
|
||
</div>
|
||
</div>
|
||
</a>
|
||
|
||
|
||
<!-- Link to next page -->
|
||
|
||
|
||
<a
|
||
href="../summary/"
|
||
class="md-footer__link md-footer__link--next"
|
||
aria-label="下一頁: 9.4 &nbsp; 小結"
|
||
rel="next"
|
||
>
|
||
<div class="md-footer__title">
|
||
<span class="md-footer__direction">
|
||
下一頁
|
||
</span>
|
||
<div class="md-ellipsis">
|
||
9.4 小結
|
||
</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 11H4Z"/></svg>
|
||
</div>
|
||
</a>
|
||
|
||
</nav>
|
||
|
||
<!-- Comment system -->
|
||
|
||
|
||
|
||
<h5 align="center" id="__comments"></h5>
|
||
|
||
<!-- Insert generated snippet here -->
|
||
<script
|
||
src="https://giscus.app/client.js"
|
||
data-repo="krahets/hello-algo"
|
||
data-repo-id="R_kgDOIXtSqw"
|
||
data-category="Announcements"
|
||
data-category-id="DIC_kwDOIXtSq84CSZk_"
|
||
data-mapping="pathname"
|
||
data-strict="1"
|
||
data-reactions-enabled="1"
|
||
data-emit-metadata="0"
|
||
data-input-position="top"
|
||
data-theme="light"
|
||
data-lang="
|
||
|
||
"
|
||
crossorigin="anonymous"
|
||
async
|
||
>
|
||
</script>
|
||
<!-- Synchronize Giscus theme with palette -->
|
||
<script>
|
||
var giscus = document.querySelector("script[src*=giscus]")
|
||
|
||
/* Set palette on initial load */
|
||
var palette = __md_get("__palette")
|
||
if (palette && typeof palette.color === "object") {
|
||
var theme = palette.color.scheme === "slate" ? "dark_dimmed" : "light"
|
||
giscus.setAttribute("data-theme", theme)
|
||
}
|
||
|
||
/* Register event handlers after documented loaded */
|
||
document.addEventListener("DOMContentLoaded", function() {
|
||
var ref = document.querySelector("[data-md-component=palette]")
|
||
ref.addEventListener("change", function() {
|
||
var palette = __md_get("__palette")
|
||
if (palette && typeof palette.color === "object") {
|
||
var theme = palette.color.scheme === "slate" ? "dark_dimmed" : "light"
|
||
|
||
/* Instruct Giscus to change theme */
|
||
var frame = document.querySelector(".giscus-frame")
|
||
frame.contentWindow.postMessage(
|
||
{ giscus: { setConfig: { theme } } },
|
||
"https://giscus.app"
|
||
)
|
||
}
|
||
})
|
||
})
|
||
</script>
|
||
|
||
|
||
</article>
|
||
</div>
|
||
|
||
|
||
<script>var tabs=__md_get("__tabs");if(Array.isArray(tabs))e:for(var set of document.querySelectorAll(".tabbed-set")){var tab,labels=set.querySelector(".tabbed-labels");for(tab of tabs)for(var label of labels.getElementsByTagName("label"))if(label.innerText.trim()===tab){var input=document.getElementById(label.htmlFor);input.checked=!0;continue e}}</script>
|
||
|
||
<script>var target=document.getElementById(location.hash.slice(1));target&&target.name&&(target.checked=target.name.startsWith("__tabbed_"))</script>
|
||
</div>
|
||
|
||
<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 8v12Z"/></svg>
|
||
回到頂部
|
||
</button>
|
||
|
||
</main>
|
||
|
||
<footer class="md-footer">
|
||
|
||
|
||
|
||
<nav class="md-footer__inner md-grid" aria-label="頁脚" >
|
||
|
||
|
||
<a href="../graph_operations/" class="md-footer__link md-footer__link--prev" aria-label="上一頁: 9.2 &nbsp; 圖基礎操作">
|
||
<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 11h12Z"/></svg>
|
||
</div>
|
||
<div class="md-footer__title">
|
||
<span class="md-footer__direction">
|
||
上一頁
|
||
</span>
|
||
<div class="md-ellipsis">
|
||
9.2 圖基礎操作
|
||
</div>
|
||
</div>
|
||
</a>
|
||
|
||
|
||
|
||
<a href="../summary/" class="md-footer__link md-footer__link--next" aria-label="下一頁: 9.4 &nbsp; 小結">
|
||
<div class="md-footer__title">
|
||
<span class="md-footer__direction">
|
||
下一頁
|
||
</span>
|
||
<div class="md-ellipsis">
|
||
9.4 小結
|
||
</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 11H4Z"/></svg>
|
||
</div>
|
||
</a>
|
||
|
||
</nav>
|
||
|
||
|
||
<div class="md-footer-meta md-typeset">
|
||
<div class="md-footer-meta__inner md-grid">
|
||
<div class="md-copyright">
|
||
|
||
<div class="md-copyright__highlight">
|
||
Copyright © 2022-2024 krahets<br>The website content is licensed under <a href="https://creativecommons.org/licenses/by-nc-sa/4.0/">CC BY-NC-SA 4.0</a>
|
||
</div>
|
||
|
||
|
||
</div>
|
||
|
||
<div class="md-social">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<a href="https://github.com/krahets" target="_blank" rel="noopener" title="github.com" class="md-social__link">
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 496 512"><!--! Font Awesome Free 6.5.1 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 2023 Fonticons, Inc.--><path d="M165.9 397.4c0 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 3.6zm-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 2.3zm44.2-1.7c-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-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 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 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-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-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-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-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg>
|
||
</a>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<a href="https://twitter.com/krahets" target="_blank" rel="noopener" title="twitter.com" class="md-social__link">
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 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 2023 Fonticons, Inc.--><path d="M389.2 48h70.6L305.6 224.2 487 464H345L233.7 318.6 106.5 464H35.8l164.9-188.5L26.8 48h145.6l100.5 132.9L389.2 48zm-24.8 373.8h39.1L151.1 88h-42l255.3 333.8z"/></svg>
|
||
</a>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<a href="https://leetcode.cn/u/jyd/" target="_blank" rel="noopener" title="leetcode.cn" class="md-social__link">
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 640 512"><!--! Font Awesome Free 6.5.1 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 2023 Fonticons, Inc.--><path d="M392.8 1.2c-17-4.9-34.7 5-39.6 22l-128 448c-4.9 17 5 34.7 22 39.6s34.7-5 39.6-22l128-448c4.9-17-5-34.7-22-39.6zm80.6 120.1c-12.5 12.5-12.5 32.8 0 45.3l89.3 89.4-89.4 89.4c-12.5 12.5-12.5 32.8 0 45.3s32.8 12.5 45.3 0l112-112c12.5-12.5 12.5-32.8 0-45.3l-112-112c-12.5-12.5-32.8-12.5-45.3 0zm-306.7 0c-12.5-12.5-32.8-12.5-45.3 0l-112 112c-12.5 12.5-12.5 32.8 0 45.3l112 112c12.5 12.5 32.8 12.5 45.3 0s12.5-32.8 0-45.3L77.3 256l89.4-89.4c12.5-12.5 12.5-32.8 0-45.3z"/></svg>
|
||
</a>
|
||
|
||
</div>
|
||
|
||
</div>
|
||
</div>
|
||
</footer>
|
||
|
||
</div>
|
||
<div class="md-dialog" data-md-component="dialog">
|
||
<div class="md-dialog__inner md-typeset"></div>
|
||
</div>
|
||
|
||
|
||
<script id="__config" type="application/json">{"base": "../..", "features": ["announce.dismiss", "content.action.edit", "content.code.annotate", "content.code.copy", "content.tabs.link", "content.tooltips", "navigation.indexes", "navigation.top", "navigation.footer", "navigation.tracking", "search.highlight", "search.share", "search.suggest", "toc.follow"], "search": "../../assets/javascripts/workers/search.b8dbb3d2.min.js", "translations": {"clipboard.copied": "\u5df2\u62f7\u8c9d", "clipboard.copy": "\u62f7\u8c9d", "search.result.more.one": "\u6b64\u9801\u5c1a\u6709 1 \u500b\u7b26\u5408\u7684\u9805\u76ee", "search.result.more.other": "\u6b64\u9801\u5c1a\u6709 # \u500b\u7b26\u5408\u7684\u9805\u76ee", "search.result.none": "\u6c92\u6709\u627e\u5230\u7b26\u5408\u689d\u4ef6\u7684\u7d50\u679c", "search.result.one": "\u627e\u5230 1 \u4e2a\u7b26\u5408\u689d\u4ef6\u7684\u7d50\u679c", "search.result.other": "\u627e\u5230 # \u500b\u7b26\u5408\u689d\u4ef6\u7684\u7d50\u679c", "search.result.placeholder": "\u9375\u5165\u4ee5\u958b\u59cb\u6aa2\u7d22", "search.result.term.missing": "\u7f3a\u5931", "select.version": "\u9078\u64c7\u7248\u672c"}}</script>
|
||
|
||
|
||
<script src="../../assets/javascripts/bundle.c18c5fb9.min.js"></script>
|
||
|
||
<script src="../../javascripts/mathjax.js"></script>
|
||
|
||
<script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
|
||
|
||
<script src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
|
||
|
||
|
||
<script>document$.subscribe(() => {const lightbox = GLightbox({"touchNavigation": true, "loop": false, "zoomable": true, "draggable": false, "openEffect": "zoom", "closeEffect": "zoom", "slideEffect": "none"});})</script></body>
|
||
</html> |