mirror of
https://github.com/krahets/hello-algo.git
synced 2024-12-26 14:26:29 +08:00
5402 lines
No EOL
430 KiB
HTML
5402 lines
No EOL
430 KiB
HTML
|
||
<!doctype html>
|
||
<html lang="zh" class="no-js">
|
||
<head>
|
||
|
||
<meta charset="utf-8">
|
||
<meta name="viewport" content="width=device-width,initial-scale=1">
|
||
|
||
<meta name="description" content="动画图解、一键运行的数据结构与算法教程">
|
||
|
||
|
||
<meta name="author" content="Krahets">
|
||
|
||
|
||
<link rel="canonical" href="https://www.hello-algo.com/chapter_heap/heap/">
|
||
|
||
|
||
<link rel="prev" href="../">
|
||
|
||
|
||
<link rel="next" href="../build_heap/">
|
||
|
||
|
||
<link rel="icon" href="../../assets/images/favicon.png">
|
||
<meta name="generator" content="mkdocs-1.5.3, mkdocs-material-9.5.2">
|
||
|
||
|
||
|
||
<title>8.1 堆 - Hello 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="indigo">
|
||
|
||
|
||
<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="#81" class="md-skip">
|
||
跳转至
|
||
</a>
|
||
|
||
</div>
|
||
<div data-md-component="announce">
|
||
|
||
</div>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<header class="md-header md-header--shadow" data-md-component="header">
|
||
<nav class="md-header__inner md-grid" aria-label="页眉">
|
||
<a href="../.." title="Hello 算法" class="md-header__button md-logo" aria-label="Hello 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 算法
|
||
</span>
|
||
</div>
|
||
<div class="md-header__topic" data-md-component="header-topic">
|
||
<span class="md-ellipsis">
|
||
|
||
8.1 堆
|
||
|
||
</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="indigo" aria-label="Switch to dark mode" type="radio" name="__palette" id="__palette_0">
|
||
|
||
<label class="md-header__button md-icon" title="Switch to dark mode" 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="grey" data-md-color-accent="indigo" aria-label="Switch to light mode" type="radio" name="__palette" id="__palette_1">
|
||
|
||
<label class="md-header__button md-icon" title="Switch to light mode" 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="选择当前语言">
|
||
<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">
|
||
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="搜索" placeholder="搜索" 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="查找">
|
||
|
||
<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="清空当前内容" aria-label="清空当前内容" 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">
|
||
正在初始化搜索引擎
|
||
</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="前往仓库" 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="导航栏" data-md-level="0">
|
||
<label class="md-nav__title" for="__drawer">
|
||
<a href="../.." title="Hello 算法" class="md-nav__button md-logo" aria-label="Hello 算法" data-md-component="logo">
|
||
|
||
<img src="../../assets/images/logo.svg" alt="logo">
|
||
|
||
</a>
|
||
Hello 算法
|
||
</label>
|
||
|
||
<div class="md-nav__source">
|
||
<a href="https://github.com/krahets/hello-algo" title="前往仓库" 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_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_1" id="__nav_1_label" tabindex="0">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</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>
|
||
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 关于本书
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_preface/suggestions/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
0.2 如何使用本书
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_preface/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
0.3 小结
|
||
</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_2" >
|
||
|
||
|
||
|
||
<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 初识算法
|
||
</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 1 章 初识算法
|
||
</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 算法无处不在
|
||
</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 算法是什么
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_introduction/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
1.3 小结
|
||
</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_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 复杂度分析
|
||
</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 2 章 复杂度分析
|
||
</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 算法效率评估
|
||
</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 迭代与递归
|
||
</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 时间复杂度
|
||
</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 空间复杂度
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
2.5 小结
|
||
</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_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 数据结构
|
||
</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 3 章 数据结构
|
||
</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 数据结构分类
|
||
</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 基本数据类型
|
||
</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 数字编码 *
|
||
</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 字符编码 *
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_data_structure/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
3.5 小结
|
||
</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_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 数组与链表
|
||
</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 4 章 数组与链表
|
||
</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 数组
|
||
</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 链表
|
||
</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 列表
|
||
</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 内存与缓存 *
|
||
</span>
|
||
|
||
|
||
|
||
|
||
<span class="md-status md-status--new" title="最近添加">
|
||
</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 小结
|
||
</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_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 栈与队列
|
||
</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 5 章 栈与队列
|
||
</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 栈
|
||
</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 队列
|
||
</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 双向队列
|
||
</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 小结
|
||
</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_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 哈希表
|
||
</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 6 章 哈希表
|
||
</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 哈希表
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
6.2 哈希冲突
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
6.3 哈希算法
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_hashing/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
6.4 小结
|
||
</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_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 树
|
||
</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 7 章 树
|
||
</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 二叉树
|
||
</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 二叉树遍历
|
||
</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 二叉树数组表示
|
||
</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 二叉搜索树
|
||
</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 树 *
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_tree/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
7.6 小结
|
||
</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_9" 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 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
|
||
</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="true">
|
||
<label class="md-nav__title" for="__nav_9">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
第 8 章 堆
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<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">
|
||
8.1 堆
|
||
</span>
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<a href="./" class="md-nav__link md-nav__link--active">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
8.1 堆
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
|
||
|
||
<nav class="md-nav md-nav--secondary" aria-label="目录">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__title" for="__toc">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
目录
|
||
</label>
|
||
<ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#811" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
8.1.1 堆的常用操作
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#812" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
8.1.2 堆的实现
|
||
</span>
|
||
</a>
|
||
|
||
<nav class="md-nav" aria-label="8.1.2 堆的实现">
|
||
<ul class="md-nav__list">
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#1" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
1. 堆的存储与表示
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#2" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
2. 访问堆顶元素
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#3" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
3. 元素入堆
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#4" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
4. 堆顶元素出堆
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#813" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
8.1.3 堆的常见应用
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../build_heap/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
8.2 建堆操作
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../top_k/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
8.3 Top-k 问题
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
8.4 小结
|
||
</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_graph/" 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 图
|
||
</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 9 章 图
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_graph/graph/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
9.1 图
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_graph/graph_operations/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
9.2 图基础操作
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
9.3 图的遍历
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_graph/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
9.4 小结
|
||
</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_11" >
|
||
|
||
|
||
|
||
<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 搜索
|
||
</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="false">
|
||
<label class="md-nav__title" for="__nav_11">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
第 10 章 搜索
|
||
</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 二分查找
|
||
</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 二分查找插入点
|
||
</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 二分查找边界
|
||
</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 哈希优化策略
|
||
</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 重识搜索算法
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.6 小结
|
||
</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_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_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 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 选择排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.3 冒泡排序
|
||
</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 归并排序
|
||
</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 计数排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.10 基数排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.11 小结
|
||
</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_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_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 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 分治搜索策略
|
||
</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 构建树问题
|
||
</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 汉诺塔问题
|
||
</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 小结
|
||
</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_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_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 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 全排列问题
|
||
</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 子集和问题
|
||
</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 皇后问题
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_backtracking/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
13.5 小结
|
||
</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_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 动态规划
|
||
</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 14 章 动态规划
|
||
</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 初探动态规划
|
||
</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 问题特性
|
||
</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 解题思路
|
||
</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 背包问题
|
||
</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 完全背包问题
|
||
</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 编辑距离问题
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
14.7 小结
|
||
</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_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 贪心
|
||
</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 15 章 贪心
|
||
</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 贪心算法
|
||
</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 分数背包问题
|
||
</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 最大容量问题
|
||
</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 最大切分乘积问题
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_greedy/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
15.5 小结
|
||
</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_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 附录
|
||
</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 16 章 附录
|
||
</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 编程环境安装
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_appendix/contribution/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
16.2 一起参与创作
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_appendix/terminology/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
16.3 术语表
|
||
</span>
|
||
|
||
|
||
|
||
|
||
<span class="md-status md-status--new" title="最近添加">
|
||
</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_reference/" class="md-nav__link ">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
参考文献
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
</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>
|
||
参考文献
|
||
</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="目录">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__title" for="__toc">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
目录
|
||
</label>
|
||
<ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#811" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
8.1.1 堆的常用操作
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#812" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
8.1.2 堆的实现
|
||
</span>
|
||
</a>
|
||
|
||
<nav class="md-nav" aria-label="8.1.2 堆的实现">
|
||
<ul class="md-nav__list">
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#1" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
1. 堆的存储与表示
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#2" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
2. 访问堆顶元素
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#3" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
3. 元素入堆
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#4" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
4. 堆顶元素出堆
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#813" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
8.1.3 堆的常见应用
|
||
</span>
|
||
</a>
|
||
|
||
</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/docs/chapter_heap/heap.md"
|
||
title="编辑此页"
|
||
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="81">8.1 堆<a class="headerlink" href="#81" title="Permanent link">¶</a></h1>
|
||
<p>「堆 heap」是一种满足特定条件的完全二叉树，主要可分为两种类型，如图 8-1 所示。</p>
|
||
<ul>
|
||
<li>「小顶堆 min heap」：任意节点的值 <span class="arithmatex">\(\leq\)</span> 其子节点的值。</li>
|
||
<li>「大顶堆 max heap」：任意节点的值 <span class="arithmatex">\(\geq\)</span> 其子节点的值。</li>
|
||
</ul>
|
||
<p><a class="glightbox" href="../heap.assets/min_heap_and_max_heap.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="小顶堆与大顶堆" class="animation-figure" src="../heap.assets/min_heap_and_max_heap.png" /></a></p>
|
||
<p align="center"> 图 8-1 小顶堆与大顶堆 </p>
|
||
|
||
<p>堆作为完全二叉树的一个特例，具有以下特性。</p>
|
||
<ul>
|
||
<li>最底层节点靠左填充，其他层的节点都被填满。</li>
|
||
<li>我们将二叉树的根节点称为“堆顶”，将底层最靠右的节点称为“堆底”。</li>
|
||
<li>对于大顶堆（小顶堆），堆顶元素（根节点）的值是最大（最小）的。</li>
|
||
</ul>
|
||
<h2 id="811">8.1.1 堆的常用操作<a class="headerlink" href="#811" title="Permanent link">¶</a></h2>
|
||
<p>需要指出的是，许多编程语言提供的是「优先队列 priority queue」，这是一种抽象的数据结构，定义为具有优先级排序的队列。</p>
|
||
<p>实际上，<strong>堆通常用于实现优先队列，大顶堆相当于元素按从大到小的顺序出队的优先队列</strong>。从使用角度来看，我们可以将“优先队列”和“堆”看作等价的数据结构。因此，本书对两者不做特别区分，统一称作“堆”。</p>
|
||
<p>堆的常用操作见表 8-1 ，方法名需要根据编程语言来确定。</p>
|
||
<p align="center"> 表 8-1 堆的操作效率 </p>
|
||
|
||
<div class="center-table">
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>方法名</th>
|
||
<th>描述</th>
|
||
<th>时间复杂度</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr>
|
||
<td><code>push()</code></td>
|
||
<td>元素入堆</td>
|
||
<td><span class="arithmatex">\(O(\log n)\)</span></td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>pop()</code></td>
|
||
<td>堆顶元素出堆</td>
|
||
<td><span class="arithmatex">\(O(\log n)\)</span></td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>peek()</code></td>
|
||
<td>访问堆顶元素（对于大 / 小顶堆分别为最大 / 小值）</td>
|
||
<td><span class="arithmatex">\(O(1)\)</span></td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>size()</code></td>
|
||
<td>获取堆的元素数量</td>
|
||
<td><span class="arithmatex">\(O(1)\)</span></td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>isEmpty()</code></td>
|
||
<td>判断堆是否为空</td>
|
||
<td><span class="arithmatex">\(O(1)\)</span></td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
</div>
|
||
<p>在实际应用中，我们可以直接使用编程语言提供的堆类（或优先队列类）。</p>
|
||
<p>类似于排序算法中的“从小到大排列”和“从大到小排列”，我们可以通过设置一个 <code>flag</code> 或修改 <code>Comparator</code> 实现“小顶堆”与“大顶堆”之间的转换。代码如下所示：</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="1:12"><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" /><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">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">heap.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># 初始化小顶堆</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="n">min_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">=</span> <span class="p">[],</span> <span class="mi">1</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="c1"># 初始化大顶堆</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="n">max_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">=</span> <span class="p">[],</span> <span class="o">-</span><span class="mi">1</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="c1"># Python 的 heapq 模块默认实现小顶堆</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="c1"># 考虑将“元素取负”后再入堆，这样就可以将大小关系颠倒，从而实现大顶堆</span>
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="c1"># 在本示例中，flag = 1 时对应小顶堆，flag = -1 时对应大顶堆</span>
|
||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>
|
||
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="c1"># 元素入堆</span>
|
||
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a><span class="n">heapq</span><span class="o">.</span><span class="n">heappush</span><span class="p">(</span><span class="n">max_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">*</span> <span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="n">heapq</span><span class="o">.</span><span class="n">heappush</span><span class="p">(</span><span class="n">max_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">*</span> <span class="mi">3</span><span class="p">)</span>
|
||
<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a><span class="n">heapq</span><span class="o">.</span><span class="n">heappush</span><span class="p">(</span><span class="n">max_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">*</span> <span class="mi">2</span><span class="p">)</span>
|
||
<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a><span class="n">heapq</span><span class="o">.</span><span class="n">heappush</span><span class="p">(</span><span class="n">max_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">*</span> <span class="mi">5</span><span class="p">)</span>
|
||
<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a><span class="n">heapq</span><span class="o">.</span><span class="n">heappush</span><span class="p">(</span><span class="n">max_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">*</span> <span class="mi">4</span><span class="p">)</span>
|
||
<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>
|
||
<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a><span class="c1"># 获取堆顶元素</span>
|
||
<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a><span class="n">peek</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">flag</span> <span class="o">*</span> <span class="n">max_heap</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="c1"># 5</span>
|
||
<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>
|
||
<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a><span class="c1"># 堆顶元素出堆</span>
|
||
<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a><span class="c1"># 出堆元素会形成一个从大到小的序列</span>
|
||
<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a><span class="n">val</span> <span class="o">=</span> <span class="n">flag</span> <span class="o">*</span> <span class="n">heapq</span><span class="o">.</span><span class="n">heappop</span><span class="p">(</span><span class="n">max_heap</span><span class="p">)</span> <span class="c1"># 5</span>
|
||
<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a><span class="n">val</span> <span class="o">=</span> <span class="n">flag</span> <span class="o">*</span> <span class="n">heapq</span><span class="o">.</span><span class="n">heappop</span><span class="p">(</span><span class="n">max_heap</span><span class="p">)</span> <span class="c1"># 4</span>
|
||
<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a><span class="n">val</span> <span class="o">=</span> <span class="n">flag</span> <span class="o">*</span> <span class="n">heapq</span><span class="o">.</span><span class="n">heappop</span><span class="p">(</span><span class="n">max_heap</span><span class="p">)</span> <span class="c1"># 3</span>
|
||
<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a><span class="n">val</span> <span class="o">=</span> <span class="n">flag</span> <span class="o">*</span> <span class="n">heapq</span><span class="o">.</span><span class="n">heappop</span><span class="p">(</span><span class="n">max_heap</span><span class="p">)</span> <span class="c1"># 2</span>
|
||
<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a><span class="n">val</span> <span class="o">=</span> <span class="n">flag</span> <span class="o">*</span> <span class="n">heapq</span><span class="o">.</span><span class="n">heappop</span><span class="p">(</span><span class="n">max_heap</span><span class="p">)</span> <span class="c1"># 1</span>
|
||
<a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a>
|
||
<a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a><span class="c1"># 获取堆大小</span>
|
||
<a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a><span class="n">size</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">max_heap</span><span class="p">)</span>
|
||
<a id="__codelineno-0-30" name="__codelineno-0-30" href="#__codelineno-0-30"></a>
|
||
<a id="__codelineno-0-31" name="__codelineno-0-31" href="#__codelineno-0-31"></a><span class="c1"># 判断堆是否为空</span>
|
||
<a id="__codelineno-0-32" name="__codelineno-0-32" href="#__codelineno-0-32"></a><span class="n">is_empty</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="ow">not</span> <span class="n">max_heap</span>
|
||
<a id="__codelineno-0-33" name="__codelineno-0-33" href="#__codelineno-0-33"></a>
|
||
<a id="__codelineno-0-34" name="__codelineno-0-34" href="#__codelineno-0-34"></a><span class="c1"># 输入列表并建堆</span>
|
||
<a id="__codelineno-0-35" name="__codelineno-0-35" href="#__codelineno-0-35"></a><span class="n">min_heap</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">4</span><span class="p">]</span>
|
||
<a id="__codelineno-0-36" name="__codelineno-0-36" href="#__codelineno-0-36"></a><span class="n">heapq</span><span class="o">.</span><span class="n">heapify</span><span class="p">(</span><span class="n">min_heap</span><span class="p">)</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">heap.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 初始化堆 */</span>
|
||
<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="c1">// 初始化小顶堆</span>
|
||
<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="n">priority_queue</span><span class="o"><</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="p">,</span><span class="w"> </span><span class="n">greater</span><span class="o"><</span><span class="kt">int</span><span class="o">>></span><span class="w"> </span><span class="n">minHeap</span><span class="p">;</span>
|
||
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="c1">// 初始化大顶堆</span>
|
||
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="n">priority_queue</span><span class="o"><</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="p">,</span><span class="w"> </span><span class="n">less</span><span class="o"><</span><span class="kt">int</span><span class="o">>></span><span class="w"> </span><span class="n">maxHeap</span><span class="p">;</span>
|
||
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a>
|
||
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="cm">/* 元素入堆 */</span>
|
||
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
|
||
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
|
||
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
|
||
<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
|
||
<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
|
||
<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a>
|
||
<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="cm">/* 获取堆顶元素 */</span>
|
||
<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">top</span><span class="p">();</span><span class="w"> </span><span class="c1">// 5</span>
|
||
<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a>
|
||
<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="cm">/* 堆顶元素出堆 */</span>
|
||
<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="c1">// 出堆元素会形成一个从大到小的序列</span>
|
||
<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span><span class="w"> </span><span class="c1">// 5</span>
|
||
<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span><span class="w"> </span><span class="c1">// 4</span>
|
||
<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span><span class="w"> </span><span class="c1">// 3</span>
|
||
<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span><span class="w"> </span><span class="c1">// 2</span>
|
||
<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span><span class="w"> </span><span class="c1">// 1</span>
|
||
<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a>
|
||
<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="cm">/* 获取堆大小 */</span>
|
||
<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
|
||
<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a>
|
||
<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="cm">/* 判断堆是否为空 */</span>
|
||
<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">empty</span><span class="p">();</span>
|
||
<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a>
|
||
<a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a><span class="cm">/* 输入列表并建堆 */</span>
|
||
<a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">input</span><span class="p">{</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">};</span>
|
||
<a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a><span class="n">priority_queue</span><span class="o"><</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="p">,</span><span class="w"> </span><span class="n">greater</span><span class="o"><</span><span class="kt">int</span><span class="o">>></span><span class="w"> </span><span class="n">minHeap</span><span class="p">(</span><span class="n">input</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">input</span><span class="p">.</span><span class="n">end</span><span class="p">());</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">heap.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 初始化堆 */</span>
|
||
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="c1">// 初始化小顶堆</span>
|
||
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="n">Queue</span><span class="o"><</span><span class="n">Integer</span><span class="o">></span><span class="w"> </span><span class="n">minHeap</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">PriorityQueue</span><span class="o"><></span><span class="p">();</span>
|
||
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="c1">// 初始化大顶堆（使用 lambda 表达式修改 Comparator 即可）</span>
|
||
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="n">Queue</span><span class="o"><</span><span class="n">Integer</span><span class="o">></span><span class="w"> </span><span class="n">maxHeap</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">PriorityQueue</span><span class="o"><></span><span class="p">((</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="p">)</span><span class="w"> </span><span class="o">-></span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">a</span><span class="p">);</span>
|
||
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a>
|
||
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="cm">/* 元素入堆 */</span>
|
||
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
|
||
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
|
||
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
|
||
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
|
||
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
|
||
<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a>
|
||
<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="cm">/* 获取堆顶元素 */</span>
|
||
<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">peek</span><span class="p">();</span><span class="w"> </span><span class="c1">// 5</span>
|
||
<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a>
|
||
<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="cm">/* 堆顶元素出堆 */</span>
|
||
<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="c1">// 出堆元素会形成一个从大到小的序列</span>
|
||
<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span><span class="w"> </span><span class="c1">// 5</span>
|
||
<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span><span class="w"> </span><span class="c1">// 4</span>
|
||
<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span><span class="w"> </span><span class="c1">// 3</span>
|
||
<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span><span class="w"> </span><span class="c1">// 2</span>
|
||
<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span><span class="w"> </span><span class="c1">// 1</span>
|
||
<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a>
|
||
<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="cm">/* 获取堆大小 */</span>
|
||
<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">size</span><span class="p">();</span>
|
||
<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a>
|
||
<a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="cm">/* 判断堆是否为空 */</span>
|
||
<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="kt">boolean</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">isEmpty</span><span class="p">();</span>
|
||
<a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a>
|
||
<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a><span class="cm">/* 输入列表并建堆 */</span>
|
||
<a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a><span class="n">minHeap</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">PriorityQueue</span><span class="o"><></span><span class="p">(</span><span class="n">Arrays</span><span class="p">.</span><span class="na">asList</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">));</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">heap.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 初始化堆 */</span>
|
||
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="c1">// 初始化小顶堆</span>
|
||
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="n">PriorityQueue</span><span class="o"><</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">minHeap</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-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="c1">// 初始化大顶堆（使用 lambda 表达式修改 Comparator 即可）</span>
|
||
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="n">PriorityQueue</span><span class="o"><</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">maxHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="n">Comparer</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="p">.</span><span class="n">Create</span><span class="p">((</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">y</span><span class="p">)</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="n">y</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">x</span><span class="p">));</span>
|
||
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a>
|
||
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="cm">/* 元素入堆 */</span>
|
||
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
|
||
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="m">3</span><span class="p">,</span><span class="w"> </span><span class="m">3</span><span class="p">);</span>
|
||
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="m">2</span><span class="p">);</span>
|
||
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="m">5</span><span class="p">,</span><span class="w"> </span><span class="m">5</span><span class="p">);</span>
|
||
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="m">4</span><span class="p">,</span><span class="w"> </span><span class="m">4</span><span class="p">);</span>
|
||
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a>
|
||
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="cm">/* 获取堆顶元素 */</span>
|
||
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Peek</span><span class="p">();</span><span class="c1">//5</span>
|
||
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a>
|
||
<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="cm">/* 堆顶元素出堆 */</span>
|
||
<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="c1">// 出堆元素会形成一个从大到小的序列</span>
|
||
<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Dequeue</span><span class="p">();</span><span class="w"> </span><span class="c1">// 5</span>
|
||
<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Dequeue</span><span class="p">();</span><span class="w"> </span><span class="c1">// 4</span>
|
||
<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Dequeue</span><span class="p">();</span><span class="w"> </span><span class="c1">// 3</span>
|
||
<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Dequeue</span><span class="p">();</span><span class="w"> </span><span class="c1">// 2</span>
|
||
<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Dequeue</span><span class="p">();</span><span class="w"> </span><span class="c1">// 1</span>
|
||
<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a>
|
||
<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="cm">/* 获取堆大小 */</span>
|
||
<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Count</span><span class="p">;</span>
|
||
<a id="__codelineno-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></a>
|
||
<a id="__codelineno-3-28" name="__codelineno-3-28" href="#__codelineno-3-28"></a><span class="cm">/* 判断堆是否为空 */</span>
|
||
<a id="__codelineno-3-29" name="__codelineno-3-29" href="#__codelineno-3-29"></a><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</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>
|
||
<a id="__codelineno-3-30" name="__codelineno-3-30" href="#__codelineno-3-30"></a>
|
||
<a id="__codelineno-3-31" name="__codelineno-3-31" href="#__codelineno-3-31"></a><span class="cm">/* 输入列表并建堆 */</span>
|
||
<a id="__codelineno-3-32" name="__codelineno-3-32" href="#__codelineno-3-32"></a><span class="n">minHeap</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">PriorityQueue</span><span class="o"><</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">></span><span class="p">([(</span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">1</span><span class="p">),</span><span class="w"> </span><span class="p">(</span><span class="m">3</span><span class="p">,</span><span class="w"> </span><span class="m">3</span><span class="p">),</span><span class="w"> </span><span class="p">(</span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="m">2</span><span class="p">),</span><span class="w"> </span><span class="p">(</span><span class="m">5</span><span class="p">,</span><span class="w"> </span><span class="m">5</span><span class="p">),</span><span class="w"> </span><span class="p">(</span><span class="m">4</span><span class="p">,</span><span class="w"> </span><span class="m">4</span><span class="p">)]);</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">heap.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="c1">// Go 语言中可以通过实现 heap.Interface 来构建整数大顶堆</span>
|
||
<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="c1">// 实现 heap.Interface 需要同时实现 sort.Interface</span>
|
||
<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="kd">type</span><span class="w"> </span><span class="nx">intHeap</span><span class="w"> </span><span class="p">[]</span><span class="kt">any</span>
|
||
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a>
|
||
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="c1">// Push heap.Interface 的方法，实现推入元素到堆</span>
|
||
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">intHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">Push</span><span class="p">(</span><span class="nx">x</span><span class="w"> </span><span class="kt">any</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w"> </span><span class="c1">// Push 和 Pop 使用 pointer receiver 作为参数</span>
|
||
<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w"> </span><span class="c1">// 因为它们不仅会对切片的内容进行调整，还会修改切片的长度。</span>
|
||
<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w"> </span><span class="o">*</span><span class="nx">h</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">h</span><span class="p">,</span><span class="w"> </span><span class="nx">x</span><span class="p">.(</span><span class="kt">int</span><span class="p">))</span>
|
||
<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="p">}</span>
|
||
<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a>
|
||
<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="c1">// Pop heap.Interface 的方法，实现弹出堆顶元素</span>
|
||
<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">intHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">Pop</span><span class="p">()</span><span class="w"> </span><span class="kt">any</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">// 待出堆元素存放在最后</span>
|
||
<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w"> </span><span class="nx">last</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)</span><span class="o">-</span><span class="mi">1</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="o">*</span><span class="nx">h</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[:</span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)</span><span class="o">-</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="k">return</span><span class="w"> </span><span class="nx">last</span>
|
||
<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="p">}</span>
|
||
<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a>
|
||
<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="c1">// Len sort.Interface 的方法</span>
|
||
<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">intHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">Len</span><span class="p">()</span><span class="w"> </span><span class="kt">int</span><span class="w"> </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="k">return</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)</span>
|
||
<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="p">}</span>
|
||
<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a>
|
||
<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></a><span class="c1">// Less sort.Interface 的方法</span>
|
||
<a id="__codelineno-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">intHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">Less</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">bool</span><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="c1">// 如果实现小顶堆，则需要调整为小于号</span>
|
||
<a id="__codelineno-4-28" name="__codelineno-4-28" href="#__codelineno-4-28"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="nx">i</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">></span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="nx">j</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span>
|
||
<a id="__codelineno-4-29" name="__codelineno-4-29" href="#__codelineno-4-29"></a><span class="p">}</span>
|
||
<a id="__codelineno-4-30" name="__codelineno-4-30" href="#__codelineno-4-30"></a>
|
||
<a id="__codelineno-4-31" name="__codelineno-4-31" href="#__codelineno-4-31"></a><span class="c1">// Swap sort.Interface 的方法</span>
|
||
<a id="__codelineno-4-32" name="__codelineno-4-32" href="#__codelineno-4-32"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">intHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">Swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-4-33" name="__codelineno-4-33" href="#__codelineno-4-33"></a><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="nx">j</span><span class="p">],</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span>
|
||
<a id="__codelineno-4-34" name="__codelineno-4-34" href="#__codelineno-4-34"></a><span class="p">}</span>
|
||
<a id="__codelineno-4-35" name="__codelineno-4-35" href="#__codelineno-4-35"></a>
|
||
<a id="__codelineno-4-36" name="__codelineno-4-36" href="#__codelineno-4-36"></a><span class="c1">// Top 获取堆顶元素</span>
|
||
<a id="__codelineno-4-37" name="__codelineno-4-37" href="#__codelineno-4-37"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">intHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">Top</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-4-38" name="__codelineno-4-38" href="#__codelineno-4-38"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
|
||
<a id="__codelineno-4-39" name="__codelineno-4-39" href="#__codelineno-4-39"></a><span class="p">}</span>
|
||
<a id="__codelineno-4-40" name="__codelineno-4-40" href="#__codelineno-4-40"></a>
|
||
<a id="__codelineno-4-41" name="__codelineno-4-41" href="#__codelineno-4-41"></a><span class="cm">/* Driver Code */</span>
|
||
<a id="__codelineno-4-42" name="__codelineno-4-42" href="#__codelineno-4-42"></a><span class="kd">func</span><span class="w"> </span><span class="nx">TestHeap</span><span class="p">(</span><span class="nx">t</span><span class="w"> </span><span class="o">*</span><span class="nx">testing</span><span class="p">.</span><span class="nx">T</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-4-43" name="__codelineno-4-43" href="#__codelineno-4-43"></a><span class="w"> </span><span class="cm">/* 初始化堆 */</span>
|
||
<a id="__codelineno-4-44" name="__codelineno-4-44" href="#__codelineno-4-44"></a><span class="w"> </span><span class="c1">// 初始化大顶堆</span>
|
||
<a id="__codelineno-4-45" name="__codelineno-4-45" href="#__codelineno-4-45"></a><span class="w"> </span><span class="nx">maxHeap</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="o">&</span><span class="nx">intHeap</span><span class="p">{}</span>
|
||
<a id="__codelineno-4-46" name="__codelineno-4-46" href="#__codelineno-4-46"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Init</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">)</span>
|
||
<a id="__codelineno-4-47" name="__codelineno-4-47" href="#__codelineno-4-47"></a><span class="w"> </span><span class="cm">/* 元素入堆 */</span>
|
||
<a id="__codelineno-4-48" name="__codelineno-4-48" href="#__codelineno-4-48"></a><span class="w"> </span><span class="c1">// 调用 heap.Interface 的方法，来添加元素</span>
|
||
<a id="__codelineno-4-49" name="__codelineno-4-49" href="#__codelineno-4-49"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Push</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-4-50" name="__codelineno-4-50" href="#__codelineno-4-50"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Push</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span>
|
||
<a id="__codelineno-4-51" name="__codelineno-4-51" href="#__codelineno-4-51"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Push</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
|
||
<a id="__codelineno-4-52" name="__codelineno-4-52" href="#__codelineno-4-52"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Push</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span>
|
||
<a id="__codelineno-4-53" name="__codelineno-4-53" href="#__codelineno-4-53"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Push</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">)</span>
|
||
<a id="__codelineno-4-54" name="__codelineno-4-54" href="#__codelineno-4-54"></a>
|
||
<a id="__codelineno-4-55" name="__codelineno-4-55" href="#__codelineno-4-55"></a><span class="w"> </span><span class="cm">/* 获取堆顶元素 */</span>
|
||
<a id="__codelineno-4-56" name="__codelineno-4-56" href="#__codelineno-4-56"></a><span class="w"> </span><span class="nx">top</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">maxHeap</span><span class="p">.</span><span class="nx">Top</span><span class="p">()</span>
|
||
<a id="__codelineno-4-57" name="__codelineno-4-57" href="#__codelineno-4-57"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Printf</span><span class="p">(</span><span class="s">"堆顶元素为 %d\n"</span><span class="p">,</span><span class="w"> </span><span class="nx">top</span><span class="p">)</span>
|
||
<a id="__codelineno-4-58" name="__codelineno-4-58" href="#__codelineno-4-58"></a>
|
||
<a id="__codelineno-4-59" name="__codelineno-4-59" href="#__codelineno-4-59"></a><span class="w"> </span><span class="cm">/* 堆顶元素出堆 */</span>
|
||
<a id="__codelineno-4-60" name="__codelineno-4-60" href="#__codelineno-4-60"></a><span class="w"> </span><span class="c1">// 调用 heap.Interface 的方法，来移除元素</span>
|
||
<a id="__codelineno-4-61" name="__codelineno-4-61" href="#__codelineno-4-61"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Pop</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="c1">// 5</span>
|
||
<a id="__codelineno-4-62" name="__codelineno-4-62" href="#__codelineno-4-62"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Pop</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="c1">// 4</span>
|
||
<a id="__codelineno-4-63" name="__codelineno-4-63" href="#__codelineno-4-63"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Pop</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="c1">// 3</span>
|
||
<a id="__codelineno-4-64" name="__codelineno-4-64" href="#__codelineno-4-64"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Pop</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="c1">// 2</span>
|
||
<a id="__codelineno-4-65" name="__codelineno-4-65" href="#__codelineno-4-65"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Pop</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="c1">// 1</span>
|
||
<a id="__codelineno-4-66" name="__codelineno-4-66" href="#__codelineno-4-66"></a>
|
||
<a id="__codelineno-4-67" name="__codelineno-4-67" href="#__codelineno-4-67"></a><span class="w"> </span><span class="cm">/* 获取堆大小 */</span>
|
||
<a id="__codelineno-4-68" name="__codelineno-4-68" href="#__codelineno-4-68"></a><span class="w"> </span><span class="nx">size</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span>
|
||
<a id="__codelineno-4-69" name="__codelineno-4-69" href="#__codelineno-4-69"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Printf</span><span class="p">(</span><span class="s">"堆元素数量为 %d\n"</span><span class="p">,</span><span class="w"> </span><span class="nx">size</span><span class="p">)</span>
|
||
<a id="__codelineno-4-70" name="__codelineno-4-70" href="#__codelineno-4-70"></a>
|
||
<a id="__codelineno-4-71" name="__codelineno-4-71" href="#__codelineno-4-71"></a><span class="w"> </span><span class="cm">/* 判断堆是否为空 */</span>
|
||
<a id="__codelineno-4-72" name="__codelineno-4-72" href="#__codelineno-4-72"></a><span class="w"> </span><span class="nx">isEmpty</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
|
||
<a id="__codelineno-4-73" name="__codelineno-4-73" href="#__codelineno-4-73"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Printf</span><span class="p">(</span><span class="s">"堆是否为空 %t\n"</span><span class="p">,</span><span class="w"> </span><span class="nx">isEmpty</span><span class="p">)</span>
|
||
<a id="__codelineno-4-74" name="__codelineno-4-74" href="#__codelineno-4-74"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">heap.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="c1">// Swift 未提供内置 Heap 类</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">heap.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="c1">// JavaScript 未提供内置 Heap 类</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">heap.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="c1">// TypeScript 未提供内置 Heap 类</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">heap.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="c1">// Dart 未提供内置 Heap 类</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">heap.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span>::<span class="n">collections</span>::<span class="n">BinaryHeap</span><span class="p">;</span>
|
||
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span>::<span class="n">cmp</span>::<span class="n">Reverse</span><span class="p">;</span>
|
||
<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a>
|
||
<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="cm">/* 初始化堆 */</span>
|
||
<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="c1">// 初始化小顶堆</span>
|
||
<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">min_heap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">BinaryHeap</span>::<span class="o"><</span><span class="n">Reverse</span><span class="o"><</span><span class="kt">i32</span><span class="o">>></span>::<span class="n">new</span><span class="p">();</span>
|
||
<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="c1">// 初始化大顶堆</span>
|
||
<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">max_heap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">BinaryHeap</span>::<span class="n">new</span><span class="p">();</span>
|
||
<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a>
|
||
<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="cm">/* 元素入堆 */</span>
|
||
<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="n">max_heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
|
||
<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="n">max_heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
|
||
<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="n">max_heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
|
||
<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="n">max_heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
|
||
<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="n">max_heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">4</span><span class="p">);</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="cm">/* 获取堆顶元素 */</span>
|
||
<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="kd">let</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">peek</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span><span class="w"> </span><span class="c1">// 5</span>
|
||
<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a>
|
||
<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="cm">/* 堆顶元素出堆 */</span>
|
||
<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="c1">// 出堆元素会形成一个从大到小的序列</span>
|
||
<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="kd">let</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">pop</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span><span class="w"> </span><span class="c1">// 5</span>
|
||
<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="kd">let</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">pop</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span><span class="w"> </span><span class="c1">// 4</span>
|
||
<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a><span class="kd">let</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">pop</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span><span class="w"> </span><span class="c1">// 3</span>
|
||
<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a><span class="kd">let</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">pop</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span><span class="w"> </span><span class="c1">// 2</span>
|
||
<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a><span class="kd">let</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">pop</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span><span class="w"> </span><span class="c1">// 1</span>
|
||
<a id="__codelineno-9-27" name="__codelineno-9-27" href="#__codelineno-9-27"></a>
|
||
<a id="__codelineno-9-28" name="__codelineno-9-28" href="#__codelineno-9-28"></a><span class="cm">/* 获取堆大小 */</span>
|
||
<a id="__codelineno-9-29" name="__codelineno-9-29" href="#__codelineno-9-29"></a><span class="kd">let</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">len</span><span class="p">();</span>
|
||
<a id="__codelineno-9-30" name="__codelineno-9-30" href="#__codelineno-9-30"></a>
|
||
<a id="__codelineno-9-31" name="__codelineno-9-31" href="#__codelineno-9-31"></a><span class="cm">/* 判断堆是否为空 */</span>
|
||
<a id="__codelineno-9-32" name="__codelineno-9-32" href="#__codelineno-9-32"></a><span class="kd">let</span><span class="w"> </span><span class="n">is_empty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">is_empty</span><span class="p">();</span>
|
||
<a id="__codelineno-9-33" name="__codelineno-9-33" href="#__codelineno-9-33"></a>
|
||
<a id="__codelineno-9-34" name="__codelineno-9-34" href="#__codelineno-9-34"></a><span class="cm">/* 输入列表并建堆 */</span>
|
||
<a id="__codelineno-9-35" name="__codelineno-9-35" href="#__codelineno-9-35"></a><span class="kd">let</span><span class="w"> </span><span class="n">min_heap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">BinaryHeap</span>::<span class="n">from</span><span class="p">(</span><span class="fm">vec!</span><span class="p">[</span><span class="n">Reverse</span><span class="p">(</span><span class="mi">1</span><span class="p">),</span><span class="w"> </span><span class="n">Reverse</span><span class="p">(</span><span class="mi">3</span><span class="p">),</span><span class="w"> </span><span class="n">Reverse</span><span class="p">(</span><span class="mi">2</span><span class="p">),</span><span class="w"> </span><span class="n">Reverse</span><span class="p">(</span><span class="mi">5</span><span class="p">),</span><span class="w"> </span><span class="n">Reverse</span><span class="p">(</span><span class="mi">4</span><span class="p">)]);</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">heap.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// C 未提供内置 Heap 类</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">heap.zig</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<details class="pythontutor">
|
||
<summary>可视化运行</summary>
|
||
<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=import%20heapq%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%E5%B0%8F%E9%A1%B6%E5%A0%86%0A%20%20%20%20min_heap,%20flag%20%3D%20%5B%5D,%201%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20max_heap,%20flag%20%3D%20%5B%5D,%20-1%0A%20%20%20%20%0A%20%20%20%20%23%20Python%20%E7%9A%84%20heapq%20%E6%A8%A1%E5%9D%97%E9%BB%98%E8%AE%A4%E5%AE%9E%E7%8E%B0%E5%B0%8F%E9%A1%B6%E5%A0%86%0A%20%20%20%20%23%20%E8%80%83%E8%99%91%E5%B0%86%E2%80%9C%E5%85%83%E7%B4%A0%E5%8F%96%E8%B4%9F%E2%80%9D%E5%90%8E%E5%86%8D%E5%85%A5%E5%A0%86%EF%BC%8C%E8%BF%99%E6%A0%B7%E5%B0%B1%E5%8F%AF%E4%BB%A5%E5%B0%86%E5%A4%A7%E5%B0%8F%E5%85%B3%E7%B3%BB%E9%A2%A0%E5%80%92%EF%BC%8C%E4%BB%8E%E8%80%8C%E5%AE%9E%E7%8E%B0%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20%23%20%E5%9C%A8%E6%9C%AC%E7%A4%BA%E4%BE%8B%E4%B8%AD%EF%BC%8Cflag%20%3D%201%20%E6%97%B6%E5%AF%B9%E5%BA%94%E5%B0%8F%E9%A1%B6%E5%A0%86%EF%BC%8Cflag%20%3D%20-1%20%E6%97%B6%E5%AF%B9%E5%BA%94%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%85%83%E7%B4%A0%E5%85%A5%E5%A0%86%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%201%29%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%203%29%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%202%29%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%205%29%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%204%29%0A%20%20%20%20%0A%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%0A%20%20%20%20peek%20%3D%20flag%20*%20max_heap%5B0%5D%20%23%205%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%E5%87%BA%E5%A0%86%0A%20%20%20%20%23%20%E5%87%BA%E5%A0%86%E5%85%83%E7%B4%A0%E4%BC%9A%E5%BD%A2%E6%88%90%E4%B8%80%E4%B8%AA%E4%BB%8E%E5%A4%A7%E5%88%B0%E5%B0%8F%E7%9A%84%E5%BA%8F%E5%88%97%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%205%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%204%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%203%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%202%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%201%0A%20%20%20%20%0A%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E5%A0%86%E5%A4%A7%E5%B0%8F%0A%20%20%20%20size%20%3D%20len%28max_heap%29%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%88%A4%E6%96%AD%E5%A0%86%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%0A%20%20%20%20is_empty%20%3D%20not%20max_heap%0A%20%20%20%20%0A%20%20%20%20%23%20%E8%BE%93%E5%85%A5%E5%88%97%E8%A1%A8%E5%B9%B6%E5%BB%BA%E5%A0%86%0A%20%20%20%20min_heap%20%3D%20%5B1,%203,%202,%205,%204%5D%0A%20%20%20%20heapq.heapify%28min_heap%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&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=import%20heapq%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%E5%B0%8F%E9%A1%B6%E5%A0%86%0A%20%20%20%20min_heap,%20flag%20%3D%20%5B%5D,%201%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20max_heap,%20flag%20%3D%20%5B%5D,%20-1%0A%20%20%20%20%0A%20%20%20%20%23%20Python%20%E7%9A%84%20heapq%20%E6%A8%A1%E5%9D%97%E9%BB%98%E8%AE%A4%E5%AE%9E%E7%8E%B0%E5%B0%8F%E9%A1%B6%E5%A0%86%0A%20%20%20%20%23%20%E8%80%83%E8%99%91%E5%B0%86%E2%80%9C%E5%85%83%E7%B4%A0%E5%8F%96%E8%B4%9F%E2%80%9D%E5%90%8E%E5%86%8D%E5%85%A5%E5%A0%86%EF%BC%8C%E8%BF%99%E6%A0%B7%E5%B0%B1%E5%8F%AF%E4%BB%A5%E5%B0%86%E5%A4%A7%E5%B0%8F%E5%85%B3%E7%B3%BB%E9%A2%A0%E5%80%92%EF%BC%8C%E4%BB%8E%E8%80%8C%E5%AE%9E%E7%8E%B0%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20%23%20%E5%9C%A8%E6%9C%AC%E7%A4%BA%E4%BE%8B%E4%B8%AD%EF%BC%8Cflag%20%3D%201%20%E6%97%B6%E5%AF%B9%E5%BA%94%E5%B0%8F%E9%A1%B6%E5%A0%86%EF%BC%8Cflag%20%3D%20-1%20%E6%97%B6%E5%AF%B9%E5%BA%94%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%85%83%E7%B4%A0%E5%85%A5%E5%A0%86%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%201%29%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%203%29%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%202%29%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%205%29%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%204%29%0A%20%20%20%20%0A%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%0A%20%20%20%20peek%20%3D%20flag%20*%20max_heap%5B0%5D%20%23%205%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%E5%87%BA%E5%A0%86%0A%20%20%20%20%23%20%E5%87%BA%E5%A0%86%E5%85%83%E7%B4%A0%E4%BC%9A%E5%BD%A2%E6%88%90%E4%B8%80%E4%B8%AA%E4%BB%8E%E5%A4%A7%E5%88%B0%E5%B0%8F%E7%9A%84%E5%BA%8F%E5%88%97%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%205%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%204%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%203%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%202%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%201%0A%20%20%20%20%0A%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E5%A0%86%E5%A4%A7%E5%B0%8F%0A%20%20%20%20size%20%3D%20len%28max_heap%29%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%88%A4%E6%96%AD%E5%A0%86%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%0A%20%20%20%20is_empty%20%3D%20not%20max_heap%0A%20%20%20%20%0A%20%20%20%20%23%20%E8%BE%93%E5%85%A5%E5%88%97%E8%A1%A8%E5%B9%B6%E5%BB%BA%E5%A0%86%0A%20%20%20%20min_heap%20%3D%20%5B1,%203,%202,%205,%204%5D%0A%20%20%20%20heapq.heapify%28min_heap%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全屏观看 ></a></div></p>
|
||
</details>
|
||
<h2 id="812">8.1.2 堆的实现<a class="headerlink" href="#812" title="Permanent link">¶</a></h2>
|
||
<p>下文实现的是大顶堆。若要将其转换为小顶堆，只需将所有大小逻辑判断取逆（例如，将 <span class="arithmatex">\(\geq\)</span> 替换为 <span class="arithmatex">\(\leq\)</span> ）。感兴趣的读者可以自行实现。</p>
|
||
<h3 id="1">1. 堆的存储与表示<a class="headerlink" href="#1" title="Permanent link">¶</a></h3>
|
||
<p>“二叉树”章节讲过，完全二叉树非常适合用数组来表示。由于堆正是一种完全二叉树，<strong>因此我们将采用数组来存储堆</strong>。</p>
|
||
<p>当使用数组表示二叉树时，元素代表节点值，索引代表节点在二叉树中的位置。<strong>节点指针通过索引映射公式来实现</strong>。</p>
|
||
<p>如图 8-2 所示，给定索引 <span class="arithmatex">\(i\)</span> ，其左子节点的索引为 <span class="arithmatex">\(2i + 1\)</span> ，右子节点的索引为 <span class="arithmatex">\(2i + 2\)</span> ，父节点的索引为 <span class="arithmatex">\((i - 1) / 2\)</span>（向下整除）。当索引越界时，表示空节点或节点不存在。</p>
|
||
<p><a class="glightbox" href="../heap.assets/representation_of_heap.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="堆的表示与存储" class="animation-figure" src="../heap.assets/representation_of_heap.png" /></a></p>
|
||
<p align="center"> 图 8-2 堆的表示与存储 </p>
|
||
|
||
<p>我们可以将索引映射公式封装成函数，方便后续使用：</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="2:12"><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" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.py</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="k">def</span> <span class="nf">left</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="w"> </span><span class="sd">"""获取左子节点的索引"""</span>
|
||
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a> <span class="k">return</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span>
|
||
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>
|
||
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="k">def</span> <span class="nf">right</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="sd">"""获取右子节点的索引"""</span>
|
||
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a> <span class="k">return</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">2</span>
|
||
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a>
|
||
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="k">def</span> <span class="nf">parent</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w"> </span><span class="sd">"""获取父节点的索引"""</span>
|
||
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a> <span class="k">return</span> <span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span> <span class="c1"># 向下整除</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.cpp</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="cm">/* 获取左子节点的索引 */</span>
|
||
<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</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">1</span><span class="p">;</span>
|
||
<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>
|
||
<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a><span class="cm">/* 获取右子节点的索引 */</span>
|
||
<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a><span class="kt">int</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</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">2</span><span class="p">;</span>
|
||
<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="p">}</span>
|
||
<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>
|
||
<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a><span class="cm">/* 获取父节点的索引 */</span>
|
||
<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</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="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 向下整除</span>
|
||
<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.java</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 获取左子节点的索引 */</span>
|
||
<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</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">1</span><span class="p">;</span>
|
||
<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a>
|
||
<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="cm">/* 获取右子节点的索引 */</span>
|
||
<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="kt">int</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</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">2</span><span class="p">;</span>
|
||
<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="p">}</span>
|
||
<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a>
|
||
<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="cm">/* 获取父节点的索引 */</span>
|
||
<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </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="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</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="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 向下整除</span>
|
||
<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.cs</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 获取左子节点的索引 */</span>
|
||
<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</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="k">return</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
|
||
<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a>
|
||
<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="cm">/* 获取右子节点的索引 */</span>
|
||
<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </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">return</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">2</span><span class="p">;</span>
|
||
<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="p">}</span>
|
||
<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a>
|
||
<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="cm">/* 获取父节点的索引 */</span>
|
||
<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 向下整除</span>
|
||
<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.go</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 获取左子节点的索引 */</span>
|
||
<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</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="k">return</span><span class="w"> </span><span class="mi">2</span><span class="o">*</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
|
||
<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a>
|
||
<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="cm">/* 获取右子节点的索引 */</span>
|
||
<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </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">return</span><span class="w"> </span><span class="mi">2</span><span class="o">*</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span>
|
||
<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="p">}</span>
|
||
<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a>
|
||
<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="cm">/* 获取父节点的索引 */</span>
|
||
<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w"> </span><span class="c1">// 向下整除</span>
|
||
<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="nx">i</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="mi">2</span>
|
||
<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.swift</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 获取左子节点的索引 */</span>
|
||
<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">func</span> <span class="nf">left</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||
<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span>
|
||
<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a>
|
||
<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="cm">/* 获取右子节点的索引 */</span>
|
||
<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="kd">func</span> <span class="nf">right</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||
<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">2</span>
|
||
<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="p">}</span>
|
||
<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a>
|
||
<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="cm">/* 获取父节点的索引 */</span>
|
||
<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="kd">func</span> <span class="nf">parent</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||
<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a> <span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span> <span class="c1">// 向下整除</span>
|
||
<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.js</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 获取左子节点的索引 */</span>
|
||
<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="err">#</span><span class="nx">left</span><span class="p">(</span><span class="nx">i</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="k">return</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
|
||
<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a>
|
||
<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="cm">/* 获取右子节点的索引 */</span>
|
||
<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="err">#</span><span class="nx">right</span><span class="p">(</span><span class="nx">i</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="k">return</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
|
||
<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="p">}</span>
|
||
<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a>
|
||
<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="cm">/* 获取父节点的索引 */</span>
|
||
<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="err">#</span><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><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="k">return</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">((</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// 向下整除</span>
|
||
<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.ts</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 获取左子节点的索引 */</span>
|
||
<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
|
||
<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a>
|
||
<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="cm">/* 获取右子节点的索引 */</span>
|
||
<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">2</span><span class="p">;</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>
|
||
<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="cm">/* 获取父节点的索引 */</span>
|
||
<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">((</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// 向下整除</span>
|
||
<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.dart</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 获取左子节点的索引 */</span>
|
||
<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">_left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
|
||
<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a>
|
||
<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="cm">/* 获取右子节点的索引 */</span>
|
||
<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="kt">int</span><span class="w"> </span><span class="n">_right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</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">return</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">2</span><span class="p">;</span>
|
||
<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="p">}</span>
|
||
<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a>
|
||
<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="cm">/* 获取父节点的索引 */</span>
|
||
<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="kt">int</span><span class="w"> </span><span class="n">_parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </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="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">~/</span><span class="w"> </span><span class="m">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 向下整除</span>
|
||
<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.rs</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 获取左子节点的索引 */</span>
|
||
<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="k">fn</span> <span class="nf">left</span><span class="p">(</span><span class="n">i</span>: <span class="kt">usize</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">usize</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="mi">2</span><span class="w"> </span><span class="o">*</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">1</span>
|
||
<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a>
|
||
<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="cm">/* 获取右子节点的索引 */</span>
|
||
<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="k">fn</span> <span class="nf">right</span><span class="p">(</span><span class="n">i</span>: <span class="kt">usize</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">usize</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="mi">2</span><span class="w"> </span><span class="o">*</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">2</span>
|
||
<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="p">}</span>
|
||
<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a>
|
||
<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="cm">/* 获取父节点的索引 */</span>
|
||
<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="k">fn</span> <span class="nf">parent</span><span class="p">(</span><span class="n">i</span>: <span class="kt">usize</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">usize</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="p">(</span><span class="n">i</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="mi">2</span><span class="w"> </span><span class="c1">// 向下整除</span>
|
||
<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.c</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 获取左子节点的索引 */</span>
|
||
<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </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="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</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">1</span><span class="p">;</span>
|
||
<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a>
|
||
<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="cm">/* 获取右子节点的索引 */</span>
|
||
<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="kt">int</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><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="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</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">2</span><span class="p">;</span>
|
||
<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="p">}</span>
|
||
<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a>
|
||
<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="cm">/* 获取父节点的索引 */</span>
|
||
<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</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">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</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="mi">2</span><span class="p">;</span>
|
||
<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.zig</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="c1">// 获取左子节点的索引</span>
|
||
<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="kt">usize</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="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</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">1</span><span class="p">;</span>
|
||
<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a>
|
||
<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="c1">// 获取右子节点的索引</span>
|
||
<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="k">fn</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="kt">usize</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">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</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">2</span><span class="p">;</span>
|
||
<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="p">}</span>
|
||
<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a>
|
||
<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="c1">// 获取父节点的索引</span>
|
||
<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="k">fn</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </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="c1">// return (i - 1) / 2; // 向下整除</span>
|
||
<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">@divFloor</span><span class="p">(</span><span class="n">i</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="mi">2</span><span class="p">);</span>
|
||
<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<h3 id="2">2. 访问堆顶元素<a class="headerlink" href="#2" title="Permanent link">¶</a></h3>
|
||
<p>堆顶元素即为二叉树的根节点，也就是列表的首个元素：</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="3:12"><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" /><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">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.py</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="k">def</span> <span class="nf">peek</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||
<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="w"> </span><span class="sd">"""访问堆顶元素"""</span>
|
||
<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.cpp</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="cm">/* 访问堆顶元素 */</span>
|
||
<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">peek</span><span class="p">()</span><span class="w"> </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="k">return</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="mi">0</span><span class="p">];</span>
|
||
<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.java</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="cm">/* 访问堆顶元素 */</span>
|
||
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
|
||
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.cs</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* 访问堆顶元素 */</span>
|
||
<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="m">0</span><span class="p">];</span>
|
||
<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.go</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* 访问堆顶元素 */</span>
|
||
<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">peek</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
|
||
<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.swift</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* 访问堆顶元素 */</span>
|
||
<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kd">func</span> <span class="nf">peek</span><span class="p">()</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||
<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a> <span class="n">maxHeap</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
|
||
<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.js</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 访问堆顶元素 */</span>
|
||
<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="nx">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span>
|
||
<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.ts</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* 访问堆顶元素 */</span>
|
||
<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="nx">peek</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span>
|
||
<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.dart</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="cm">/* 访问堆顶元素 */</span>
|
||
<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">_maxHeap</span><span class="p">[</span><span class="m">0</span><span class="p">];</span>
|
||
<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.rs</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="cm">/* 访问堆顶元素 */</span>
|
||
<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="k">fn</span> <span class="nf">peek</span><span class="p">(</span><span class="o">&</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span>-> <span class="nb">Option</span><span class="o"><</span><span class="kt">i32</span><span class="o">></span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="n">first</span><span class="p">().</span><span class="n">copied</span><span class="p">()</span>
|
||
<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.c</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="cm">/* 访问堆顶元素 */</span>
|
||
<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">peek</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="mi">0</span><span class="p">];</span>
|
||
<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.zig</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="c1">// 访问堆顶元素</span>
|
||
<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">peek</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">)</span><span class="w"> </span><span class="n">T</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">items</span><span class="p">[</span><span class="mi">0</span><span class="p">];</span>
|
||
<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="p">}</span><span class="w"> </span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<details class="pythontutor">
|
||
<summary>可视化运行</summary>
|
||
<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20MaxHeap%3A%0A%20%20%20%20%22%22%22%E5%A4%A7%E9%A1%B6%E5%A0%86%22%22%22%0A%0A%20%20%20%20def%20__init__%28self,%20nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E6%9E%84%E9%80%A0%E6%96%B9%E6%B3%95%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E5%B0%86%E5%88%97%E8%A1%A8%E5%85%83%E7%B4%A0%E5%8E%9F%E5%B0%81%E4%B8%8D%E5%8A%A8%E6%B7%BB%E5%8A%A0%E8%BF%9B%E5%A0%86%0A%20%20%20%20%20%20%20%20self.max_heap%20%3D%20nums%0A%0A%20%20%20%20def%20left%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%B7%A6%E5%AD%90%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20*%20i%20%2B%201%0A%0A%20%20%20%20def%20right%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%8F%B3%E5%AD%90%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20*%20i%20%2B%202%0A%0A%20%20%20%20def%20parent%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E7%88%B6%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%20%28i%20-%201%29%20//%202%20%20%23%20%E5%90%91%E4%B8%8B%E6%95%B4%E9%99%A4%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%A0%86%E5%A4%A7%E5%B0%8F%22%22%22%0A%20%20%20%20%20%20%20%20return%20len%28self.max_heap%29%0A%0A%20%20%20%20def%20is_empty%28self%29%20-%3E%20bool%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%88%A4%E6%96%AD%E5%A0%86%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%22%22%22%0A%20%20%20%20%20%20%20%20return%20self.size%28%29%20%3D%3D%200%0A%0A%20%20%20%20def%20peek%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%AE%BF%E9%97%AE%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%22%22%22%0A%20%20%20%20%20%20%20%20return%20self.max_heap%5B0%5D%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%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20%23%20%E8%AF%B7%E6%B3%A8%E6%84%8F%EF%BC%8C%E8%BE%93%E5%85%A5%E6%95%B0%E7%BB%84%E5%B7%B2%E7%BB%8F%E6%98%AF%E4%B8%80%E4%B8%AA%E5%B7%B2%E7%BB%8F%E6%98%AF%E4%B8%80%E4%B8%AA%E5%90%88%E6%B3%95%E7%9A%84%E5%A0%86%20%0A%20%20%20%20max_heap%20%3D%20MaxHeap%28%5B9,%208,%206,%206,%207,%205,%202,%201,%204,%203,%206,%202%5D%29%0A%0A%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%0A%20%20%20%20peek%20%3D%20max_heap.peek%28%29%0A%20%20%20%20print%28f%22%5Cn%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%E4%B8%BA%20%7Bpeek%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=7&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%20MaxHeap%3A%0A%20%20%20%20%22%22%22%E5%A4%A7%E9%A1%B6%E5%A0%86%22%22%22%0A%0A%20%20%20%20def%20__init__%28self,%20nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E6%9E%84%E9%80%A0%E6%96%B9%E6%B3%95%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E5%B0%86%E5%88%97%E8%A1%A8%E5%85%83%E7%B4%A0%E5%8E%9F%E5%B0%81%E4%B8%8D%E5%8A%A8%E6%B7%BB%E5%8A%A0%E8%BF%9B%E5%A0%86%0A%20%20%20%20%20%20%20%20self.max_heap%20%3D%20nums%0A%0A%20%20%20%20def%20left%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%B7%A6%E5%AD%90%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20*%20i%20%2B%201%0A%0A%20%20%20%20def%20right%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%8F%B3%E5%AD%90%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20*%20i%20%2B%202%0A%0A%20%20%20%20def%20parent%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E7%88%B6%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%20%28i%20-%201%29%20//%202%20%20%23%20%E5%90%91%E4%B8%8B%E6%95%B4%E9%99%A4%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%A0%86%E5%A4%A7%E5%B0%8F%22%22%22%0A%20%20%20%20%20%20%20%20return%20len%28self.max_heap%29%0A%0A%20%20%20%20def%20is_empty%28self%29%20-%3E%20bool%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%88%A4%E6%96%AD%E5%A0%86%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%22%22%22%0A%20%20%20%20%20%20%20%20return%20self.size%28%29%20%3D%3D%200%0A%0A%20%20%20%20def%20peek%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%AE%BF%E9%97%AE%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%22%22%22%0A%20%20%20%20%20%20%20%20return%20self.max_heap%5B0%5D%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%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20%23%20%E8%AF%B7%E6%B3%A8%E6%84%8F%EF%BC%8C%E8%BE%93%E5%85%A5%E6%95%B0%E7%BB%84%E5%B7%B2%E7%BB%8F%E6%98%AF%E4%B8%80%E4%B8%AA%E5%B7%B2%E7%BB%8F%E6%98%AF%E4%B8%80%E4%B8%AA%E5%90%88%E6%B3%95%E7%9A%84%E5%A0%86%20%0A%20%20%20%20max_heap%20%3D%20MaxHeap%28%5B9,%208,%206,%206,%207,%205,%202,%201,%204,%203,%206,%202%5D%29%0A%0A%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%0A%20%20%20%20peek%20%3D%20max_heap.peek%28%29%0A%20%20%20%20print%28f%22%5Cn%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%E4%B8%BA%20%7Bpeek%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=7&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全屏观看 ></a></div></p>
|
||
</details>
|
||
<h3 id="3">3. 元素入堆<a class="headerlink" href="#3" title="Permanent link">¶</a></h3>
|
||
<p>给定元素 <code>val</code> ，我们首先将其添加到堆底。添加之后，由于 <code>val</code> 可能大于堆中其他元素，堆的成立条件可能已被破坏，<strong>因此需要修复从插入节点到根节点的路径上的各个节点</strong>，这个操作被称为「堆化 heapify」。</p>
|
||
<p>考虑从入堆节点开始，<strong>从底至顶执行堆化</strong>。如图 8-3 所示，我们比较插入节点与其父节点的值，如果插入节点更大，则将它们交换。然后继续执行此操作，从底至顶修复堆中的各个节点，直至越过根节点或遇到无须交换的节点时结束。</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="4:9"><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" /><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></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../heap.assets/heap_push_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="元素入堆步骤" class="animation-figure" src="../heap.assets/heap_push_step1.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../heap.assets/heap_push_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_push_step2" class="animation-figure" src="../heap.assets/heap_push_step2.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../heap.assets/heap_push_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_push_step3" class="animation-figure" src="../heap.assets/heap_push_step3.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../heap.assets/heap_push_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_push_step4" class="animation-figure" src="../heap.assets/heap_push_step4.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../heap.assets/heap_push_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_push_step5" class="animation-figure" src="../heap.assets/heap_push_step5.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../heap.assets/heap_push_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_push_step6" class="animation-figure" src="../heap.assets/heap_push_step6.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../heap.assets/heap_push_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_push_step7" class="animation-figure" src="../heap.assets/heap_push_step7.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../heap.assets/heap_push_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_push_step8" class="animation-figure" src="../heap.assets/heap_push_step8.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../heap.assets/heap_push_step9.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_push_step9" class="animation-figure" src="../heap.assets/heap_push_step9.png" /></a></p>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p align="center"> 图 8-3 元素入堆步骤 </p>
|
||
|
||
<p>设节点总数为 <span class="arithmatex">\(n\)</span> ，则树的高度为 <span class="arithmatex">\(O(\log n)\)</span> 。由此可知，堆化操作的循环轮数最多为 <span class="arithmatex">\(O(\log n)\)</span> ，<strong>元素入堆操作的时间复杂度为 <span class="arithmatex">\(O(\log n)\)</span></strong> 。代码如下所示：</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="5:12"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.py</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="k">def</span> <span class="nf">push</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
||
<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="w"> </span><span class="sd">"""元素入堆"""</span>
|
||
<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a> <span class="c1"># 添加节点</span>
|
||
<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a> <span class="c1"># 从底至顶堆化</span>
|
||
<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a> <span class="bp">self</span><span class="o">.</span><span class="n">sift_up</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a>
|
||
<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a><span class="k">def</span> <span class="nf">sift_up</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
||
<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a><span class="w"> </span><span class="sd">"""从节点 i 开始，从底至顶堆化"""</span>
|
||
<a id="__codelineno-36-10" name="__codelineno-36-10" href="#__codelineno-36-10"></a> <span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
|
||
<a id="__codelineno-36-11" name="__codelineno-36-11" href="#__codelineno-36-11"></a> <span class="c1"># 获取节点 i 的父节点</span>
|
||
<a id="__codelineno-36-12" name="__codelineno-36-12" href="#__codelineno-36-12"></a> <span class="n">p</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
|
||
<a id="__codelineno-36-13" name="__codelineno-36-13" href="#__codelineno-36-13"></a> <span class="c1"># 当“越过根节点”或“节点无须修复”时，结束堆化</span>
|
||
<a id="__codelineno-36-14" name="__codelineno-36-14" href="#__codelineno-36-14"></a> <span class="k">if</span> <span class="n">p</span> <span class="o"><</span> <span class="mi">0</span> <span class="ow">or</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o"><=</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">p</span><span class="p">]:</span>
|
||
<a id="__codelineno-36-15" name="__codelineno-36-15" href="#__codelineno-36-15"></a> <span class="k">break</span>
|
||
<a id="__codelineno-36-16" name="__codelineno-36-16" href="#__codelineno-36-16"></a> <span class="c1"># 交换两节点</span>
|
||
<a id="__codelineno-36-17" name="__codelineno-36-17" href="#__codelineno-36-17"></a> <span class="bp">self</span><span class="o">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">p</span><span class="p">)</span>
|
||
<a id="__codelineno-36-18" name="__codelineno-36-18" href="#__codelineno-36-18"></a> <span class="c1"># 循环向上堆化</span>
|
||
<a id="__codelineno-36-19" name="__codelineno-36-19" href="#__codelineno-36-19"></a> <span class="n">i</span> <span class="o">=</span> <span class="n">p</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.cpp</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="cm">/* 元素入堆 */</span>
|
||
<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w"> </span><span class="c1">// 添加节点</span>
|
||
<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
|
||
<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a><span class="w"> </span><span class="n">siftUp</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||
<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="p">}</span>
|
||
<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a>
|
||
<a id="__codelineno-37-9" name="__codelineno-37-9" href="#__codelineno-37-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
|
||
<a id="__codelineno-37-10" name="__codelineno-37-10" href="#__codelineno-37-10"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftUp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-37-11" name="__codelineno-37-11" href="#__codelineno-37-11"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nb">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-37-12" name="__codelineno-37-12" href="#__codelineno-37-12"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
|
||
<a id="__codelineno-37-13" name="__codelineno-37-13" href="#__codelineno-37-13"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
|
||
<a id="__codelineno-37-14" name="__codelineno-37-14" href="#__codelineno-37-14"></a><span class="w"> </span><span class="c1">// 当“越过根节点”或“节点无须修复”时，结束堆化</span>
|
||
<a id="__codelineno-37-15" name="__codelineno-37-15" href="#__codelineno-37-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">maxHeap</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">maxHeap</span><span class="p">[</span><span class="n">p</span><span class="p">])</span>
|
||
<a id="__codelineno-37-16" name="__codelineno-37-16" href="#__codelineno-37-16"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||
<a id="__codelineno-37-17" name="__codelineno-37-17" href="#__codelineno-37-17"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
||
<a id="__codelineno-37-18" name="__codelineno-37-18" href="#__codelineno-37-18"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">p</span><span class="p">]);</span>
|
||
<a id="__codelineno-37-19" name="__codelineno-37-19" href="#__codelineno-37-19"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
|
||
<a id="__codelineno-37-20" name="__codelineno-37-20" href="#__codelineno-37-20"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span><span class="p">;</span>
|
||
<a id="__codelineno-37-21" name="__codelineno-37-21" href="#__codelineno-37-21"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-37-22" name="__codelineno-37-22" href="#__codelineno-37-22"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.java</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="cm">/* 元素入堆 */</span>
|
||
<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="w"> </span><span class="c1">// 添加节点</span>
|
||
<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
|
||
<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="w"> </span><span class="n">siftUp</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||
<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="p">}</span>
|
||
<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a>
|
||
<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
|
||
<a id="__codelineno-38-10" name="__codelineno-38-10" href="#__codelineno-38-10"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftUp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-38-11" name="__codelineno-38-11" href="#__codelineno-38-11"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-38-12" name="__codelineno-38-12" href="#__codelineno-38-12"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
|
||
<a id="__codelineno-38-13" name="__codelineno-38-13" href="#__codelineno-38-13"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
|
||
<a id="__codelineno-38-14" name="__codelineno-38-14" href="#__codelineno-38-14"></a><span class="w"> </span><span class="c1">// 当“越过根节点”或“节点无须修复”时，结束堆化</span>
|
||
<a id="__codelineno-38-15" name="__codelineno-38-15" href="#__codelineno-38-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</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">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">p</span><span class="p">))</span>
|
||
<a id="__codelineno-38-16" name="__codelineno-38-16" href="#__codelineno-38-16"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||
<a id="__codelineno-38-17" name="__codelineno-38-17" href="#__codelineno-38-17"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
||
<a id="__codelineno-38-18" name="__codelineno-38-18" href="#__codelineno-38-18"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">p</span><span class="p">);</span>
|
||
<a id="__codelineno-38-19" name="__codelineno-38-19" href="#__codelineno-38-19"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
|
||
<a id="__codelineno-38-20" name="__codelineno-38-20" href="#__codelineno-38-20"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span><span class="p">;</span>
|
||
<a id="__codelineno-38-21" name="__codelineno-38-21" href="#__codelineno-38-21"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-38-22" name="__codelineno-38-22" href="#__codelineno-38-22"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.cs</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="cm">/* 元素入堆 */</span>
|
||
<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a><span class="w"> </span><span class="c1">// 添加节点</span>
|
||
<a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
|
||
<a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a><span class="w"> </span><span class="n">SiftUp</span><span class="p">(</span><span class="n">Size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
|
||
<a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a><span class="p">}</span>
|
||
<a id="__codelineno-39-8" name="__codelineno-39-8" href="#__codelineno-39-8"></a>
|
||
<a id="__codelineno-39-9" name="__codelineno-39-9" href="#__codelineno-39-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
|
||
<a id="__codelineno-39-10" name="__codelineno-39-10" href="#__codelineno-39-10"></a><span class="k">void</span><span class="w"> </span><span class="nf">SiftUp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-39-11" name="__codelineno-39-11" href="#__codelineno-39-11"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="k">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-39-12" name="__codelineno-39-12" href="#__codelineno-39-12"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
|
||
<a id="__codelineno-39-13" name="__codelineno-39-13" href="#__codelineno-39-13"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Parent</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
|
||
<a id="__codelineno-39-14" name="__codelineno-39-14" href="#__codelineno-39-14"></a><span class="w"> </span><span class="c1">// 若“越过根节点”或“节点无须修复”，则结束堆化</span>
|
||
<a id="__codelineno-39-15" name="__codelineno-39-15" href="#__codelineno-39-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">maxHeap</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">maxHeap</span><span class="p">[</span><span class="n">p</span><span class="p">])</span>
|
||
<a id="__codelineno-39-16" name="__codelineno-39-16" href="#__codelineno-39-16"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||
<a id="__codelineno-39-17" name="__codelineno-39-17" href="#__codelineno-39-17"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
||
<a id="__codelineno-39-18" name="__codelineno-39-18" href="#__codelineno-39-18"></a><span class="w"> </span><span class="n">Swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">p</span><span class="p">);</span>
|
||
<a id="__codelineno-39-19" name="__codelineno-39-19" href="#__codelineno-39-19"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
|
||
<a id="__codelineno-39-20" name="__codelineno-39-20" href="#__codelineno-39-20"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span><span class="p">;</span>
|
||
<a id="__codelineno-39-21" name="__codelineno-39-21" href="#__codelineno-39-21"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-39-22" name="__codelineno-39-22" href="#__codelineno-39-22"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.go</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="cm">/* 元素入堆 */</span>
|
||
<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">push</span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="kt">any</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w"> </span><span class="c1">// 添加节点</span>
|
||
<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</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">h</span><span class="p">.</span><span class="nx">data</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">)</span>
|
||
<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
|
||
<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">siftUp</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="p">}</span>
|
||
<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a>
|
||
<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
|
||
<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">siftUp</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="kc">true</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
|
||
<a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="w"> </span><span class="nx">p</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span>
|
||
<a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="w"> </span><span class="c1">// 当“越过根节点”或“节点无须修复”时，结束堆化</span>
|
||
<a id="__codelineno-40-15" name="__codelineno-40-15" href="#__codelineno-40-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">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="o">||</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nx">i</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nx">p</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-40-16" name="__codelineno-40-16" href="#__codelineno-40-16"></a><span class="w"> </span><span class="k">break</span>
|
||
<a id="__codelineno-40-17" name="__codelineno-40-17" href="#__codelineno-40-17"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-40-18" name="__codelineno-40-18" href="#__codelineno-40-18"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
||
<a id="__codelineno-40-19" name="__codelineno-40-19" href="#__codelineno-40-19"></a><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">p</span><span class="p">)</span>
|
||
<a id="__codelineno-40-20" name="__codelineno-40-20" href="#__codelineno-40-20"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
|
||
<a id="__codelineno-40-21" name="__codelineno-40-21" href="#__codelineno-40-21"></a><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">p</span>
|
||
<a id="__codelineno-40-22" name="__codelineno-40-22" href="#__codelineno-40-22"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-40-23" name="__codelineno-40-23" href="#__codelineno-40-23"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.swift</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* 元素入堆 */</span>
|
||
<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="kd">func</span> <span class="nf">push</span><span class="p">(</span><span class="n">val</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
|
||
<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a> <span class="c1">// 添加节点</span>
|
||
<a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a> <span class="n">maxHeap</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a> <span class="c1">// 从底至顶堆化</span>
|
||
<a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a> <span class="n">siftUp</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">size</span><span class="p">()</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a><span class="p">}</span>
|
||
<a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a>
|
||
<a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
|
||
<a id="__codelineno-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></a><span class="kd">func</span> <span class="nf">siftUp</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
|
||
<a id="__codelineno-41-11" name="__codelineno-41-11" href="#__codelineno-41-11"></a> <span class="kd">var</span> <span class="nv">i</span> <span class="p">=</span> <span class="n">i</span>
|
||
<a id="__codelineno-41-12" name="__codelineno-41-12" href="#__codelineno-41-12"></a> <span class="k">while</span> <span class="kc">true</span> <span class="p">{</span>
|
||
<a id="__codelineno-41-13" name="__codelineno-41-13" href="#__codelineno-41-13"></a> <span class="c1">// 获取节点 i 的父节点</span>
|
||
<a id="__codelineno-41-14" name="__codelineno-41-14" href="#__codelineno-41-14"></a> <span class="kd">let</span> <span class="nv">p</span> <span class="p">=</span> <span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">i</span><span class="p">)</span>
|
||
<a id="__codelineno-41-15" name="__codelineno-41-15" href="#__codelineno-41-15"></a> <span class="c1">// 当“越过根节点”或“节点无须修复”时，结束堆化</span>
|
||
<a id="__codelineno-41-16" name="__codelineno-41-16" href="#__codelineno-41-16"></a> <span class="k">if</span> <span class="n">p</span> <span class="o"><</span> <span class="mi">0</span> <span class="o">||</span> <span class="n">maxHeap</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o"><=</span> <span class="n">maxHeap</span><span class="p">[</span><span class="n">p</span><span class="p">]</span> <span class="p">{</span>
|
||
<a id="__codelineno-41-17" name="__codelineno-41-17" href="#__codelineno-41-17"></a> <span class="k">break</span>
|
||
<a id="__codelineno-41-18" name="__codelineno-41-18" href="#__codelineno-41-18"></a> <span class="p">}</span>
|
||
<a id="__codelineno-41-19" name="__codelineno-41-19" href="#__codelineno-41-19"></a> <span class="c1">// 交换两节点</span>
|
||
<a id="__codelineno-41-20" name="__codelineno-41-20" href="#__codelineno-41-20"></a> <span class="bp">swap</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span> <span class="n">p</span><span class="p">)</span>
|
||
<a id="__codelineno-41-21" name="__codelineno-41-21" href="#__codelineno-41-21"></a> <span class="c1">// 循环向上堆化</span>
|
||
<a id="__codelineno-41-22" name="__codelineno-41-22" href="#__codelineno-41-22"></a> <span class="n">i</span> <span class="p">=</span> <span class="n">p</span>
|
||
<a id="__codelineno-41-23" name="__codelineno-41-23" href="#__codelineno-41-23"></a> <span class="p">}</span>
|
||
<a id="__codelineno-41-24" name="__codelineno-41-24" href="#__codelineno-41-24"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.js</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="cm">/* 元素入堆 */</span>
|
||
<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="nx">push</span><span class="p">(</span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a><span class="w"> </span><span class="c1">// 添加节点</span>
|
||
<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">val</span><span class="p">);</span>
|
||
<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
|
||
<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">siftUp</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
|
||
<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a><span class="p">}</span>
|
||
<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a>
|
||
<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
|
||
<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a><span class="err">#</span><span class="nx">siftUp</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-42-12" name="__codelineno-42-12" href="#__codelineno-42-12"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
|
||
<a id="__codelineno-42-13" name="__codelineno-42-13" href="#__codelineno-42-13"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="p">);</span>
|
||
<a id="__codelineno-42-14" name="__codelineno-42-14" href="#__codelineno-42-14"></a><span class="w"> </span><span class="c1">// 当“越过根节点”或“节点无须修复”时，结束堆化</span>
|
||
<a id="__codelineno-42-15" name="__codelineno-42-15" href="#__codelineno-42-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">p</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">p</span><span class="p">])</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||
<a id="__codelineno-42-16" name="__codelineno-42-16" href="#__codelineno-42-16"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
||
<a id="__codelineno-42-17" name="__codelineno-42-17" href="#__codelineno-42-17"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">p</span><span class="p">);</span>
|
||
<a id="__codelineno-42-18" name="__codelineno-42-18" href="#__codelineno-42-18"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
|
||
<a id="__codelineno-42-19" name="__codelineno-42-19" href="#__codelineno-42-19"></a><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">p</span><span class="p">;</span>
|
||
<a id="__codelineno-42-20" name="__codelineno-42-20" href="#__codelineno-42-20"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-42-21" name="__codelineno-42-21" href="#__codelineno-42-21"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.ts</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* 元素入堆 */</span>
|
||
<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="nx">push</span><span class="p">(</span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><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-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w"> </span><span class="c1">// 添加节点</span>
|
||
<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">val</span><span class="p">);</span>
|
||
<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
|
||
<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">siftUp</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
|
||
<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="p">}</span>
|
||
<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a>
|
||
<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
|
||
<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="nx">siftUp</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><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-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-43-12" name="__codelineno-43-12" href="#__codelineno-43-12"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
|
||
<a id="__codelineno-43-13" name="__codelineno-43-13" href="#__codelineno-43-13"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="p">);</span>
|
||
<a id="__codelineno-43-14" name="__codelineno-43-14" href="#__codelineno-43-14"></a><span class="w"> </span><span class="c1">// 当“越过根节点”或“节点无须修复”时，结束堆化</span>
|
||
<a id="__codelineno-43-15" name="__codelineno-43-15" href="#__codelineno-43-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">p</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">p</span><span class="p">])</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||
<a id="__codelineno-43-16" name="__codelineno-43-16" href="#__codelineno-43-16"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
||
<a id="__codelineno-43-17" name="__codelineno-43-17" href="#__codelineno-43-17"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">p</span><span class="p">);</span>
|
||
<a id="__codelineno-43-18" name="__codelineno-43-18" href="#__codelineno-43-18"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
|
||
<a id="__codelineno-43-19" name="__codelineno-43-19" href="#__codelineno-43-19"></a><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">p</span><span class="p">;</span>
|
||
<a id="__codelineno-43-20" name="__codelineno-43-20" href="#__codelineno-43-20"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-43-21" name="__codelineno-43-21" href="#__codelineno-43-21"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.dart</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* 元素入堆 */</span>
|
||
<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="w"> </span><span class="c1">// 添加节点</span>
|
||
<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w"> </span><span class="n">_maxHeap</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
|
||
<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="w"> </span><span class="n">siftUp</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
|
||
<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="p">}</span>
|
||
<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a>
|
||
<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
|
||
<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="kt">void</span><span class="w"> </span><span class="n">siftUp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-44-12" name="__codelineno-44-12" href="#__codelineno-44-12"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
|
||
<a id="__codelineno-44-13" name="__codelineno-44-13" href="#__codelineno-44-13"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_parent</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
|
||
<a id="__codelineno-44-14" name="__codelineno-44-14" href="#__codelineno-44-14"></a><span class="w"> </span><span class="c1">// 当“越过根节点”或“节点无须修复”时，结束堆化</span>
|
||
<a id="__codelineno-44-15" name="__codelineno-44-15" href="#__codelineno-44-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">_maxHeap</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">_maxHeap</span><span class="p">[</span><span class="n">p</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-44-16" name="__codelineno-44-16" href="#__codelineno-44-16"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||
<a id="__codelineno-44-17" name="__codelineno-44-17" href="#__codelineno-44-17"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-44-18" name="__codelineno-44-18" href="#__codelineno-44-18"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
||
<a id="__codelineno-44-19" name="__codelineno-44-19" href="#__codelineno-44-19"></a><span class="w"> </span><span class="n">_swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">p</span><span class="p">);</span>
|
||
<a id="__codelineno-44-20" name="__codelineno-44-20" href="#__codelineno-44-20"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
|
||
<a id="__codelineno-44-21" name="__codelineno-44-21" href="#__codelineno-44-21"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span><span class="p">;</span>
|
||
<a id="__codelineno-44-22" name="__codelineno-44-22" href="#__codelineno-44-22"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-44-23" name="__codelineno-44-23" href="#__codelineno-44-23"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.rs</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="cm">/* 元素入堆 */</span>
|
||
<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a><span class="k">fn</span> <span class="nf">push</span><span class="p">(</span><span class="o">&</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">val</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="w"> </span><span class="c1">// 添加节点</span>
|
||
<a id="__codelineno-45-4" name="__codelineno-45-4" href="#__codelineno-45-4"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-45-5" name="__codelineno-45-5" href="#__codelineno-45-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
|
||
<a id="__codelineno-45-6" name="__codelineno-45-6" href="#__codelineno-45-6"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">sift_up</span><span class="p">(</span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||
<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="p">}</span>
|
||
<a id="__codelineno-45-8" name="__codelineno-45-8" href="#__codelineno-45-8"></a>
|
||
<a id="__codelineno-45-9" name="__codelineno-45-9" href="#__codelineno-45-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
|
||
<a id="__codelineno-45-10" name="__codelineno-45-10" href="#__codelineno-45-10"></a><span class="k">fn</span> <span class="nf">sift_up</span><span class="p">(</span><span class="o">&</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">i</span>: <span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-45-11" name="__codelineno-45-11" href="#__codelineno-45-11"></a><span class="w"> </span><span class="k">loop</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-45-12" name="__codelineno-45-12" href="#__codelineno-45-12"></a><span class="w"> </span><span class="c1">// 节点 i 已经是堆顶节点了，结束堆化</span>
|
||
<a id="__codelineno-45-13" name="__codelineno-45-13" href="#__codelineno-45-13"></a><span class="w"> </span><span class="k">if</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="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-45-14" name="__codelineno-45-14" href="#__codelineno-45-14"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||
<a id="__codelineno-45-15" name="__codelineno-45-15" href="#__codelineno-45-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-45-16" name="__codelineno-45-16" href="#__codelineno-45-16"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
|
||
<a id="__codelineno-45-17" name="__codelineno-45-17" href="#__codelineno-45-17"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
|
||
<a id="__codelineno-45-18" name="__codelineno-45-18" href="#__codelineno-45-18"></a><span class="w"> </span><span class="c1">// 当“节点无须修复”时，结束堆化</span>
|
||
<a id="__codelineno-45-19" name="__codelineno-45-19" href="#__codelineno-45-19"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</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="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">p</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-45-20" name="__codelineno-45-20" href="#__codelineno-45-20"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||
<a id="__codelineno-45-21" name="__codelineno-45-21" href="#__codelineno-45-21"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-45-22" name="__codelineno-45-22" href="#__codelineno-45-22"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
||
<a id="__codelineno-45-23" name="__codelineno-45-23" href="#__codelineno-45-23"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">p</span><span class="p">);</span>
|
||
<a id="__codelineno-45-24" name="__codelineno-45-24" href="#__codelineno-45-24"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
|
||
<a id="__codelineno-45-25" name="__codelineno-45-25" href="#__codelineno-45-25"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span><span class="p">;</span>
|
||
<a id="__codelineno-45-26" name="__codelineno-45-26" href="#__codelineno-45-26"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-45-27" name="__codelineno-45-27" href="#__codelineno-45-27"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.c</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="cm">/* 元素入堆 */</span>
|
||
<a id="__codelineno-46-2" name="__codelineno-46-2" href="#__codelineno-46-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="w"> </span><span class="c1">// 默认情况下，不应该添加这么多节点</span>
|
||
<a id="__codelineno-46-4" name="__codelineno-46-4" href="#__codelineno-46-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">maxHeap</span><span class="o">-></span><span class="n">size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-46-5" name="__codelineno-46-5" href="#__codelineno-46-5"></a><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">"heap is full!"</span><span class="p">);</span>
|
||
<a id="__codelineno-46-6" name="__codelineno-46-6" href="#__codelineno-46-6"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
||
<a id="__codelineno-46-7" name="__codelineno-46-7" href="#__codelineno-46-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-46-8" name="__codelineno-46-8" href="#__codelineno-46-8"></a><span class="w"> </span><span class="c1">// 添加节点</span>
|
||
<a id="__codelineno-46-9" name="__codelineno-46-9" href="#__codelineno-46-9"></a><span class="w"> </span><span class="n">maxHeap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="n">maxHeap</span><span class="o">-></span><span class="n">size</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
|
||
<a id="__codelineno-46-10" name="__codelineno-46-10" href="#__codelineno-46-10"></a><span class="w"> </span><span class="n">maxHeap</span><span class="o">-></span><span class="n">size</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-46-11" name="__codelineno-46-11" href="#__codelineno-46-11"></a>
|
||
<a id="__codelineno-46-12" name="__codelineno-46-12" href="#__codelineno-46-12"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
|
||
<a id="__codelineno-46-13" name="__codelineno-46-13" href="#__codelineno-46-13"></a><span class="w"> </span><span class="n">siftUp</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="n">maxHeap</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">1</span><span class="p">);</span>
|
||
<a id="__codelineno-46-14" name="__codelineno-46-14" href="#__codelineno-46-14"></a><span class="p">}</span>
|
||
<a id="__codelineno-46-15" name="__codelineno-46-15" href="#__codelineno-46-15"></a>
|
||
<a id="__codelineno-46-16" name="__codelineno-46-16" href="#__codelineno-46-16"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
|
||
<a id="__codelineno-46-17" name="__codelineno-46-17" href="#__codelineno-46-17"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftUp</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-46-18" name="__codelineno-46-18" href="#__codelineno-46-18"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nb">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-46-19" name="__codelineno-46-19" href="#__codelineno-46-19"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
|
||
<a id="__codelineno-46-20" name="__codelineno-46-20" href="#__codelineno-46-20"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
|
||
<a id="__codelineno-46-21" name="__codelineno-46-21" href="#__codelineno-46-21"></a><span class="w"> </span><span class="c1">// 当“越过根节点”或“节点无须修复”时，结束堆化</span>
|
||
<a id="__codelineno-46-22" name="__codelineno-46-22" href="#__codelineno-46-22"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-></span><span class="n">data</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">maxHeap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="n">p</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-46-23" name="__codelineno-46-23" href="#__codelineno-46-23"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||
<a id="__codelineno-46-24" name="__codelineno-46-24" href="#__codelineno-46-24"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-46-25" name="__codelineno-46-25" href="#__codelineno-46-25"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
||
<a id="__codelineno-46-26" name="__codelineno-46-26" href="#__codelineno-46-26"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">p</span><span class="p">);</span>
|
||
<a id="__codelineno-46-27" name="__codelineno-46-27" href="#__codelineno-46-27"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
|
||
<a id="__codelineno-46-28" name="__codelineno-46-28" href="#__codelineno-46-28"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span><span class="p">;</span>
|
||
<a id="__codelineno-46-29" name="__codelineno-46-29" href="#__codelineno-46-29"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-46-30" name="__codelineno-46-30" href="#__codelineno-46-30"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.zig</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="c1">// 元素入堆</span>
|
||
<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">push</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="o">:</span><span class="w"> </span><span class="n">T</span><span class="p">)</span><span class="w"> </span><span class="o">!</span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="w"> </span><span class="c1">// 添加节点</span>
|
||
<a id="__codelineno-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></a><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
|
||
<a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></a><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">siftUp</span><span class="p">(</span><span class="n">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||
<a id="__codelineno-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></a><span class="p">}</span><span class="w"> </span>
|
||
<a id="__codelineno-47-8" name="__codelineno-47-8" href="#__codelineno-47-8"></a>
|
||
<a id="__codelineno-47-9" name="__codelineno-47-9" href="#__codelineno-47-9"></a><span class="c1">// 从节点 i 开始，从底至顶堆化</span>
|
||
<a id="__codelineno-47-10" name="__codelineno-47-10" href="#__codelineno-47-10"></a><span class="k">fn</span><span class="w"> </span><span class="n">siftUp</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">,</span><span class="w"> </span><span class="n">i_</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="o">!</span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-47-11" name="__codelineno-47-11" href="#__codelineno-47-11"></a><span class="w"> </span><span class="kr">var</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">i_</span><span class="p">;</span>
|
||
<a id="__codelineno-47-12" name="__codelineno-47-12" href="#__codelineno-47-12"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-47-13" name="__codelineno-47-13" href="#__codelineno-47-13"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
|
||
<a id="__codelineno-47-14" name="__codelineno-47-14" href="#__codelineno-47-14"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
|
||
<a id="__codelineno-47-15" name="__codelineno-47-15" href="#__codelineno-47-15"></a><span class="w"> </span><span class="c1">// 当“越过根节点”或“节点无须修复”时，结束堆化</span>
|
||
<a id="__codelineno-47-16" name="__codelineno-47-16" href="#__codelineno-47-16"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="k">or</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">items</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">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">items</span><span class="p">[</span><span class="n">p</span><span class="p">])</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||
<a id="__codelineno-47-17" name="__codelineno-47-17" href="#__codelineno-47-17"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
||
<a id="__codelineno-47-18" name="__codelineno-47-18" href="#__codelineno-47-18"></a><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">p</span><span class="p">);</span>
|
||
<a id="__codelineno-47-19" name="__codelineno-47-19" href="#__codelineno-47-19"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
|
||
<a id="__codelineno-47-20" name="__codelineno-47-20" href="#__codelineno-47-20"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span><span class="p">;</span>
|
||
<a id="__codelineno-47-21" name="__codelineno-47-21" href="#__codelineno-47-21"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-47-22" name="__codelineno-47-22" href="#__codelineno-47-22"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<details class="pythontutor">
|
||
<summary>可视化运行</summary>
|
||
<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20MaxHeap%3A%0A%20%20%20%20%22%22%22%E5%A4%A7%E9%A1%B6%E5%A0%86%22%22%22%0A%0A%20%20%20%20def%20__init__%28self,%20nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E6%9E%84%E9%80%A0%E6%96%B9%E6%B3%95%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E5%B0%86%E5%88%97%E8%A1%A8%E5%85%83%E7%B4%A0%E5%8E%9F%E5%B0%81%E4%B8%8D%E5%8A%A8%E6%B7%BB%E5%8A%A0%E8%BF%9B%E5%A0%86%0A%20%20%20%20%20%20%20%20self.max_heap%20%3D%20nums%0A%0A%20%20%20%20def%20left%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%B7%A6%E5%AD%90%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20*%20i%20%2B%201%0A%0A%20%20%20%20def%20right%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%8F%B3%E5%AD%90%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20*%20i%20%2B%202%0A%0A%20%20%20%20def%20parent%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E7%88%B6%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%20%28i%20-%201%29%20//%202%20%20%23%20%E5%90%91%E4%B8%8B%E6%95%B4%E9%99%A4%0A%0A%20%20%20%20def%20swap%28self,%20i%3A%20int,%20j%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E4%BA%A4%E6%8D%A2%E5%85%83%E7%B4%A0%22%22%22%0A%20%20%20%20%20%20%20%20self.max_heap%5Bi%5D,%20self.max_heap%5Bj%5D%20%3D%20self.max_heap%5Bj%5D,%20self.max_heap%5Bi%5D%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%A0%86%E5%A4%A7%E5%B0%8F%22%22%22%0A%20%20%20%20%20%20%20%20return%20len%28self.max_heap%29%0A%0A%20%20%20%20def%20is_empty%28self%29%20-%3E%20bool%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%88%A4%E6%96%AD%E5%A0%86%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%22%22%22%0A%20%20%20%20%20%20%20%20return%20self.size%28%29%20%3D%3D%200%0A%0A%20%20%20%20def%20push%28self,%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%85%83%E7%B4%A0%E5%85%A5%E5%A0%86%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E6%B7%BB%E5%8A%A0%E8%8A%82%E7%82%B9%0A%20%20%20%20%20%20%20%20self.max_heap.append%28val%29%0A%20%20%20%20%20%20%20%20%23%20%E4%BB%8E%E5%BA%95%E8%87%B3%E9%A1%B6%E5%A0%86%E5%8C%96%0A%20%20%20%20%20%20%20%20self.sift_up%28self.size%28%29%20-%201%29%0A%0A%20%20%20%20def%20sift_up%28self,%20i%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E4%BB%8E%E8%8A%82%E7%82%B9%20i%20%E5%BC%80%E5%A7%8B%EF%BC%8C%E4%BB%8E%E5%BA%95%E8%87%B3%E9%A1%B6%E5%A0%86%E5%8C%96%22%22%22%0A%20%20%20%20%20%20%20%20while%20True%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E8%8A%82%E7%82%B9%20i%20%E7%9A%84%E7%88%B6%E8%8A%82%E7%82%B9%0A%20%20%20%20%20%20%20%20%20%20%20%20p%20%3D%20self.parent%28i%29%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E5%BD%93%E2%80%9C%E8%B6%8A%E8%BF%87%E6%A0%B9%E8%8A%82%E7%82%B9%E2%80%9D%E6%88%96%E2%80%9C%E8%8A%82%E7%82%B9%E6%97%A0%E9%A1%BB%E4%BF%AE%E5%A4%8D%E2%80%9D%E6%97%B6%EF%BC%8C%E7%BB%93%E6%9D%9F%E5%A0%86%E5%8C%96%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20p%20%3C%200%20or%20self.max_heap%5Bi%5D%20%3C%3D%20self.max_heap%5Bp%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20break%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E4%BA%A4%E6%8D%A2%E4%B8%A4%E8%8A%82%E7%82%B9%0A%20%20%20%20%20%20%20%20%20%20%20%20self.swap%28i,%20p%29%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E5%BE%AA%E7%8E%AF%E5%90%91%E4%B8%8A%E5%A0%86%E5%8C%96%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%3D%20p%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%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20%23%20%E8%AF%B7%E6%B3%A8%E6%84%8F%EF%BC%8C%E8%BE%93%E5%85%A5%E6%95%B0%E7%BB%84%E5%B7%B2%E7%BB%8F%E6%98%AF%E4%B8%80%E4%B8%AA%E5%B7%B2%E7%BB%8F%E6%98%AF%E4%B8%80%E4%B8%AA%E5%90%88%E6%B3%95%E7%9A%84%E5%A0%86%0A%20%20%20%20max_heap%20%3D%20MaxHeap%28%5B9,%208,%206,%206,%207,%205,%202,%201,%204,%203,%206,%202%5D%29%0A%0A%20%20%20%20%23%20%E5%85%83%E7%B4%A0%E5%85%A5%E5%A0%86%0A%20%20%20%20val%20%3D%207%0A%20%20%20%20max_heap.push%28val%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=8&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%20MaxHeap%3A%0A%20%20%20%20%22%22%22%E5%A4%A7%E9%A1%B6%E5%A0%86%22%22%22%0A%0A%20%20%20%20def%20__init__%28self,%20nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E6%9E%84%E9%80%A0%E6%96%B9%E6%B3%95%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E5%B0%86%E5%88%97%E8%A1%A8%E5%85%83%E7%B4%A0%E5%8E%9F%E5%B0%81%E4%B8%8D%E5%8A%A8%E6%B7%BB%E5%8A%A0%E8%BF%9B%E5%A0%86%0A%20%20%20%20%20%20%20%20self.max_heap%20%3D%20nums%0A%0A%20%20%20%20def%20left%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%B7%A6%E5%AD%90%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20*%20i%20%2B%201%0A%0A%20%20%20%20def%20right%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%8F%B3%E5%AD%90%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20*%20i%20%2B%202%0A%0A%20%20%20%20def%20parent%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E7%88%B6%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%20%28i%20-%201%29%20//%202%20%20%23%20%E5%90%91%E4%B8%8B%E6%95%B4%E9%99%A4%0A%0A%20%20%20%20def%20swap%28self,%20i%3A%20int,%20j%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E4%BA%A4%E6%8D%A2%E5%85%83%E7%B4%A0%22%22%22%0A%20%20%20%20%20%20%20%20self.max_heap%5Bi%5D,%20self.max_heap%5Bj%5D%20%3D%20self.max_heap%5Bj%5D,%20self.max_heap%5Bi%5D%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%A0%86%E5%A4%A7%E5%B0%8F%22%22%22%0A%20%20%20%20%20%20%20%20return%20len%28self.max_heap%29%0A%0A%20%20%20%20def%20is_empty%28self%29%20-%3E%20bool%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%88%A4%E6%96%AD%E5%A0%86%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%22%22%22%0A%20%20%20%20%20%20%20%20return%20self.size%28%29%20%3D%3D%200%0A%0A%20%20%20%20def%20push%28self,%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%85%83%E7%B4%A0%E5%85%A5%E5%A0%86%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E6%B7%BB%E5%8A%A0%E8%8A%82%E7%82%B9%0A%20%20%20%20%20%20%20%20self.max_heap.append%28val%29%0A%20%20%20%20%20%20%20%20%23%20%E4%BB%8E%E5%BA%95%E8%87%B3%E9%A1%B6%E5%A0%86%E5%8C%96%0A%20%20%20%20%20%20%20%20self.sift_up%28self.size%28%29%20-%201%29%0A%0A%20%20%20%20def%20sift_up%28self,%20i%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E4%BB%8E%E8%8A%82%E7%82%B9%20i%20%E5%BC%80%E5%A7%8B%EF%BC%8C%E4%BB%8E%E5%BA%95%E8%87%B3%E9%A1%B6%E5%A0%86%E5%8C%96%22%22%22%0A%20%20%20%20%20%20%20%20while%20True%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E8%8A%82%E7%82%B9%20i%20%E7%9A%84%E7%88%B6%E8%8A%82%E7%82%B9%0A%20%20%20%20%20%20%20%20%20%20%20%20p%20%3D%20self.parent%28i%29%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E5%BD%93%E2%80%9C%E8%B6%8A%E8%BF%87%E6%A0%B9%E8%8A%82%E7%82%B9%E2%80%9D%E6%88%96%E2%80%9C%E8%8A%82%E7%82%B9%E6%97%A0%E9%A1%BB%E4%BF%AE%E5%A4%8D%E2%80%9D%E6%97%B6%EF%BC%8C%E7%BB%93%E6%9D%9F%E5%A0%86%E5%8C%96%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20p%20%3C%200%20or%20self.max_heap%5Bi%5D%20%3C%3D%20self.max_heap%5Bp%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20break%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E4%BA%A4%E6%8D%A2%E4%B8%A4%E8%8A%82%E7%82%B9%0A%20%20%20%20%20%20%20%20%20%20%20%20self.swap%28i,%20p%29%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E5%BE%AA%E7%8E%AF%E5%90%91%E4%B8%8A%E5%A0%86%E5%8C%96%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%3D%20p%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%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20%23%20%E8%AF%B7%E6%B3%A8%E6%84%8F%EF%BC%8C%E8%BE%93%E5%85%A5%E6%95%B0%E7%BB%84%E5%B7%B2%E7%BB%8F%E6%98%AF%E4%B8%80%E4%B8%AA%E5%B7%B2%E7%BB%8F%E6%98%AF%E4%B8%80%E4%B8%AA%E5%90%88%E6%B3%95%E7%9A%84%E5%A0%86%0A%20%20%20%20max_heap%20%3D%20MaxHeap%28%5B9,%208,%206,%206,%207,%205,%202,%201,%204,%203,%206,%202%5D%29%0A%0A%20%20%20%20%23%20%E5%85%83%E7%B4%A0%E5%85%A5%E5%A0%86%0A%20%20%20%20val%20%3D%207%0A%20%20%20%20max_heap.push%28val%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=8&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全屏观看 ></a></div></p>
|
||
</details>
|
||
<h3 id="4">4. 堆顶元素出堆<a class="headerlink" href="#4" title="Permanent link">¶</a></h3>
|
||
<p>堆顶元素是二叉树的根节点，即列表首元素。如果我们直接从列表中删除首元素，那么二叉树中所有节点的索引都会发生变化，这将使得后续使用堆化进行修复变得困难。为了尽量减少元素索引的变动，我们采用以下操作步骤。</p>
|
||
<ol>
|
||
<li>交换堆顶元素与堆底元素（交换根节点与最右叶节点）。</li>
|
||
<li>交换完成后，将堆底从列表中删除（注意，由于已经交换，因此实际上删除的是原来的堆顶元素）。</li>
|
||
<li>从根节点开始，<strong>从顶至底执行堆化</strong>。</li>
|
||
</ol>
|
||
<p>如图 8-4 所示，<strong>“从顶至底堆化”的操作方向与“从底至顶堆化”相反</strong>，我们将根节点的值与其两个子节点的值进行比较，将最大的子节点与根节点交换。然后循环执行此操作，直到越过叶节点或遇到无须交换的节点时结束。</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="6:10"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1"><1></label><label for="__tabbed_6_2"><2></label><label for="__tabbed_6_3"><3></label><label for="__tabbed_6_4"><4></label><label for="__tabbed_6_5"><5></label><label for="__tabbed_6_6"><6></label><label for="__tabbed_6_7"><7></label><label for="__tabbed_6_8"><8></label><label for="__tabbed_6_9"><9></label><label for="__tabbed_6_10"><10></label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../heap.assets/heap_pop_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="堆顶元素出堆步骤" class="animation-figure" src="../heap.assets/heap_pop_step1.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../heap.assets/heap_pop_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step2" class="animation-figure" src="../heap.assets/heap_pop_step2.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../heap.assets/heap_pop_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step3" class="animation-figure" src="../heap.assets/heap_pop_step3.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../heap.assets/heap_pop_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step4" class="animation-figure" src="../heap.assets/heap_pop_step4.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../heap.assets/heap_pop_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step5" class="animation-figure" src="../heap.assets/heap_pop_step5.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../heap.assets/heap_pop_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step6" class="animation-figure" src="../heap.assets/heap_pop_step6.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../heap.assets/heap_pop_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step7" class="animation-figure" src="../heap.assets/heap_pop_step7.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../heap.assets/heap_pop_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step8" class="animation-figure" src="../heap.assets/heap_pop_step8.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../heap.assets/heap_pop_step9.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step9" class="animation-figure" src="../heap.assets/heap_pop_step9.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../heap.assets/heap_pop_step10.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step10" class="animation-figure" src="../heap.assets/heap_pop_step10.png" /></a></p>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p align="center"> 图 8-4 堆顶元素出堆步骤 </p>
|
||
|
||
<p>与元素入堆操作相似，堆顶元素出堆操作的时间复杂度也为 <span class="arithmatex">\(O(\log n)\)</span> 。代码如下所示：</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="7:12"><input checked="checked" id="__tabbed_7_1" name="__tabbed_7" type="radio" /><input id="__tabbed_7_2" name="__tabbed_7" type="radio" /><input id="__tabbed_7_3" name="__tabbed_7" type="radio" /><input id="__tabbed_7_4" name="__tabbed_7" type="radio" /><input id="__tabbed_7_5" name="__tabbed_7" type="radio" /><input id="__tabbed_7_6" name="__tabbed_7" type="radio" /><input id="__tabbed_7_7" name="__tabbed_7" type="radio" /><input id="__tabbed_7_8" name="__tabbed_7" type="radio" /><input id="__tabbed_7_9" name="__tabbed_7" type="radio" /><input id="__tabbed_7_10" name="__tabbed_7" type="radio" /><input id="__tabbed_7_11" name="__tabbed_7" type="radio" /><input id="__tabbed_7_12" name="__tabbed_7" type="radio" /><div class="tabbed-labels"><label for="__tabbed_7_1">Python</label><label for="__tabbed_7_2">C++</label><label for="__tabbed_7_3">Java</label><label for="__tabbed_7_4">C#</label><label for="__tabbed_7_5">Go</label><label for="__tabbed_7_6">Swift</label><label for="__tabbed_7_7">JS</label><label for="__tabbed_7_8">TS</label><label for="__tabbed_7_9">Dart</label><label for="__tabbed_7_10">Rust</label><label for="__tabbed_7_11">C</label><label for="__tabbed_7_12">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.py</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="k">def</span> <span class="nf">pop</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||
<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a><span class="w"> </span><span class="sd">"""元素出堆"""</span>
|
||
<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a> <span class="c1"># 判空处理</span>
|
||
<a id="__codelineno-48-4" name="__codelineno-48-4" href="#__codelineno-48-4"></a> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
|
||
<a id="__codelineno-48-5" name="__codelineno-48-5" href="#__codelineno-48-5"></a> <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">"堆为空"</span><span class="p">)</span>
|
||
<a id="__codelineno-48-6" name="__codelineno-48-6" href="#__codelineno-48-6"></a> <span class="c1"># 交换根节点与最右叶节点（交换首元素与尾元素）</span>
|
||
<a id="__codelineno-48-7" name="__codelineno-48-7" href="#__codelineno-48-7"></a> <span class="bp">self</span><span class="o">.</span><span class="n">swap</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-48-8" name="__codelineno-48-8" href="#__codelineno-48-8"></a> <span class="c1"># 删除节点</span>
|
||
<a id="__codelineno-48-9" name="__codelineno-48-9" href="#__codelineno-48-9"></a> <span class="n">val</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
|
||
<a id="__codelineno-48-10" name="__codelineno-48-10" href="#__codelineno-48-10"></a> <span class="c1"># 从顶至底堆化</span>
|
||
<a id="__codelineno-48-11" name="__codelineno-48-11" href="#__codelineno-48-11"></a> <span class="bp">self</span><span class="o">.</span><span class="n">sift_down</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-48-12" name="__codelineno-48-12" href="#__codelineno-48-12"></a> <span class="c1"># 返回堆顶元素</span>
|
||
<a id="__codelineno-48-13" name="__codelineno-48-13" href="#__codelineno-48-13"></a> <span class="k">return</span> <span class="n">val</span>
|
||
<a id="__codelineno-48-14" name="__codelineno-48-14" href="#__codelineno-48-14"></a>
|
||
<a id="__codelineno-48-15" name="__codelineno-48-15" href="#__codelineno-48-15"></a><span class="k">def</span> <span class="nf">sift_down</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
||
<a id="__codelineno-48-16" name="__codelineno-48-16" href="#__codelineno-48-16"></a><span class="w"> </span><span class="sd">"""从节点 i 开始，从顶至底堆化"""</span>
|
||
<a id="__codelineno-48-17" name="__codelineno-48-17" href="#__codelineno-48-17"></a> <span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
|
||
<a id="__codelineno-48-18" name="__codelineno-48-18" href="#__codelineno-48-18"></a> <span class="c1"># 判断节点 i, l, r 中值最大的节点，记为 ma</span>
|
||
<a id="__codelineno-48-19" name="__codelineno-48-19" href="#__codelineno-48-19"></a> <span class="n">l</span><span class="p">,</span> <span class="n">r</span><span class="p">,</span> <span class="n">ma</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span> <span class="bp">self</span><span class="o">.</span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span> <span class="n">i</span>
|
||
<a id="__codelineno-48-20" name="__codelineno-48-20" href="#__codelineno-48-20"></a> <span class="k">if</span> <span class="n">l</span> <span class="o"><</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="ow">and</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">l</span><span class="p">]</span> <span class="o">></span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">ma</span><span class="p">]:</span>
|
||
<a id="__codelineno-48-21" name="__codelineno-48-21" href="#__codelineno-48-21"></a> <span class="n">ma</span> <span class="o">=</span> <span class="n">l</span>
|
||
<a id="__codelineno-48-22" name="__codelineno-48-22" href="#__codelineno-48-22"></a> <span class="k">if</span> <span class="n">r</span> <span class="o"><</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="ow">and</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">r</span><span class="p">]</span> <span class="o">></span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">ma</span><span class="p">]:</span>
|
||
<a id="__codelineno-48-23" name="__codelineno-48-23" href="#__codelineno-48-23"></a> <span class="n">ma</span> <span class="o">=</span> <span class="n">r</span>
|
||
<a id="__codelineno-48-24" name="__codelineno-48-24" href="#__codelineno-48-24"></a> <span class="c1"># 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
|
||
<a id="__codelineno-48-25" name="__codelineno-48-25" href="#__codelineno-48-25"></a> <span class="k">if</span> <span class="n">ma</span> <span class="o">==</span> <span class="n">i</span><span class="p">:</span>
|
||
<a id="__codelineno-48-26" name="__codelineno-48-26" href="#__codelineno-48-26"></a> <span class="k">break</span>
|
||
<a id="__codelineno-48-27" name="__codelineno-48-27" href="#__codelineno-48-27"></a> <span class="c1"># 交换两节点</span>
|
||
<a id="__codelineno-48-28" name="__codelineno-48-28" href="#__codelineno-48-28"></a> <span class="bp">self</span><span class="o">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">ma</span><span class="p">)</span>
|
||
<a id="__codelineno-48-29" name="__codelineno-48-29" href="#__codelineno-48-29"></a> <span class="c1"># 循环向下堆化</span>
|
||
<a id="__codelineno-48-30" name="__codelineno-48-30" href="#__codelineno-48-30"></a> <span class="n">i</span> <span class="o">=</span> <span class="n">ma</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.cpp</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="cm">/* 元素出堆 */</span>
|
||
<a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></a><span class="w"> </span><span class="c1">// 判空处理</span>
|
||
<a id="__codelineno-49-4" name="__codelineno-49-4" href="#__codelineno-49-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-49-5" name="__codelineno-49-5" href="#__codelineno-49-5"></a><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">"堆为空"</span><span class="p">);</span>
|
||
<a id="__codelineno-49-6" name="__codelineno-49-6" href="#__codelineno-49-6"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-49-7" name="__codelineno-49-7" href="#__codelineno-49-7"></a><span class="w"> </span><span class="c1">// 交换根节点与最右叶节点（交换首元素与尾元素）</span>
|
||
<a id="__codelineno-49-8" name="__codelineno-49-8" href="#__codelineno-49-8"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
|
||
<a id="__codelineno-49-9" name="__codelineno-49-9" href="#__codelineno-49-9"></a><span class="w"> </span><span class="c1">// 删除节点</span>
|
||
<a id="__codelineno-49-10" name="__codelineno-49-10" href="#__codelineno-49-10"></a><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
|
||
<a id="__codelineno-49-11" name="__codelineno-49-11" href="#__codelineno-49-11"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
|
||
<a id="__codelineno-49-12" name="__codelineno-49-12" href="#__codelineno-49-12"></a><span class="w"> </span><span class="n">siftDown</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
|
||
<a id="__codelineno-49-13" name="__codelineno-49-13" href="#__codelineno-49-13"></a><span class="p">}</span>
|
||
<a id="__codelineno-49-14" name="__codelineno-49-14" href="#__codelineno-49-14"></a>
|
||
<a id="__codelineno-49-15" name="__codelineno-49-15" href="#__codelineno-49-15"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
|
||
<a id="__codelineno-49-16" name="__codelineno-49-16" href="#__codelineno-49-16"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftDown</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-49-17" name="__codelineno-49-17" href="#__codelineno-49-17"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nb">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-49-18" name="__codelineno-49-18" href="#__codelineno-49-18"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 ma</span>
|
||
<a id="__codelineno-49-19" name="__codelineno-49-19" href="#__codelineno-49-19"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
|
||
<a id="__codelineno-49-20" name="__codelineno-49-20" href="#__codelineno-49-20"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</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="o">&&</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span>
|
||
<a id="__codelineno-49-21" name="__codelineno-49-21" href="#__codelineno-49-21"></a><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
|
||
<a id="__codelineno-49-22" name="__codelineno-49-22" href="#__codelineno-49-22"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</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="o">&&</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span>
|
||
<a id="__codelineno-49-23" name="__codelineno-49-23" href="#__codelineno-49-23"></a><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
|
||
<a id="__codelineno-49-24" name="__codelineno-49-24" href="#__codelineno-49-24"></a><span class="w"> </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
|
||
<a id="__codelineno-49-25" name="__codelineno-49-25" href="#__codelineno-49-25"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
|
||
<a id="__codelineno-49-26" name="__codelineno-49-26" href="#__codelineno-49-26"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||
<a id="__codelineno-49-27" name="__codelineno-49-27" href="#__codelineno-49-27"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">]);</span>
|
||
<a id="__codelineno-49-28" name="__codelineno-49-28" href="#__codelineno-49-28"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
|
||
<a id="__codelineno-49-29" name="__codelineno-49-29" href="#__codelineno-49-29"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
|
||
<a id="__codelineno-49-30" name="__codelineno-49-30" href="#__codelineno-49-30"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-49-31" name="__codelineno-49-31" href="#__codelineno-49-31"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.java</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="cm">/* 元素出堆 */</span>
|
||
<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a><span class="w"> </span><span class="c1">// 判空处理</span>
|
||
<a id="__codelineno-50-4" name="__codelineno-50-4" href="#__codelineno-50-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
|
||
<a id="__codelineno-50-5" name="__codelineno-50-5" href="#__codelineno-50-5"></a><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
|
||
<a id="__codelineno-50-6" name="__codelineno-50-6" href="#__codelineno-50-6"></a><span class="w"> </span><span class="c1">// 交换根节点与最右叶节点（交换首元素与尾元素）</span>
|
||
<a id="__codelineno-50-7" name="__codelineno-50-7" href="#__codelineno-50-7"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||
<a id="__codelineno-50-8" name="__codelineno-50-8" href="#__codelineno-50-8"></a><span class="w"> </span><span class="c1">// 删除节点</span>
|
||
<a id="__codelineno-50-9" name="__codelineno-50-9" href="#__codelineno-50-9"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||
<a id="__codelineno-50-10" name="__codelineno-50-10" href="#__codelineno-50-10"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
|
||
<a id="__codelineno-50-11" name="__codelineno-50-11" href="#__codelineno-50-11"></a><span class="w"> </span><span class="n">siftDown</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
|
||
<a id="__codelineno-50-12" name="__codelineno-50-12" href="#__codelineno-50-12"></a><span class="w"> </span><span class="c1">// 返回堆顶元素</span>
|
||
<a id="__codelineno-50-13" name="__codelineno-50-13" href="#__codelineno-50-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
|
||
<a id="__codelineno-50-14" name="__codelineno-50-14" href="#__codelineno-50-14"></a><span class="p">}</span>
|
||
<a id="__codelineno-50-15" name="__codelineno-50-15" href="#__codelineno-50-15"></a>
|
||
<a id="__codelineno-50-16" name="__codelineno-50-16" href="#__codelineno-50-16"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
|
||
<a id="__codelineno-50-17" name="__codelineno-50-17" href="#__codelineno-50-17"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftDown</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-50-18" name="__codelineno-50-18" href="#__codelineno-50-18"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-50-19" name="__codelineno-50-19" href="#__codelineno-50-19"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 ma</span>
|
||
<a id="__codelineno-50-20" name="__codelineno-50-20" href="#__codelineno-50-20"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
|
||
<a id="__codelineno-50-21" name="__codelineno-50-21" href="#__codelineno-50-21"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</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="o">&&</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">l</span><span class="p">)</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">ma</span><span class="p">))</span>
|
||
<a id="__codelineno-50-22" name="__codelineno-50-22" href="#__codelineno-50-22"></a><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
|
||
<a id="__codelineno-50-23" name="__codelineno-50-23" href="#__codelineno-50-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</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="o">&&</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">ma</span><span class="p">))</span>
|
||
<a id="__codelineno-50-24" name="__codelineno-50-24" href="#__codelineno-50-24"></a><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
|
||
<a id="__codelineno-50-25" name="__codelineno-50-25" href="#__codelineno-50-25"></a><span class="w"> </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
|
||
<a id="__codelineno-50-26" name="__codelineno-50-26" href="#__codelineno-50-26"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
|
||
<a id="__codelineno-50-27" name="__codelineno-50-27" href="#__codelineno-50-27"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||
<a id="__codelineno-50-28" name="__codelineno-50-28" href="#__codelineno-50-28"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
||
<a id="__codelineno-50-29" name="__codelineno-50-29" href="#__codelineno-50-29"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">ma</span><span class="p">);</span>
|
||
<a id="__codelineno-50-30" name="__codelineno-50-30" href="#__codelineno-50-30"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
|
||
<a id="__codelineno-50-31" name="__codelineno-50-31" href="#__codelineno-50-31"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
|
||
<a id="__codelineno-50-32" name="__codelineno-50-32" href="#__codelineno-50-32"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-50-33" name="__codelineno-50-33" href="#__codelineno-50-33"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.cs</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="cm">/* 元素出堆 */</span>
|
||
<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="w"> </span><span class="c1">// 判空处理</span>
|
||
<a id="__codelineno-51-4" name="__codelineno-51-4" href="#__codelineno-51-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">IsEmpty</span><span class="p">())</span>
|
||
<a id="__codelineno-51-5" name="__codelineno-51-5" href="#__codelineno-51-5"></a><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="nf">IndexOutOfRangeException</span><span class="p">();</span>
|
||
<a id="__codelineno-51-6" name="__codelineno-51-6" href="#__codelineno-51-6"></a><span class="w"> </span><span class="c1">// 交换根节点与最右叶节点（交换首元素与尾元素）</span>
|
||
<a id="__codelineno-51-7" name="__codelineno-51-7" href="#__codelineno-51-7"></a><span class="w"> </span><span class="n">Swap</span><span class="p">(</span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">Size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
|
||
<a id="__codelineno-51-8" name="__codelineno-51-8" href="#__codelineno-51-8"></a><span class="w"> </span><span class="c1">// 删除节点</span>
|
||
<a id="__codelineno-51-9" name="__codelineno-51-9" href="#__codelineno-51-9"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Last</span><span class="p">();</span>
|
||
<a id="__codelineno-51-10" name="__codelineno-51-10" href="#__codelineno-51-10"></a><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">RemoveAt</span><span class="p">(</span><span class="n">Size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
|
||
<a id="__codelineno-51-11" name="__codelineno-51-11" href="#__codelineno-51-11"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
|
||
<a id="__codelineno-51-12" name="__codelineno-51-12" href="#__codelineno-51-12"></a><span class="w"> </span><span class="n">SiftDown</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
|
||
<a id="__codelineno-51-13" name="__codelineno-51-13" href="#__codelineno-51-13"></a><span class="w"> </span><span class="c1">// 返回堆顶元素</span>
|
||
<a id="__codelineno-51-14" name="__codelineno-51-14" href="#__codelineno-51-14"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
|
||
<a id="__codelineno-51-15" name="__codelineno-51-15" href="#__codelineno-51-15"></a><span class="p">}</span>
|
||
<a id="__codelineno-51-16" name="__codelineno-51-16" href="#__codelineno-51-16"></a>
|
||
<a id="__codelineno-51-17" name="__codelineno-51-17" href="#__codelineno-51-17"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
|
||
<a id="__codelineno-51-18" name="__codelineno-51-18" href="#__codelineno-51-18"></a><span class="k">void</span><span class="w"> </span><span class="nf">SiftDown</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-51-19" name="__codelineno-51-19" href="#__codelineno-51-19"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="k">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-51-20" name="__codelineno-51-20" href="#__codelineno-51-20"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 ma</span>
|
||
<a id="__codelineno-51-21" name="__codelineno-51-21" href="#__codelineno-51-21"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
|
||
<a id="__codelineno-51-22" name="__codelineno-51-22" href="#__codelineno-51-22"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</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="o">&&</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span>
|
||
<a id="__codelineno-51-23" name="__codelineno-51-23" href="#__codelineno-51-23"></a><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
|
||
<a id="__codelineno-51-24" name="__codelineno-51-24" href="#__codelineno-51-24"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</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="o">&&</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span>
|
||
<a id="__codelineno-51-25" name="__codelineno-51-25" href="#__codelineno-51-25"></a><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
|
||
<a id="__codelineno-51-26" name="__codelineno-51-26" href="#__codelineno-51-26"></a><span class="w"> </span><span class="c1">// 若“节点 i 最大”或“越过叶节点”，则结束堆化</span>
|
||
<a id="__codelineno-51-27" name="__codelineno-51-27" href="#__codelineno-51-27"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||
<a id="__codelineno-51-28" name="__codelineno-51-28" href="#__codelineno-51-28"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
||
<a id="__codelineno-51-29" name="__codelineno-51-29" href="#__codelineno-51-29"></a><span class="w"> </span><span class="n">Swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">ma</span><span class="p">);</span>
|
||
<a id="__codelineno-51-30" name="__codelineno-51-30" href="#__codelineno-51-30"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
|
||
<a id="__codelineno-51-31" name="__codelineno-51-31" href="#__codelineno-51-31"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
|
||
<a id="__codelineno-51-32" name="__codelineno-51-32" href="#__codelineno-51-32"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-51-33" name="__codelineno-51-33" href="#__codelineno-51-33"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.go</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="cm">/* 元素出堆 */</span>
|
||
<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">pop</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></a><span class="w"> </span><span class="c1">// 判空处理</span>
|
||
<a id="__codelineno-52-4" name="__codelineno-52-4" href="#__codelineno-52-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-52-5" name="__codelineno-52-5" href="#__codelineno-52-5"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="s">"error"</span><span class="p">)</span>
|
||
<a id="__codelineno-52-6" name="__codelineno-52-6" href="#__codelineno-52-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
|
||
<a id="__codelineno-52-7" name="__codelineno-52-7" href="#__codelineno-52-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-52-8" name="__codelineno-52-8" href="#__codelineno-52-8"></a><span class="w"> </span><span class="c1">// 交换根节点与最右叶节点（交换首元素与尾元素）</span>
|
||
<a id="__codelineno-52-9" name="__codelineno-52-9" href="#__codelineno-52-9"></a><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-52-10" name="__codelineno-52-10" href="#__codelineno-52-10"></a><span class="w"> </span><span class="c1">// 删除节点</span>
|
||
<a id="__codelineno-52-11" name="__codelineno-52-11" href="#__codelineno-52-11"></a><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nb">len</span><span class="p">(</span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
|
||
<a id="__codelineno-52-12" name="__codelineno-52-12" href="#__codelineno-52-12"></a><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[:</span><span class="nb">len</span><span class="p">(</span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
|
||
<a id="__codelineno-52-13" name="__codelineno-52-13" href="#__codelineno-52-13"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
|
||
<a id="__codelineno-52-14" name="__codelineno-52-14" href="#__codelineno-52-14"></a><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">siftDown</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-52-15" name="__codelineno-52-15" href="#__codelineno-52-15"></a>
|
||
<a id="__codelineno-52-16" name="__codelineno-52-16" href="#__codelineno-52-16"></a><span class="w"> </span><span class="c1">// 返回堆顶元素</span>
|
||
<a id="__codelineno-52-17" name="__codelineno-52-17" href="#__codelineno-52-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">val</span>
|
||
<a id="__codelineno-52-18" name="__codelineno-52-18" href="#__codelineno-52-18"></a><span class="p">}</span>
|
||
<a id="__codelineno-52-19" name="__codelineno-52-19" href="#__codelineno-52-19"></a>
|
||
<a id="__codelineno-52-20" name="__codelineno-52-20" href="#__codelineno-52-20"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
|
||
<a id="__codelineno-52-21" name="__codelineno-52-21" href="#__codelineno-52-21"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">siftDown</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-52-22" name="__codelineno-52-22" href="#__codelineno-52-22"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="kc">true</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-52-23" name="__codelineno-52-23" href="#__codelineno-52-23"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 max</span>
|
||
<a id="__codelineno-52-24" name="__codelineno-52-24" href="#__codelineno-52-24"></a><span class="w"> </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">r</span><span class="p">,</span><span class="w"> </span><span class="nx">max</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="p">),</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="p">),</span><span class="w"> </span><span class="nx">i</span>
|
||
<a id="__codelineno-52-25" name="__codelineno-52-25" href="#__codelineno-52-25"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nx">l</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">></span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nx">max</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-52-26" name="__codelineno-52-26" href="#__codelineno-52-26"></a><span class="w"> </span><span class="nx">max</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">l</span>
|
||
<a id="__codelineno-52-27" name="__codelineno-52-27" href="#__codelineno-52-27"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-52-28" name="__codelineno-52-28" href="#__codelineno-52-28"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nx">r</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">></span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nx">max</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-52-29" name="__codelineno-52-29" href="#__codelineno-52-29"></a><span class="w"> </span><span class="nx">max</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">r</span>
|
||
<a id="__codelineno-52-30" name="__codelineno-52-30" href="#__codelineno-52-30"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-52-31" name="__codelineno-52-31" href="#__codelineno-52-31"></a><span class="w"> </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
|
||
<a id="__codelineno-52-32" name="__codelineno-52-32" href="#__codelineno-52-32"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">max</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-52-33" name="__codelineno-52-33" href="#__codelineno-52-33"></a><span class="w"> </span><span class="k">break</span>
|
||
<a id="__codelineno-52-34" name="__codelineno-52-34" href="#__codelineno-52-34"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-52-35" name="__codelineno-52-35" href="#__codelineno-52-35"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
||
<a id="__codelineno-52-36" name="__codelineno-52-36" href="#__codelineno-52-36"></a><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">max</span><span class="p">)</span>
|
||
<a id="__codelineno-52-37" name="__codelineno-52-37" href="#__codelineno-52-37"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
|
||
<a id="__codelineno-52-38" name="__codelineno-52-38" href="#__codelineno-52-38"></a><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">max</span>
|
||
<a id="__codelineno-52-39" name="__codelineno-52-39" href="#__codelineno-52-39"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-52-40" name="__codelineno-52-40" href="#__codelineno-52-40"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.swift</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="cm">/* 元素出堆 */</span>
|
||
<a id="__codelineno-53-2" name="__codelineno-53-2" href="#__codelineno-53-2"></a><span class="kd">func</span> <span class="nf">pop</span><span class="p">()</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||
<a id="__codelineno-53-3" name="__codelineno-53-3" href="#__codelineno-53-3"></a> <span class="c1">// 判空处理</span>
|
||
<a id="__codelineno-53-4" name="__codelineno-53-4" href="#__codelineno-53-4"></a> <span class="k">if</span> <span class="bp">isEmpty</span><span class="p">()</span> <span class="p">{</span>
|
||
<a id="__codelineno-53-5" name="__codelineno-53-5" href="#__codelineno-53-5"></a> <span class="bp">fatalError</span><span class="p">(</span><span class="s">"堆为空"</span><span class="p">)</span>
|
||
<a id="__codelineno-53-6" name="__codelineno-53-6" href="#__codelineno-53-6"></a> <span class="p">}</span>
|
||
<a id="__codelineno-53-7" name="__codelineno-53-7" href="#__codelineno-53-7"></a> <span class="c1">// 交换根节点与最右叶节点（交换首元素与尾元素）</span>
|
||
<a id="__codelineno-53-8" name="__codelineno-53-8" href="#__codelineno-53-8"></a> <span class="bp">swap</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span> <span class="n">size</span><span class="p">()</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-53-9" name="__codelineno-53-9" href="#__codelineno-53-9"></a> <span class="c1">// 删除节点</span>
|
||
<a id="__codelineno-53-10" name="__codelineno-53-10" href="#__codelineno-53-10"></a> <span class="kd">let</span> <span class="nv">val</span> <span class="p">=</span> <span class="n">maxHeap</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">at</span><span class="p">:</span> <span class="n">size</span><span class="p">()</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-53-11" name="__codelineno-53-11" href="#__codelineno-53-11"></a> <span class="c1">// 从顶至底堆化</span>
|
||
<a id="__codelineno-53-12" name="__codelineno-53-12" href="#__codelineno-53-12"></a> <span class="n">siftDown</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-53-13" name="__codelineno-53-13" href="#__codelineno-53-13"></a> <span class="c1">// 返回堆顶元素</span>
|
||
<a id="__codelineno-53-14" name="__codelineno-53-14" href="#__codelineno-53-14"></a> <span class="k">return</span> <span class="n">val</span>
|
||
<a id="__codelineno-53-15" name="__codelineno-53-15" href="#__codelineno-53-15"></a><span class="p">}</span>
|
||
<a id="__codelineno-53-16" name="__codelineno-53-16" href="#__codelineno-53-16"></a>
|
||
<a id="__codelineno-53-17" name="__codelineno-53-17" href="#__codelineno-53-17"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
|
||
<a id="__codelineno-53-18" name="__codelineno-53-18" href="#__codelineno-53-18"></a><span class="kd">func</span> <span class="nf">siftDown</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
|
||
<a id="__codelineno-53-19" name="__codelineno-53-19" href="#__codelineno-53-19"></a> <span class="kd">var</span> <span class="nv">i</span> <span class="p">=</span> <span class="n">i</span>
|
||
<a id="__codelineno-53-20" name="__codelineno-53-20" href="#__codelineno-53-20"></a> <span class="k">while</span> <span class="kc">true</span> <span class="p">{</span>
|
||
<a id="__codelineno-53-21" name="__codelineno-53-21" href="#__codelineno-53-21"></a> <span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 ma</span>
|
||
<a id="__codelineno-53-22" name="__codelineno-53-22" href="#__codelineno-53-22"></a> <span class="kd">let</span> <span class="nv">l</span> <span class="p">=</span> <span class="kr">left</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">i</span><span class="p">)</span>
|
||
<a id="__codelineno-53-23" name="__codelineno-53-23" href="#__codelineno-53-23"></a> <span class="kd">let</span> <span class="nv">r</span> <span class="p">=</span> <span class="kr">right</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">i</span><span class="p">)</span>
|
||
<a id="__codelineno-53-24" name="__codelineno-53-24" href="#__codelineno-53-24"></a> <span class="kd">var</span> <span class="nv">ma</span> <span class="p">=</span> <span class="n">i</span>
|
||
<a id="__codelineno-53-25" name="__codelineno-53-25" href="#__codelineno-53-25"></a> <span class="k">if</span> <span class="n">l</span> <span class="o"><</span> <span class="n">size</span><span class="p">(),</span> <span class="n">maxHeap</span><span class="p">[</span><span class="n">l</span><span class="p">]</span> <span class="o">></span> <span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">]</span> <span class="p">{</span>
|
||
<a id="__codelineno-53-26" name="__codelineno-53-26" href="#__codelineno-53-26"></a> <span class="n">ma</span> <span class="p">=</span> <span class="n">l</span>
|
||
<a id="__codelineno-53-27" name="__codelineno-53-27" href="#__codelineno-53-27"></a> <span class="p">}</span>
|
||
<a id="__codelineno-53-28" name="__codelineno-53-28" href="#__codelineno-53-28"></a> <span class="k">if</span> <span class="n">r</span> <span class="o"><</span> <span class="n">size</span><span class="p">(),</span> <span class="n">maxHeap</span><span class="p">[</span><span class="n">r</span><span class="p">]</span> <span class="o">></span> <span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">]</span> <span class="p">{</span>
|
||
<a id="__codelineno-53-29" name="__codelineno-53-29" href="#__codelineno-53-29"></a> <span class="n">ma</span> <span class="p">=</span> <span class="n">r</span>
|
||
<a id="__codelineno-53-30" name="__codelineno-53-30" href="#__codelineno-53-30"></a> <span class="p">}</span>
|
||
<a id="__codelineno-53-31" name="__codelineno-53-31" href="#__codelineno-53-31"></a> <span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
|
||
<a id="__codelineno-53-32" name="__codelineno-53-32" href="#__codelineno-53-32"></a> <span class="k">if</span> <span class="n">ma</span> <span class="p">==</span> <span class="n">i</span> <span class="p">{</span>
|
||
<a id="__codelineno-53-33" name="__codelineno-53-33" href="#__codelineno-53-33"></a> <span class="k">break</span>
|
||
<a id="__codelineno-53-34" name="__codelineno-53-34" href="#__codelineno-53-34"></a> <span class="p">}</span>
|
||
<a id="__codelineno-53-35" name="__codelineno-53-35" href="#__codelineno-53-35"></a> <span class="c1">// 交换两节点</span>
|
||
<a id="__codelineno-53-36" name="__codelineno-53-36" href="#__codelineno-53-36"></a> <span class="bp">swap</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span> <span class="n">ma</span><span class="p">)</span>
|
||
<a id="__codelineno-53-37" name="__codelineno-53-37" href="#__codelineno-53-37"></a> <span class="c1">// 循环向下堆化</span>
|
||
<a id="__codelineno-53-38" name="__codelineno-53-38" href="#__codelineno-53-38"></a> <span class="n">i</span> <span class="p">=</span> <span class="n">ma</span>
|
||
<a id="__codelineno-53-39" name="__codelineno-53-39" href="#__codelineno-53-39"></a> <span class="p">}</span>
|
||
<a id="__codelineno-53-40" name="__codelineno-53-40" href="#__codelineno-53-40"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.js</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="cm">/* 元素出堆 */</span>
|
||
<a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="nx">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a><span class="w"> </span><span class="c1">// 判空处理</span>
|
||
<a id="__codelineno-54-4" name="__codelineno-54-4" href="#__codelineno-54-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">'堆为空'</span><span class="p">);</span>
|
||
<a id="__codelineno-54-5" name="__codelineno-54-5" href="#__codelineno-54-5"></a><span class="w"> </span><span class="c1">// 交换根节点与最右叶节点（交换首元素与尾元素）</span>
|
||
<a id="__codelineno-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">swap</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
|
||
<a id="__codelineno-54-7" name="__codelineno-54-7" href="#__codelineno-54-7"></a><span class="w"> </span><span class="c1">// 删除节点</span>
|
||
<a id="__codelineno-54-8" name="__codelineno-54-8" href="#__codelineno-54-8"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
|
||
<a id="__codelineno-54-9" name="__codelineno-54-9" href="#__codelineno-54-9"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
|
||
<a id="__codelineno-54-10" name="__codelineno-54-10" href="#__codelineno-54-10"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">siftDown</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
|
||
<a id="__codelineno-54-11" name="__codelineno-54-11" href="#__codelineno-54-11"></a><span class="w"> </span><span class="c1">// 返回堆顶元素</span>
|
||
<a id="__codelineno-54-12" name="__codelineno-54-12" href="#__codelineno-54-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">val</span><span class="p">;</span>
|
||
<a id="__codelineno-54-13" name="__codelineno-54-13" href="#__codelineno-54-13"></a><span class="p">}</span>
|
||
<a id="__codelineno-54-14" name="__codelineno-54-14" href="#__codelineno-54-14"></a>
|
||
<a id="__codelineno-54-15" name="__codelineno-54-15" href="#__codelineno-54-15"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
|
||
<a id="__codelineno-54-16" name="__codelineno-54-16" href="#__codelineno-54-16"></a><span class="err">#</span><span class="nx">siftDown</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-54-17" name="__codelineno-54-17" href="#__codelineno-54-17"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-54-18" name="__codelineno-54-18" href="#__codelineno-54-18"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 ma</span>
|
||
<a id="__codelineno-54-19" name="__codelineno-54-19" href="#__codelineno-54-19"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="p">),</span>
|
||
<a id="__codelineno-54-20" name="__codelineno-54-20" href="#__codelineno-54-20"></a><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="p">);</span>
|
||
<a id="__codelineno-54-21" name="__codelineno-54-21" href="#__codelineno-54-21"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
|
||
<a id="__codelineno-54-22" name="__codelineno-54-22" href="#__codelineno-54-22"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">l</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">l</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">ma</span><span class="p">])</span><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">l</span><span class="p">;</span>
|
||
<a id="__codelineno-54-23" name="__codelineno-54-23" href="#__codelineno-54-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">r</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">r</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">ma</span><span class="p">])</span><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">r</span><span class="p">;</span>
|
||
<a id="__codelineno-54-24" name="__codelineno-54-24" href="#__codelineno-54-24"></a><span class="w"> </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
|
||
<a id="__codelineno-54-25" name="__codelineno-54-25" href="#__codelineno-54-25"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">ma</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||
<a id="__codelineno-54-26" name="__codelineno-54-26" href="#__codelineno-54-26"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
||
<a id="__codelineno-54-27" name="__codelineno-54-27" href="#__codelineno-54-27"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">ma</span><span class="p">);</span>
|
||
<a id="__codelineno-54-28" name="__codelineno-54-28" href="#__codelineno-54-28"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
|
||
<a id="__codelineno-54-29" name="__codelineno-54-29" href="#__codelineno-54-29"></a><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">ma</span><span class="p">;</span>
|
||
<a id="__codelineno-54-30" name="__codelineno-54-30" href="#__codelineno-54-30"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-54-31" name="__codelineno-54-31" href="#__codelineno-54-31"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.ts</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="cm">/* 元素出堆 */</span>
|
||
<a id="__codelineno-55-2" name="__codelineno-55-2" href="#__codelineno-55-2"></a><span class="nx">pop</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-55-3" name="__codelineno-55-3" href="#__codelineno-55-3"></a><span class="w"> </span><span class="c1">// 判空处理</span>
|
||
<a id="__codelineno-55-4" name="__codelineno-55-4" href="#__codelineno-55-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">RangeError</span><span class="p">(</span><span class="s1">'Heap is empty.'</span><span class="p">);</span>
|
||
<a id="__codelineno-55-5" name="__codelineno-55-5" href="#__codelineno-55-5"></a><span class="w"> </span><span class="c1">// 交换根节点与最右叶节点（交换首元素与尾元素）</span>
|
||
<a id="__codelineno-55-6" name="__codelineno-55-6" href="#__codelineno-55-6"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
|
||
<a id="__codelineno-55-7" name="__codelineno-55-7" href="#__codelineno-55-7"></a><span class="w"> </span><span class="c1">// 删除节点</span>
|
||
<a id="__codelineno-55-8" name="__codelineno-55-8" href="#__codelineno-55-8"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
|
||
<a id="__codelineno-55-9" name="__codelineno-55-9" href="#__codelineno-55-9"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
|
||
<a id="__codelineno-55-10" name="__codelineno-55-10" href="#__codelineno-55-10"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">siftDown</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
|
||
<a id="__codelineno-55-11" name="__codelineno-55-11" href="#__codelineno-55-11"></a><span class="w"> </span><span class="c1">// 返回堆顶元素</span>
|
||
<a id="__codelineno-55-12" name="__codelineno-55-12" href="#__codelineno-55-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">val</span><span class="p">;</span>
|
||
<a id="__codelineno-55-13" name="__codelineno-55-13" href="#__codelineno-55-13"></a><span class="p">}</span>
|
||
<a id="__codelineno-55-14" name="__codelineno-55-14" href="#__codelineno-55-14"></a>
|
||
<a id="__codelineno-55-15" name="__codelineno-55-15" href="#__codelineno-55-15"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
|
||
<a id="__codelineno-55-16" name="__codelineno-55-16" href="#__codelineno-55-16"></a><span class="nx">siftDown</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><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-55-17" name="__codelineno-55-17" href="#__codelineno-55-17"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-55-18" name="__codelineno-55-18" href="#__codelineno-55-18"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 ma</span>
|
||
<a id="__codelineno-55-19" name="__codelineno-55-19" href="#__codelineno-55-19"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="p">),</span>
|
||
<a id="__codelineno-55-20" name="__codelineno-55-20" href="#__codelineno-55-20"></a><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="p">);</span>
|
||
<a id="__codelineno-55-21" name="__codelineno-55-21" href="#__codelineno-55-21"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
|
||
<a id="__codelineno-55-22" name="__codelineno-55-22" href="#__codelineno-55-22"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">l</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">l</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">ma</span><span class="p">])</span><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">l</span><span class="p">;</span>
|
||
<a id="__codelineno-55-23" name="__codelineno-55-23" href="#__codelineno-55-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">r</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">r</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">ma</span><span class="p">])</span><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">r</span><span class="p">;</span>
|
||
<a id="__codelineno-55-24" name="__codelineno-55-24" href="#__codelineno-55-24"></a><span class="w"> </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
|
||
<a id="__codelineno-55-25" name="__codelineno-55-25" href="#__codelineno-55-25"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">ma</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||
<a id="__codelineno-55-26" name="__codelineno-55-26" href="#__codelineno-55-26"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
||
<a id="__codelineno-55-27" name="__codelineno-55-27" href="#__codelineno-55-27"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">ma</span><span class="p">);</span>
|
||
<a id="__codelineno-55-28" name="__codelineno-55-28" href="#__codelineno-55-28"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
|
||
<a id="__codelineno-55-29" name="__codelineno-55-29" href="#__codelineno-55-29"></a><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">ma</span><span class="p">;</span>
|
||
<a id="__codelineno-55-30" name="__codelineno-55-30" href="#__codelineno-55-30"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-55-31" name="__codelineno-55-31" href="#__codelineno-55-31"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.dart</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="cm">/* 元素出堆 */</span>
|
||
<a id="__codelineno-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a><span class="w"> </span><span class="c1">// 判空处理</span>
|
||
<a id="__codelineno-56-4" name="__codelineno-56-4" href="#__codelineno-56-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="n">Exception</span><span class="p">(</span><span class="s1">'堆为空'</span><span class="p">);</span>
|
||
<a id="__codelineno-56-5" name="__codelineno-56-5" href="#__codelineno-56-5"></a><span class="w"> </span><span class="c1">// 交换根节点与最右叶节点（交换首元素与尾元素）</span>
|
||
<a id="__codelineno-56-6" name="__codelineno-56-6" href="#__codelineno-56-6"></a><span class="w"> </span><span class="n">_swap</span><span class="p">(</span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
|
||
<a id="__codelineno-56-7" name="__codelineno-56-7" href="#__codelineno-56-7"></a><span class="w"> </span><span class="c1">// 删除节点</span>
|
||
<a id="__codelineno-56-8" name="__codelineno-56-8" href="#__codelineno-56-8"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_maxHeap</span><span class="p">.</span><span class="n">removeLast</span><span class="p">();</span>
|
||
<a id="__codelineno-56-9" name="__codelineno-56-9" href="#__codelineno-56-9"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
|
||
<a id="__codelineno-56-10" name="__codelineno-56-10" href="#__codelineno-56-10"></a><span class="w"> </span><span class="n">siftDown</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
|
||
<a id="__codelineno-56-11" name="__codelineno-56-11" href="#__codelineno-56-11"></a><span class="w"> </span><span class="c1">// 返回堆顶元素</span>
|
||
<a id="__codelineno-56-12" name="__codelineno-56-12" href="#__codelineno-56-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
|
||
<a id="__codelineno-56-13" name="__codelineno-56-13" href="#__codelineno-56-13"></a><span class="p">}</span>
|
||
<a id="__codelineno-56-14" name="__codelineno-56-14" href="#__codelineno-56-14"></a>
|
||
<a id="__codelineno-56-15" name="__codelineno-56-15" href="#__codelineno-56-15"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
|
||
<a id="__codelineno-56-16" name="__codelineno-56-16" href="#__codelineno-56-16"></a><span class="kt">void</span><span class="w"> </span><span class="n">siftDown</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-56-17" name="__codelineno-56-17" href="#__codelineno-56-17"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-56-18" name="__codelineno-56-18" href="#__codelineno-56-18"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 ma</span>
|
||
<a id="__codelineno-56-19" name="__codelineno-56-19" href="#__codelineno-56-19"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_left</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
|
||
<a id="__codelineno-56-20" name="__codelineno-56-20" href="#__codelineno-56-20"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_right</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
|
||
<a id="__codelineno-56-21" name="__codelineno-56-21" href="#__codelineno-56-21"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
|
||
<a id="__codelineno-56-22" name="__codelineno-56-22" href="#__codelineno-56-22"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</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="o">&&</span><span class="w"> </span><span class="n">_maxHeap</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">_maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
|
||
<a id="__codelineno-56-23" name="__codelineno-56-23" href="#__codelineno-56-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</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="o">&&</span><span class="w"> </span><span class="n">_maxHeap</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">_maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
|
||
<a id="__codelineno-56-24" name="__codelineno-56-24" href="#__codelineno-56-24"></a><span class="w"> </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
|
||
<a id="__codelineno-56-25" name="__codelineno-56-25" href="#__codelineno-56-25"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||
<a id="__codelineno-56-26" name="__codelineno-56-26" href="#__codelineno-56-26"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
||
<a id="__codelineno-56-27" name="__codelineno-56-27" href="#__codelineno-56-27"></a><span class="w"> </span><span class="n">_swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">ma</span><span class="p">);</span>
|
||
<a id="__codelineno-56-28" name="__codelineno-56-28" href="#__codelineno-56-28"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
|
||
<a id="__codelineno-56-29" name="__codelineno-56-29" href="#__codelineno-56-29"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
|
||
<a id="__codelineno-56-30" name="__codelineno-56-30" href="#__codelineno-56-30"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-56-31" name="__codelineno-56-31" href="#__codelineno-56-31"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.rs</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="cm">/* 元素出堆 */</span>
|
||
<a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a><span class="k">fn</span> <span class="nf">pop</span><span class="p">(</span><span class="o">&</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">i32</span> <span class="p">{</span>
|
||
<a id="__codelineno-57-3" name="__codelineno-57-3" href="#__codelineno-57-3"></a><span class="w"> </span><span class="c1">// 判空处理</span>
|
||
<a id="__codelineno-57-4" name="__codelineno-57-4" href="#__codelineno-57-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="bp">self</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-57-5" name="__codelineno-57-5" href="#__codelineno-57-5"></a><span class="w"> </span><span class="fm">panic!</span><span class="p">(</span><span class="s">"index out of bounds"</span><span class="p">);</span>
|
||
<a id="__codelineno-57-6" name="__codelineno-57-6" href="#__codelineno-57-6"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-57-7" name="__codelineno-57-7" href="#__codelineno-57-7"></a><span class="w"> </span><span class="c1">// 交换根节点与最右叶节点（交换首元素与尾元素）</span>
|
||
<a id="__codelineno-57-8" name="__codelineno-57-8" href="#__codelineno-57-8"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||
<a id="__codelineno-57-9" name="__codelineno-57-9" href="#__codelineno-57-9"></a><span class="w"> </span><span class="c1">// 删除节点</span>
|
||
<a id="__codelineno-57-10" name="__codelineno-57-10" href="#__codelineno-57-10"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||
<a id="__codelineno-57-11" name="__codelineno-57-11" href="#__codelineno-57-11"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
|
||
<a id="__codelineno-57-12" name="__codelineno-57-12" href="#__codelineno-57-12"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">sift_down</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
|
||
<a id="__codelineno-57-13" name="__codelineno-57-13" href="#__codelineno-57-13"></a><span class="w"> </span><span class="c1">// 返回堆顶元素</span>
|
||
<a id="__codelineno-57-14" name="__codelineno-57-14" href="#__codelineno-57-14"></a><span class="w"> </span><span class="n">val</span>
|
||
<a id="__codelineno-57-15" name="__codelineno-57-15" href="#__codelineno-57-15"></a><span class="p">}</span>
|
||
<a id="__codelineno-57-16" name="__codelineno-57-16" href="#__codelineno-57-16"></a>
|
||
<a id="__codelineno-57-17" name="__codelineno-57-17" href="#__codelineno-57-17"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
|
||
<a id="__codelineno-57-18" name="__codelineno-57-18" href="#__codelineno-57-18"></a><span class="k">fn</span> <span class="nf">sift_down</span><span class="p">(</span><span class="o">&</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">i</span>: <span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-57-19" name="__codelineno-57-19" href="#__codelineno-57-19"></a><span class="w"> </span><span class="k">loop</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-57-20" name="__codelineno-57-20" href="#__codelineno-57-20"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 ma</span>
|
||
<a id="__codelineno-57-21" name="__codelineno-57-21" href="#__codelineno-57-21"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">,</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">ma</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="bp">Self</span>::<span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
|
||
<a id="__codelineno-57-22" name="__codelineno-57-22" href="#__codelineno-57-22"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">ma</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-57-23" name="__codelineno-57-23" href="#__codelineno-57-23"></a><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
|
||
<a id="__codelineno-57-24" name="__codelineno-57-24" href="#__codelineno-57-24"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-57-25" name="__codelineno-57-25" href="#__codelineno-57-25"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">ma</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-57-26" name="__codelineno-57-26" href="#__codelineno-57-26"></a><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
|
||
<a id="__codelineno-57-27" name="__codelineno-57-27" href="#__codelineno-57-27"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-57-28" name="__codelineno-57-28" href="#__codelineno-57-28"></a><span class="w"> </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
|
||
<a id="__codelineno-57-29" name="__codelineno-57-29" href="#__codelineno-57-29"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-57-30" name="__codelineno-57-30" href="#__codelineno-57-30"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||
<a id="__codelineno-57-31" name="__codelineno-57-31" href="#__codelineno-57-31"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-57-32" name="__codelineno-57-32" href="#__codelineno-57-32"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
||
<a id="__codelineno-57-33" name="__codelineno-57-33" href="#__codelineno-57-33"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">ma</span><span class="p">);</span>
|
||
<a id="__codelineno-57-34" name="__codelineno-57-34" href="#__codelineno-57-34"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
|
||
<a id="__codelineno-57-35" name="__codelineno-57-35" href="#__codelineno-57-35"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
|
||
<a id="__codelineno-57-36" name="__codelineno-57-36" href="#__codelineno-57-36"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-57-37" name="__codelineno-57-37" href="#__codelineno-57-37"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.c</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="cm">/* 元素出堆 */</span>
|
||
<a id="__codelineno-58-2" name="__codelineno-58-2" href="#__codelineno-58-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-58-3" name="__codelineno-58-3" href="#__codelineno-58-3"></a><span class="w"> </span><span class="c1">// 判空处理</span>
|
||
<a id="__codelineno-58-4" name="__codelineno-58-4" href="#__codelineno-58-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-58-5" name="__codelineno-58-5" href="#__codelineno-58-5"></a><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">"heap is empty!"</span><span class="p">);</span>
|
||
<a id="__codelineno-58-6" name="__codelineno-58-6" href="#__codelineno-58-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">;</span>
|
||
<a id="__codelineno-58-7" name="__codelineno-58-7" href="#__codelineno-58-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-58-8" name="__codelineno-58-8" href="#__codelineno-58-8"></a><span class="w"> </span><span class="c1">// 交换根节点与最右叶节点（交换首元素与尾元素）</span>
|
||
<a id="__codelineno-58-9" name="__codelineno-58-9" href="#__codelineno-58-9"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||
<a id="__codelineno-58-10" name="__codelineno-58-10" href="#__codelineno-58-10"></a><span class="w"> </span><span class="c1">// 删除节点</span>
|
||
<a id="__codelineno-58-11" name="__codelineno-58-11" href="#__codelineno-58-11"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="n">maxHeap</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">1</span><span class="p">];</span>
|
||
<a id="__codelineno-58-12" name="__codelineno-58-12" href="#__codelineno-58-12"></a><span class="w"> </span><span class="n">maxHeap</span><span class="o">-></span><span class="n">size</span><span class="o">--</span><span class="p">;</span>
|
||
<a id="__codelineno-58-13" name="__codelineno-58-13" href="#__codelineno-58-13"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
|
||
<a id="__codelineno-58-14" name="__codelineno-58-14" href="#__codelineno-58-14"></a><span class="w"> </span><span class="n">siftDown</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
|
||
<a id="__codelineno-58-15" name="__codelineno-58-15" href="#__codelineno-58-15"></a>
|
||
<a id="__codelineno-58-16" name="__codelineno-58-16" href="#__codelineno-58-16"></a><span class="w"> </span><span class="c1">// 返回堆顶元素</span>
|
||
<a id="__codelineno-58-17" name="__codelineno-58-17" href="#__codelineno-58-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
|
||
<a id="__codelineno-58-18" name="__codelineno-58-18" href="#__codelineno-58-18"></a><span class="p">}</span>
|
||
<a id="__codelineno-58-19" name="__codelineno-58-19" href="#__codelineno-58-19"></a>
|
||
<a id="__codelineno-58-20" name="__codelineno-58-20" href="#__codelineno-58-20"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
|
||
<a id="__codelineno-58-21" name="__codelineno-58-21" href="#__codelineno-58-21"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftDown</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-58-22" name="__codelineno-58-22" href="#__codelineno-58-22"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nb">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-58-23" name="__codelineno-58-23" href="#__codelineno-58-23"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 max</span>
|
||
<a id="__codelineno-58-24" name="__codelineno-58-24" href="#__codelineno-58-24"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
|
||
<a id="__codelineno-58-25" name="__codelineno-58-25" href="#__codelineno-58-25"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
|
||
<a id="__codelineno-58-26" name="__codelineno-58-26" href="#__codelineno-58-26"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">max</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
|
||
<a id="__codelineno-58-27" name="__codelineno-58-27" href="#__codelineno-58-27"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">size</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="n">max</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-58-28" name="__codelineno-58-28" href="#__codelineno-58-28"></a><span class="w"> </span><span class="n">max</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
|
||
<a id="__codelineno-58-29" name="__codelineno-58-29" href="#__codelineno-58-29"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-58-30" name="__codelineno-58-30" href="#__codelineno-58-30"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">size</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="n">max</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-58-31" name="__codelineno-58-31" href="#__codelineno-58-31"></a><span class="w"> </span><span class="n">max</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
|
||
<a id="__codelineno-58-32" name="__codelineno-58-32" href="#__codelineno-58-32"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-58-33" name="__codelineno-58-33" href="#__codelineno-58-33"></a><span class="w"> </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
|
||
<a id="__codelineno-58-34" name="__codelineno-58-34" href="#__codelineno-58-34"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">max</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-58-35" name="__codelineno-58-35" href="#__codelineno-58-35"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||
<a id="__codelineno-58-36" name="__codelineno-58-36" href="#__codelineno-58-36"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-58-37" name="__codelineno-58-37" href="#__codelineno-58-37"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
||
<a id="__codelineno-58-38" name="__codelineno-58-38" href="#__codelineno-58-38"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">max</span><span class="p">);</span>
|
||
<a id="__codelineno-58-39" name="__codelineno-58-39" href="#__codelineno-58-39"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
|
||
<a id="__codelineno-58-40" name="__codelineno-58-40" href="#__codelineno-58-40"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">;</span>
|
||
<a id="__codelineno-58-41" name="__codelineno-58-41" href="#__codelineno-58-41"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-58-42" name="__codelineno-58-42" href="#__codelineno-58-42"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">my_heap.zig</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="c1">// 元素出堆</span>
|
||
<a id="__codelineno-59-2" name="__codelineno-59-2" href="#__codelineno-59-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">pop</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">)</span><span class="w"> </span><span class="o">!</span><span class="n">T</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-59-3" name="__codelineno-59-3" href="#__codelineno-59-3"></a><span class="w"> </span><span class="c1">// 判断处理</span>
|
||
<a id="__codelineno-59-4" name="__codelineno-59-4" href="#__codelineno-59-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">self</span><span class="p">.</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">unreachable</span><span class="p">;</span>
|
||
<a id="__codelineno-59-5" name="__codelineno-59-5" href="#__codelineno-59-5"></a><span class="w"> </span><span class="c1">// 交换根节点与最右叶节点（交换首元素与尾元素）</span>
|
||
<a id="__codelineno-59-6" name="__codelineno-59-6" href="#__codelineno-59-6"></a><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||
<a id="__codelineno-59-7" name="__codelineno-59-7" href="#__codelineno-59-7"></a><span class="w"> </span><span class="c1">// 删除节点</span>
|
||
<a id="__codelineno-59-8" name="__codelineno-59-8" href="#__codelineno-59-8"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span>
|
||
<a id="__codelineno-59-9" name="__codelineno-59-9" href="#__codelineno-59-9"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
|
||
<a id="__codelineno-59-10" name="__codelineno-59-10" href="#__codelineno-59-10"></a><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">siftDown</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
|
||
<a id="__codelineno-59-11" name="__codelineno-59-11" href="#__codelineno-59-11"></a><span class="w"> </span><span class="c1">// 返回堆顶元素</span>
|
||
<a id="__codelineno-59-12" name="__codelineno-59-12" href="#__codelineno-59-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
|
||
<a id="__codelineno-59-13" name="__codelineno-59-13" href="#__codelineno-59-13"></a><span class="p">}</span><span class="w"> </span>
|
||
<a id="__codelineno-59-14" name="__codelineno-59-14" href="#__codelineno-59-14"></a>
|
||
<a id="__codelineno-59-15" name="__codelineno-59-15" href="#__codelineno-59-15"></a><span class="c1">// 从节点 i 开始，从顶至底堆化</span>
|
||
<a id="__codelineno-59-16" name="__codelineno-59-16" href="#__codelineno-59-16"></a><span class="k">fn</span><span class="w"> </span><span class="n">siftDown</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">,</span><span class="w"> </span><span class="n">i_</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="o">!</span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-59-17" name="__codelineno-59-17" href="#__codelineno-59-17"></a><span class="w"> </span><span class="kr">var</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">i_</span><span class="p">;</span>
|
||
<a id="__codelineno-59-18" name="__codelineno-59-18" href="#__codelineno-59-18"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-59-19" name="__codelineno-59-19" href="#__codelineno-59-19"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 ma</span>
|
||
<a id="__codelineno-59-20" name="__codelineno-59-20" href="#__codelineno-59-20"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
|
||
<a id="__codelineno-59-21" name="__codelineno-59-21" href="#__codelineno-59-21"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
|
||
<a id="__codelineno-59-22" name="__codelineno-59-22" href="#__codelineno-59-22"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
|
||
<a id="__codelineno-59-23" name="__codelineno-59-23" href="#__codelineno-59-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="k">and</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">items</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">items</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
|
||
<a id="__codelineno-59-24" name="__codelineno-59-24" href="#__codelineno-59-24"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="k">and</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">items</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">items</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
|
||
<a id="__codelineno-59-25" name="__codelineno-59-25" href="#__codelineno-59-25"></a><span class="w"> </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
|
||
<a id="__codelineno-59-26" name="__codelineno-59-26" href="#__codelineno-59-26"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||
<a id="__codelineno-59-27" name="__codelineno-59-27" href="#__codelineno-59-27"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
||
<a id="__codelineno-59-28" name="__codelineno-59-28" href="#__codelineno-59-28"></a><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">ma</span><span class="p">);</span>
|
||
<a id="__codelineno-59-29" name="__codelineno-59-29" href="#__codelineno-59-29"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
|
||
<a id="__codelineno-59-30" name="__codelineno-59-30" href="#__codelineno-59-30"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
|
||
<a id="__codelineno-59-31" name="__codelineno-59-31" href="#__codelineno-59-31"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-59-32" name="__codelineno-59-32" href="#__codelineno-59-32"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<details class="pythontutor">
|
||
<summary>可视化运行</summary>
|
||
<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20MaxHeap%3A%0A%20%20%20%20%22%22%22%E5%A4%A7%E9%A1%B6%E5%A0%86%22%22%22%0A%0A%20%20%20%20def%20__init__%28self,%20nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E6%9E%84%E9%80%A0%E6%96%B9%E6%B3%95%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E5%B0%86%E5%88%97%E8%A1%A8%E5%85%83%E7%B4%A0%E5%8E%9F%E5%B0%81%E4%B8%8D%E5%8A%A8%E6%B7%BB%E5%8A%A0%E8%BF%9B%E5%A0%86%0A%20%20%20%20%20%20%20%20self.max_heap%20%3D%20nums%0A%0A%20%20%20%20def%20left%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%B7%A6%E5%AD%90%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20*%20i%20%2B%201%0A%0A%20%20%20%20def%20right%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%8F%B3%E5%AD%90%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20*%20i%20%2B%202%0A%0A%20%20%20%20def%20parent%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E7%88%B6%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%20%28i%20-%201%29%20//%202%20%20%23%20%E5%90%91%E4%B8%8B%E6%95%B4%E9%99%A4%0A%0A%20%20%20%20def%20swap%28self,%20i%3A%20int,%20j%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E4%BA%A4%E6%8D%A2%E5%85%83%E7%B4%A0%22%22%22%0A%20%20%20%20%20%20%20%20self.max_heap%5Bi%5D,%20self.max_heap%5Bj%5D%20%3D%20self.max_heap%5Bj%5D,%20self.max_heap%5Bi%5D%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%A0%86%E5%A4%A7%E5%B0%8F%22%22%22%0A%20%20%20%20%20%20%20%20return%20len%28self.max_heap%29%0A%0A%20%20%20%20def%20is_empty%28self%29%20-%3E%20bool%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%88%A4%E6%96%AD%E5%A0%86%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%22%22%22%0A%20%20%20%20%20%20%20%20return%20self.size%28%29%20%3D%3D%200%0A%0A%20%20%20%20def%20pop%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%85%83%E7%B4%A0%E5%87%BA%E5%A0%86%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E5%88%A4%E7%A9%BA%E5%A4%84%E7%90%86%0A%20%20%20%20%20%20%20%20if%20self.is_empty%28%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20IndexError%28%22%E5%A0%86%E4%B8%BA%E7%A9%BA%22%29%0A%20%20%20%20%20%20%20%20%23%20%E4%BA%A4%E6%8D%A2%E6%A0%B9%E8%8A%82%E7%82%B9%E4%B8%8E%E6%9C%80%E5%8F%B3%E5%8F%B6%E8%8A%82%E7%82%B9%EF%BC%88%E4%BA%A4%E6%8D%A2%E9%A6%96%E5%85%83%E7%B4%A0%E4%B8%8E%E5%B0%BE%E5%85%83%E7%B4%A0%EF%BC%89%0A%20%20%20%20%20%20%20%20self.swap%280,%20self.size%28%29%20-%201%29%0A%20%20%20%20%20%20%20%20%23%20%E5%88%A0%E9%99%A4%E8%8A%82%E7%82%B9%0A%20%20%20%20%20%20%20%20val%20%3D%20self.max_heap.pop%28%29%0A%20%20%20%20%20%20%20%20%23%20%E4%BB%8E%E9%A1%B6%E8%87%B3%E5%BA%95%E5%A0%86%E5%8C%96%0A%20%20%20%20%20%20%20%20self.sift_down%280%29%0A%20%20%20%20%20%20%20%20%23%20%E8%BF%94%E5%9B%9E%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%0A%20%20%20%20%20%20%20%20return%20val%0A%0A%20%20%20%20def%20sift_down%28self,%20i%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E4%BB%8E%E8%8A%82%E7%82%B9%20i%20%E5%BC%80%E5%A7%8B%EF%BC%8C%E4%BB%8E%E9%A1%B6%E8%87%B3%E5%BA%95%E5%A0%86%E5%8C%96%22%22%22%0A%20%20%20%20%20%20%20%20while%20True%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E5%88%A4%E6%96%AD%E8%8A%82%E7%82%B9%20i,%20l,%20r%20%E4%B8%AD%E5%80%BC%E6%9C%80%E5%A4%A7%E7%9A%84%E8%8A%82%E7%82%B9%EF%BC%8C%E8%AE%B0%E4%B8%BA%20ma%0A%20%20%20%20%20%20%20%20%20%20%20%20l,%20r,%20ma%20%3D%20self.left%28i%29,%20self.right%28i%29,%20i%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20l%20%3C%20self.size%28%29%20and%20self.max_heap%5Bl%5D%20%3E%20self.max_heap%5Bma%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20ma%20%3D%20l%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20r%20%3C%20self.size%28%29%20and%20self.max_heap%5Br%5D%20%3E%20self.max_heap%5Bma%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20ma%20%3D%20r%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E8%8B%A5%E8%8A%82%E7%82%B9%20i%20%E6%9C%80%E5%A4%A7%E6%88%96%E7%B4%A2%E5%BC%95%20l,%20r%20%E8%B6%8A%E7%95%8C%EF%BC%8C%E5%88%99%E6%97%A0%E9%A1%BB%E7%BB%A7%E7%BB%AD%E5%A0%86%E5%8C%96%EF%BC%8C%E8%B7%B3%E5%87%BA%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20ma%20%3D%3D%20i%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20break%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E4%BA%A4%E6%8D%A2%E4%B8%A4%E8%8A%82%E7%82%B9%0A%20%20%20%20%20%20%20%20%20%20%20%20self.swap%28i,%20ma%29%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E5%BE%AA%E7%8E%AF%E5%90%91%E4%B8%8B%E5%A0%86%E5%8C%96%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%3D%20ma%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%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20%23%20%E8%AF%B7%E6%B3%A8%E6%84%8F%EF%BC%8C%E8%BE%93%E5%85%A5%E6%95%B0%E7%BB%84%E5%B7%B2%E7%BB%8F%E6%98%AF%E4%B8%80%E4%B8%AA%E5%B7%B2%E7%BB%8F%E6%98%AF%E4%B8%80%E4%B8%AA%E5%90%88%E6%B3%95%E7%9A%84%E5%A0%86%0A%20%20%20%20max_heap%20%3D%20MaxHeap%28%5B9,%208,%207,%206,%207,%206,%202,%201,%204,%203,%206,%202,%205%5D%29%0A%0A%20%20%20%20%23%20%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%E5%87%BA%E5%A0%86%0A%20%20%20%20peek%20%3D%20max_heap.pop%28%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=8&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%20MaxHeap%3A%0A%20%20%20%20%22%22%22%E5%A4%A7%E9%A1%B6%E5%A0%86%22%22%22%0A%0A%20%20%20%20def%20__init__%28self,%20nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E6%9E%84%E9%80%A0%E6%96%B9%E6%B3%95%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E5%B0%86%E5%88%97%E8%A1%A8%E5%85%83%E7%B4%A0%E5%8E%9F%E5%B0%81%E4%B8%8D%E5%8A%A8%E6%B7%BB%E5%8A%A0%E8%BF%9B%E5%A0%86%0A%20%20%20%20%20%20%20%20self.max_heap%20%3D%20nums%0A%0A%20%20%20%20def%20left%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%B7%A6%E5%AD%90%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20*%20i%20%2B%201%0A%0A%20%20%20%20def%20right%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%8F%B3%E5%AD%90%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20*%20i%20%2B%202%0A%0A%20%20%20%20def%20parent%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E7%88%B6%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%20%28i%20-%201%29%20//%202%20%20%23%20%E5%90%91%E4%B8%8B%E6%95%B4%E9%99%A4%0A%0A%20%20%20%20def%20swap%28self,%20i%3A%20int,%20j%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E4%BA%A4%E6%8D%A2%E5%85%83%E7%B4%A0%22%22%22%0A%20%20%20%20%20%20%20%20self.max_heap%5Bi%5D,%20self.max_heap%5Bj%5D%20%3D%20self.max_heap%5Bj%5D,%20self.max_heap%5Bi%5D%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%A0%86%E5%A4%A7%E5%B0%8F%22%22%22%0A%20%20%20%20%20%20%20%20return%20len%28self.max_heap%29%0A%0A%20%20%20%20def%20is_empty%28self%29%20-%3E%20bool%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%88%A4%E6%96%AD%E5%A0%86%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%22%22%22%0A%20%20%20%20%20%20%20%20return%20self.size%28%29%20%3D%3D%200%0A%0A%20%20%20%20def%20pop%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%85%83%E7%B4%A0%E5%87%BA%E5%A0%86%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E5%88%A4%E7%A9%BA%E5%A4%84%E7%90%86%0A%20%20%20%20%20%20%20%20if%20self.is_empty%28%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20IndexError%28%22%E5%A0%86%E4%B8%BA%E7%A9%BA%22%29%0A%20%20%20%20%20%20%20%20%23%20%E4%BA%A4%E6%8D%A2%E6%A0%B9%E8%8A%82%E7%82%B9%E4%B8%8E%E6%9C%80%E5%8F%B3%E5%8F%B6%E8%8A%82%E7%82%B9%EF%BC%88%E4%BA%A4%E6%8D%A2%E9%A6%96%E5%85%83%E7%B4%A0%E4%B8%8E%E5%B0%BE%E5%85%83%E7%B4%A0%EF%BC%89%0A%20%20%20%20%20%20%20%20self.swap%280,%20self.size%28%29%20-%201%29%0A%20%20%20%20%20%20%20%20%23%20%E5%88%A0%E9%99%A4%E8%8A%82%E7%82%B9%0A%20%20%20%20%20%20%20%20val%20%3D%20self.max_heap.pop%28%29%0A%20%20%20%20%20%20%20%20%23%20%E4%BB%8E%E9%A1%B6%E8%87%B3%E5%BA%95%E5%A0%86%E5%8C%96%0A%20%20%20%20%20%20%20%20self.sift_down%280%29%0A%20%20%20%20%20%20%20%20%23%20%E8%BF%94%E5%9B%9E%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%0A%20%20%20%20%20%20%20%20return%20val%0A%0A%20%20%20%20def%20sift_down%28self,%20i%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E4%BB%8E%E8%8A%82%E7%82%B9%20i%20%E5%BC%80%E5%A7%8B%EF%BC%8C%E4%BB%8E%E9%A1%B6%E8%87%B3%E5%BA%95%E5%A0%86%E5%8C%96%22%22%22%0A%20%20%20%20%20%20%20%20while%20True%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E5%88%A4%E6%96%AD%E8%8A%82%E7%82%B9%20i,%20l,%20r%20%E4%B8%AD%E5%80%BC%E6%9C%80%E5%A4%A7%E7%9A%84%E8%8A%82%E7%82%B9%EF%BC%8C%E8%AE%B0%E4%B8%BA%20ma%0A%20%20%20%20%20%20%20%20%20%20%20%20l,%20r,%20ma%20%3D%20self.left%28i%29,%20self.right%28i%29,%20i%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20l%20%3C%20self.size%28%29%20and%20self.max_heap%5Bl%5D%20%3E%20self.max_heap%5Bma%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20ma%20%3D%20l%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20r%20%3C%20self.size%28%29%20and%20self.max_heap%5Br%5D%20%3E%20self.max_heap%5Bma%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20ma%20%3D%20r%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E8%8B%A5%E8%8A%82%E7%82%B9%20i%20%E6%9C%80%E5%A4%A7%E6%88%96%E7%B4%A2%E5%BC%95%20l,%20r%20%E8%B6%8A%E7%95%8C%EF%BC%8C%E5%88%99%E6%97%A0%E9%A1%BB%E7%BB%A7%E7%BB%AD%E5%A0%86%E5%8C%96%EF%BC%8C%E8%B7%B3%E5%87%BA%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20ma%20%3D%3D%20i%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20break%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E4%BA%A4%E6%8D%A2%E4%B8%A4%E8%8A%82%E7%82%B9%0A%20%20%20%20%20%20%20%20%20%20%20%20self.swap%28i,%20ma%29%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E5%BE%AA%E7%8E%AF%E5%90%91%E4%B8%8B%E5%A0%86%E5%8C%96%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%3D%20ma%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%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20%23%20%E8%AF%B7%E6%B3%A8%E6%84%8F%EF%BC%8C%E8%BE%93%E5%85%A5%E6%95%B0%E7%BB%84%E5%B7%B2%E7%BB%8F%E6%98%AF%E4%B8%80%E4%B8%AA%E5%B7%B2%E7%BB%8F%E6%98%AF%E4%B8%80%E4%B8%AA%E5%90%88%E6%B3%95%E7%9A%84%E5%A0%86%0A%20%20%20%20max_heap%20%3D%20MaxHeap%28%5B9,%208,%207,%206,%207,%206,%202,%201,%204,%203,%206,%202,%205%5D%29%0A%0A%20%20%20%20%23%20%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%E5%87%BA%E5%A0%86%0A%20%20%20%20peek%20%3D%20max_heap.pop%28%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=8&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全屏观看 ></a></div></p>
|
||
</details>
|
||
<h2 id="813">8.1.3 堆的常见应用<a class="headerlink" href="#813" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li><strong>优先队列</strong>：堆通常作为实现优先队列的首选数据结构，其入队和出队操作的时间复杂度均为 <span class="arithmatex">\(O(\log n)\)</span> ，而建队操作为 <span class="arithmatex">\(O(n)\)</span> ，这些操作都非常高效。</li>
|
||
<li><strong>堆排序</strong>：给定一组数据，我们可以用它们建立一个堆，然后不断地执行元素出堆操作，从而得到有序数据。然而，我们通常会使用一种更优雅的方式实现堆排序，详见“堆排序”章节。</li>
|
||
<li><strong>获取最大的 <span class="arithmatex">\(k\)</span> 个元素</strong>：这是一个经典的算法问题，同时也是一种典型应用，例如选择热度前 10 的新闻作为微博热搜，选取销量前 10 的商品等。</li>
|
||
</ul>
|
||
|
||
<!-- Source file information -->
|
||
|
||
|
||
<!-- Was this page helpful? -->
|
||
|
||
|
||
|
||
|
||
<!-- Previous and next pages link -->
|
||
<nav
|
||
class="md-footer__inner md-grid"
|
||
aria-label="页脚"
|
||
|
||
>
|
||
|
||
<!-- Link to previous page -->
|
||
|
||
|
||
<a
|
||
href="../"
|
||
class="md-footer__link md-footer__link--prev"
|
||
aria-label="上一页: 第 8 章 &nbsp; 堆"
|
||
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">
|
||
上一页
|
||
</span>
|
||
<div class="md-ellipsis">
|
||
第 8 章 堆
|
||
</div>
|
||
</div>
|
||
</a>
|
||
|
||
|
||
<!-- Link to next page -->
|
||
|
||
|
||
<a
|
||
href="../build_heap/"
|
||
class="md-footer__link md-footer__link--next"
|
||
aria-label="下一页: 8.2 &nbsp; 建堆操作"
|
||
rel="next"
|
||
>
|
||
<div class="md-footer__title">
|
||
<span class="md-footer__direction">
|
||
下一页
|
||
</span>
|
||
<div class="md-ellipsis">
|
||
8.2 建堆操作
|
||
</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">欢迎在评论区留下你的见解、问题或建议</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="preferred_color_scheme"
|
||
data-lang="zh-CN"
|
||
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>
|
||
回到页面顶部
|
||
</button>
|
||
|
||
</main>
|
||
|
||
<footer class="md-footer">
|
||
|
||
|
||
|
||
<nav class="md-footer__inner md-grid" aria-label="页脚" >
|
||
|
||
|
||
<a href="../" class="md-footer__link md-footer__link--prev" aria-label="上一页: 第 8 章 &nbsp; 堆">
|
||
<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">
|
||
上一页
|
||
</span>
|
||
<div class="md-ellipsis">
|
||
第 8 章 堆
|
||
</div>
|
||
</div>
|
||
</a>
|
||
|
||
|
||
|
||
<a href="../build_heap/" class="md-footer__link md-footer__link--next" aria-label="下一页: 8.2 &nbsp; 建堆操作">
|
||
<div class="md-footer__title">
|
||
<span class="md-footer__direction">
|
||
下一页
|
||
</span>
|
||
<div class="md-ellipsis">
|
||
8.2 建堆操作
|
||
</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
|
||
</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="M459.37 151.716c.325 4.548.325 9.097.325 13.645 0 138.72-105.583 298.558-298.558 298.558-59.452 0-114.68-17.219-161.137-47.106 8.447.974 16.568 1.299 25.34 1.299 49.055 0 94.213-16.568 130.274-44.832-46.132-.975-84.792-31.188-98.112-72.772 6.498.974 12.995 1.624 19.818 1.624 9.421 0 18.843-1.3 27.614-3.573-48.081-9.747-84.143-51.98-84.143-102.985v-1.299c13.969 7.797 30.214 12.67 47.431 13.319-28.264-18.843-46.781-51.005-46.781-87.391 0-19.492 5.197-37.36 14.294-52.954 51.655 63.675 129.3 105.258 216.365 109.807-1.624-7.797-2.599-15.918-2.599-24.04 0-57.828 46.782-104.934 104.934-104.934 30.213 0 57.502 12.67 76.67 33.137 23.715-4.548 46.456-13.32 66.599-25.34-7.798 24.366-24.366 44.833-46.132 57.827 21.117-2.273 41.584-8.122 60.426-16.243-14.292 20.791-32.161 39.308-52.628 54.253z"/></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": ["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.f886a092.min.js", "translations": {"clipboard.copied": "\u5df2\u590d\u5236", "clipboard.copy": "\u590d\u5236", "search.result.more.one": "\u5728\u8be5\u9875\u4e0a\u8fd8\u6709 1 \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c", "search.result.more.other": "\u5728\u8be5\u9875\u4e0a\u8fd8\u6709 # \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c", "search.result.none": "\u6ca1\u6709\u627e\u5230\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c", "search.result.one": "\u627e\u5230 1 \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c", "search.result.other": "# \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c", "search.result.placeholder": "\u952e\u5165\u4ee5\u5f00\u59cb\u641c\u7d22", "search.result.term.missing": "\u7f3a\u5c11", "select.version": "\u9009\u62e9\u5f53\u524d\u7248\u672c"}}</script>
|
||
|
||
|
||
<script src="../../assets/javascripts/bundle.d7c377c4.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> |