|
|
|
|
|
<!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_greedy/greedy_algorithm/">
|
|
|
|
|
|
|
|
|
<link rel="prev" href="../">
|
|
|
|
|
|
|
|
|
<link rel="next" href="../fractional_knapsack_problem/">
|
|
|
|
|
|
|
|
|
<link rel="icon" href="../../assets/images/favicon.png">
|
|
|
<meta name="generator" content="mkdocs-1.5.3, mkdocs-material-9.4.2">
|
|
|
|
|
|
|
|
|
|
|
|
<title>15.1 贪心算法 - Hello 算法</title>
|
|
|
|
|
|
|
|
|
|
|
|
<link rel="stylesheet" href="../../assets/stylesheets/main.d451bc0e.min.css">
|
|
|
|
|
|
|
|
|
<link rel="stylesheet" href="../../assets/stylesheets/palette.a5377069.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">
|
|
|
|
|
|
|
|
|
|
|
|
<script>var palette=__md_get("__palette");if(palette&&"object"==typeof palette.color)for(var key of Object.keys(palette.color))document.body.setAttribute("data-md-color-"+key,palette.color[key])</script>
|
|
|
|
|
|
<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="#151" 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.png" 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">
|
|
|
|
|
|
15.1 贪心算法
|
|
|
|
|
|
</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_1">
|
|
|
|
|
|
<label class="md-header__button md-icon" title="Switch to dark mode" for="__palette_2" 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_2">
|
|
|
|
|
|
<label class="md-header__button md-icon" title="Switch to light 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>
|
|
|
|
|
|
|
|
|
</form>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<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 6.4.2 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.png" 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 6.4.2 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>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<span class="md-status md-status--new" title="最近添加">
|
|
|
</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/summary/" class="md-nav__link">
|
|
|
|
|
|
|
|
|
<span class="md-ellipsis">
|
|
|
4.4 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_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--nested">
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
|
|
|
|
|
|
|
|
|
|
|
|
<div class="md-nav__link md-nav__container">
|
|
|
<a href="../../chapter_heap/" class="md-nav__link ">
|
|
|
|
|
|
|
|
|
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
|
|
|
|
|
|
<span class="md-ellipsis">
|
|
|
第 8 章 堆
|
|
|
</span>
|
|
|
|
|
|
|
|
|
</a>
|
|
|
|
|
|
|
|
|
<label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
|
|
|
|
|
</div>
|
|
|
|
|
|
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
|
|
|
<label class="md-nav__title" for="__nav_9">
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
第 8 章 堆
|
|
|
</label>
|
|
|
<ul class="md-nav__list" data-md-scrollfix>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_heap/heap/" class="md-nav__link">
|
|
|
|
|
|
|
|
|
<span class="md-ellipsis">
|
|
|
8.1 堆
|
|
|
</span>
|
|
|
|
|
|
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_heap/build_heap/" class="md-nav__link">
|
|
|
|
|
|
|
|
|
<span class="md-ellipsis">
|
|
|
8.2 建堆操作
|
|
|
</span>
|
|
|
|
|
|
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_heap/top_k/" class="md-nav__link">
|
|
|
|
|
|
|
|
|
<span class="md-ellipsis">
|
|
|
8.3 Top-K 问题
|
|
|
</span>
|
|
|
|
|
|
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_heap/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--active md-nav__item--nested">
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" 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="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="true">
|
|
|
<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 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">
|
|
|
15.1 贪心算法
|
|
|
</span>
|
|
|
|
|
|
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
|
|
|
|
|
<a href="./" class="md-nav__link md-nav__link--active">
|
|
|
|
|
|
|
|
|
<span class="md-ellipsis">
|
|
|
15.1 贪心算法
|
|
|
</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="#1511" class="md-nav__link">
|
|
|
15.1.1 贪心优点与局限性
|
|
|
</a>
|
|
|
|
|
|
</li>
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="#1512" class="md-nav__link">
|
|
|
15.1.2 贪心算法特性
|
|
|
</a>
|
|
|
|
|
|
</li>
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="#1513" class="md-nav__link">
|
|
|
15.1.3 贪心解题步骤
|
|
|
</a>
|
|
|
|
|
|
</li>
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="#1514" class="md-nav__link">
|
|
|
15.1.4 贪心典型例题
|
|
|
</a>
|
|
|
|
|
|
</li>
|
|
|
|
|
|
</ul>
|
|
|
|
|
|
</nav>
|
|
|
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../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="../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="../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="../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>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
</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="#1511" class="md-nav__link">
|
|
|
15.1.1 贪心优点与局限性
|
|
|
</a>
|
|
|
|
|
|
</li>
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="#1512" class="md-nav__link">
|
|
|
15.1.2 贪心算法特性
|
|
|
</a>
|
|
|
|
|
|
</li>
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="#1513" class="md-nav__link">
|
|
|
15.1.3 贪心解题步骤
|
|
|
</a>
|
|
|
|
|
|
</li>
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="#1514" class="md-nav__link">
|
|
|
15.1.4 贪心典型例题
|
|
|
</a>
|
|
|
|
|
|
</li>
|
|
|
|
|
|
</ul>
|
|
|
|
|
|
</nav>
|
|
|
</div>
|
|
|
</div>
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
|
|
<div class="md-content" data-md-component="content">
|
|
|
<article class="md-content__inner md-typeset">
|
|
|
|
|
|
<!--
|
|
|
Copyright (c) 2016-2023 Martin Donath <martin.donath@squidfunk.com>
|
|
|
|
|
|
Permission is hereby granted, free of charge, to any person obtaining a copy
|
|
|
of this software and associated documentation files (the "Software"), to
|
|
|
deal in the Software without restriction, including without limitation the
|
|
|
rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
|
|
|
sell copies of the Software, and to permit persons to whom the Software is
|
|
|
furnished to do so, subject to the following conditions:
|
|
|
|
|
|
The above copyright notice and this permission notice shall be included in
|
|
|
all copies or substantial portions of the Software.
|
|
|
|
|
|
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
|
|
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
|
|
FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
|
|
|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
|
|
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
|
|
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
|
|
|
IN THE SOFTWARE.
|
|
|
-->
|
|
|
|
|
|
<!-- Tags -->
|
|
|
|
|
|
|
|
|
<!-- Actions -->
|
|
|
|
|
|
|
|
|
<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_greedy/greedy_algorithm.md" title="编辑此页" class="md-content__button md-icon">
|
|
|
|
|
|
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M10 20H6V4h7v5h5v3.1l2-2V8l-6-6H6c-1.1 0-2 .9-2 2v16c0 1.1.9 2 2 2h4v-2m10.2-7c.1 0 .3.1.4.2l1.3 1.3c.2.2.2.6 0 .8l-1 1-2.1-2.1 1-1c.1-.1.2-.2.4-.2m0 3.9L14.1 23H12v-2.1l6.1-6.1 2.1 2.1Z"/></svg>
|
|
|
</a>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<!--
|
|
|
Hack: check whether the content contains a h1 headline. If it doesn't, the
|
|
|
page title (or respectively site name) is used as the main headline.
|
|
|
-->
|
|
|
|
|
|
|
|
|
<!-- Page content -->
|
|
|
<h1 id="151">15.1 贪心算法<a class="headerlink" href="#151" title="Permanent link">¶</a></h1>
|
|
|
<p>「贪心算法 greedy algorithm」是一种常见的解决优化问题的算法，其基本思想是在问题的每个决策阶段，都选择当前看起来最优的选择，即贪心地做出局部最优的决策，以期望获得全局最优解。贪心算法简洁且高效，在许多实际问题中都有着广泛的应用。</p>
|
|
|
<p>贪心算法和动态规划都常用于解决优化问题。它们之间存在一些相似之处，比如都依赖最优子结构性质，但工作原理是不同的。</p>
|
|
|
<ul>
|
|
|
<li>动态规划会根据之前阶段的所有决策来考虑当前决策，并使用过去子问题的解来构建当前子问题的解。</li>
|
|
|
<li>贪心算法不会重新考虑过去的决策，而是一路向前地进行贪心选择，不断缩小问题范围，直至问题被解决。</li>
|
|
|
</ul>
|
|
|
<p>我们先通过例题“零钱兑换”了解贪心算法的工作原理。这道题已经在动态规划章节中介绍过，相信你对它并不陌生。</p>
|
|
|
<div class="admonition question">
|
|
|
<p class="admonition-title">Question</p>
|
|
|
<p>给定 <span class="arithmatex">\(n\)</span> 种硬币，第 <span class="arithmatex">\(i\)</span> 种硬币的面值为 <span class="arithmatex">\(coins[i - 1]\)</span> ，目标金额为 <span class="arithmatex">\(amt\)</span> ，每种硬币可以重复选取，问能够凑出目标金额的最少硬币个数。如果无法凑出目标金额则返回 <span class="arithmatex">\(-1\)</span> 。</p>
|
|
|
</div>
|
|
|
<p>本题的贪心策略如图 15-1 所示。给定目标金额，<strong>我们贪心地选择不大于且最接近它的硬币</strong>，不断循环该步骤，直至凑出目标金额为止。</p>
|
|
|
<p><a class="glightbox" href="../greedy_algorithm.assets/coin_change_greedy_strategy.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="零钱兑换的贪心策略" src="../greedy_algorithm.assets/coin_change_greedy_strategy.png" /></a></p>
|
|
|
<p align="center"> 图 15-1 零钱兑换的贪心策略 </p>
|
|
|
|
|
|
<p>实现代码如下所示。你可能会不由地发出感叹：So Clean ！贪心算法仅用十行代码就解决了零钱兑换问题。</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">coin_change_greedy.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span> <span class="nf">coin_change_greedy</span><span class="p">(</span><span class="n">coins</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="n">amt</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-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w"> </span><span class="sd">"""零钱兑换：贪心"""</span>
|
|
|
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="c1"># 假设 coins 列表有序</span>
|
|
|
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="n">i</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">coins</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> <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
|
|
|
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="c1"># 循环进行贪心选择，直到无剩余金额</span>
|
|
|
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="k">while</span> <span class="n">amt</span> <span class="o">></span> <span class="mi">0</span><span class="p">:</span>
|
|
|
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a> <span class="c1"># 找到小于且最接近剩余金额的硬币</span>
|
|
|
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a> <span class="k">while</span> <span class="n">i</span> <span class="o">></span> <span class="mi">0</span> <span class="ow">and</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">></span> <span class="n">amt</span><span class="p">:</span>
|
|
|
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a> <span class="n">i</span> <span class="o">-=</span> <span class="mi">1</span>
|
|
|
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a> <span class="c1"># 选择 coins[i]</span>
|
|
|
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a> <span class="n">amt</span> <span class="o">-=</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
|
|
|
<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a> <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
|
|
|
<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a> <span class="c1"># 若未找到可行方案，则返回 -1</span>
|
|
|
<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a> <span class="k">return</span> <span class="n">count</span> <span class="k">if</span> <span class="n">amt</span> <span class="o">==</span> <span class="mi">0</span> <span class="k">else</span> <span class="o">-</span><span class="mi">1</span>
|
|
|
</code></pre></div>
|
|
|
</div>
|
|
|
<div class="tabbed-block">
|
|
|
<div class="highlight"><span class="filename">coin_change_greedy.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 零钱兑换：贪心 */</span>
|
|
|
<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">coinChangeGreedy</span><span class="p">(</span><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="o">&</span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w"> </span><span class="c1">// 假设 coins 列表有序</span>
|
|
|
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</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-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
|
|
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w"> </span><span class="c1">// 循环进行贪心选择，直到无剩余金额</span>
|
|
|
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w"> </span><span class="c1">// 找到小于且最接近剩余金额的硬币</span>
|
|
|
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w"> </span><span class="k">while</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">0</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">coins</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">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">;</span>
|
|
|
<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w"> </span><span class="p">}</span>
|
|
|
<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w"> </span><span class="c1">// 选择 coins[i]</span>
|
|
|
<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
|
|
|
<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
|
|
<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w"> </span><span class="p">}</span>
|
|
|
<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w"> </span><span class="c1">// 若未找到可行方案，则返回 -1</span>
|
|
|
<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">amt</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">count</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-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="p">}</span>
|
|
|
</code></pre></div>
|
|
|
</div>
|
|
|
<div class="tabbed-block">
|
|
|
<div class="highlight"><span class="filename">coin_change_greedy.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 零钱兑换：贪心 */</span>
|
|
|
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">coinChangeGreedy</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w"> </span><span class="c1">// 假设 coins 列表有序</span>
|
|
|
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="na">length</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-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
|
|
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w"> </span><span class="c1">// 循环进行贪心选择，直到无剩余金额</span>
|
|
|
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w"> </span><span class="c1">// 找到小于且最接近剩余金额的硬币</span>
|
|
|
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w"> </span><span class="k">while</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">0</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">;</span>
|
|
|
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w"> </span><span class="p">}</span>
|
|
|
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w"> </span><span class="c1">// 选择 coins[i]</span>
|
|
|
<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
|
|
|
<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
|
|
<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w"> </span><span class="p">}</span>
|
|
|
<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w"> </span><span class="c1">// 若未找到可行方案，则返回 -1</span>
|
|
|
<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">amt</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">count</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
|
|
|
<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="p">}</span>
|
|
|
</code></pre></div>
|
|
|
</div>
|
|
|
<div class="tabbed-block">
|
|
|
<div class="highlight"><span class="filename">coin_change_greedy.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 零钱兑换：贪心 */</span>
|
|
|
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">coinChangeGreedy</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w"> </span><span class="c1">// 假设 coins 列表有序</span>
|
|
|
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">Length</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-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </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-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="c1">// 循环进行贪心选择，直到无剩余金额</span>
|
|
|
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w"> </span><span class="c1">// 找到小于且最接近剩余金额的硬币</span>
|
|
|
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w"> </span><span class="k">while</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">0</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">coins</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">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">;</span>
|
|
|
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w"> </span><span class="p">}</span>
|
|
|
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w"> </span><span class="c1">// 选择 coins[i]</span>
|
|
|
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
|
|
|
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
|
|
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w"> </span><span class="p">}</span>
|
|
|
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w"> </span><span class="c1">// 若未找到可行方案，则返回 -1</span>
|
|
|
<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">amt</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">count</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">;</span>
|
|
|
<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="p">}</span>
|
|
|
</code></pre></div>
|
|
|
</div>
|
|
|
<div class="tabbed-block">
|
|
|
<div class="highlight"><span class="filename">coin_change_greedy.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 零钱兑换：贪心 */</span>
|
|
|
<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">coinChangeGreedy</span><span class="p">(</span><span class="nx">coins</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">amt</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-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w"> </span><span class="c1">// 假设 coins 列表有序</span>
|
|
|
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">coins</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
|
|
|
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
|
|
|
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w"> </span><span class="c1">// 循环进行贪心选择，直到无剩余金额</span>
|
|
|
<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="p">></span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w"> </span><span class="c1">// 找到小于且最接近剩余金额的硬币</span>
|
|
|
<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</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">coins</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">></span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w"> </span><span class="nx">i</span><span class="o">--</span>
|
|
|
<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w"> </span><span class="p">}</span>
|
|
|
<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w"> </span><span class="c1">// 选择 coins[i]</span>
|
|
|
<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</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="nx">count</span><span class="o">++</span>
|
|
|
<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w"> </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="c1">// 若未找到可行方案，则返回 -1</span>
|
|
|
<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">amt</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-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
|
|
|
<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w"> </span><span class="p">}</span>
|
|
|
<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
|
|
|
<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="p">}</span>
|
|
|
</code></pre></div>
|
|
|
</div>
|
|
|
<div class="tabbed-block">
|
|
|
<div class="highlight"><span class="filename">coin_change_greedy.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 零钱兑换：贪心 */</span>
|
|
|
<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span> <span class="nf">coinChangeGreedy</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">amt</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-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a> <span class="c1">// 假设 coins 列表有序</span>
|
|
|
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a> <span class="kd">var</span> <span class="nv">i</span> <span class="p">=</span> <span class="n">coins</span><span class="p">.</span><span class="bp">count</span> <span class="o">-</span> <span class="mi">1</span>
|
|
|
<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a> <span class="kd">var</span> <span class="nv">count</span> <span class="p">=</span> <span class="mi">0</span>
|
|
|
<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a> <span class="kd">var</span> <span class="nv">amt</span> <span class="p">=</span> <span class="n">amt</span>
|
|
|
<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a> <span class="c1">// 循环进行贪心选择，直到无剩余金额</span>
|
|
|
<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a> <span class="k">while</span> <span class="n">amt</span> <span class="o">></span> <span class="mi">0</span> <span class="p">{</span>
|
|
|
<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a> <span class="c1">// 找到小于且最接近剩余金额的硬币</span>
|
|
|
<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a> <span class="k">while</span> <span class="n">i</span> <span class="o">></span> <span class="mi">0</span> <span class="o">&&</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">></span> <span class="n">amt</span> <span class="p">{</span>
|
|
|
<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a> <span class="n">i</span> <span class="o">-=</span> <span class="mi">1</span>
|
|
|
<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a> <span class="p">}</span>
|
|
|
<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a> <span class="c1">// 选择 coins[i]</span>
|
|
|
<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a> <span class="n">amt</span> <span class="o">-=</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
|
|
|
<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a> <span class="bp">count</span> <span class="o">+=</span> <span class="mi">1</span>
|
|
|
<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a> <span class="p">}</span>
|
|
|
<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a> <span class="c1">// 若未找到可行方案，则返回 -1</span>
|
|
|
<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a> <span class="k">return</span> <span class="n">amt</span> <span class="p">==</span> <span class="mi">0</span> <span class="p">?</span> <span class="bp">count</span> <span class="p">:</span> <span class="o">-</span><span class="mi">1</span>
|
|
|
<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="p">}</span>
|
|
|
</code></pre></div>
|
|
|
</div>
|
|
|
<div class="tabbed-block">
|
|
|
<div class="highlight"><span class="filename">coin_change_greedy.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 零钱兑换：贪心 */</span>
|
|
|
<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">coinChangeGreedy</span><span class="p">(</span><span class="nx">coins</span><span class="p">,</span><span class="w"> </span><span class="nx">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w"> </span><span class="c1">// 假设 coins 数组有序</span>
|
|
|
<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coins</span><span class="p">.</span><span class="nx">length</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-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
|
|
|
<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w"> </span><span class="c1">// 循环进行贪心选择，直到无剩余金额</span>
|
|
|
<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">amt</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w"> </span><span class="c1">// 找到小于且最接近剩余金额的硬币</span>
|
|
|
<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w"> </span><span class="k">while</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="mf">0</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="nx">coins</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="nx">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="p">;</span>
|
|
|
<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w"> </span><span class="p">}</span>
|
|
|
<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w"> </span><span class="c1">// 选择 coins[i]</span>
|
|
|
<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
|
|
|
<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
|
|
|
<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w"> </span><span class="p">}</span>
|
|
|
<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w"> </span><span class="c1">// 若未找到可行方案，则返回 -1</span>
|
|
|
<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">amt</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="nx">count</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span>
|
|
|
<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="p">}</span>
|
|
|
</code></pre></div>
|
|
|
</div>
|
|
|
<div class="tabbed-block">
|
|
|
<div class="highlight"><span class="filename">coin_change_greedy.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 零钱兑换：贪心 */</span>
|
|
|
<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">coinChangeGreedy</span><span class="p">(</span><span class="nx">coins</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">amt</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-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w"> </span><span class="c1">// 假设 coins 数组有序</span>
|
|
|
<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coins</span><span class="p">.</span><span class="nx">length</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-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
|
|
|
<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w"> </span><span class="c1">// 循环进行贪心选择，直到无剩余金额</span>
|
|
|
<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">amt</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w"> </span><span class="c1">// 找到小于且最接近剩余金额的硬币</span>
|
|
|
<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w"> </span><span class="k">while</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="mf">0</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="nx">coins</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="nx">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="p">;</span>
|
|
|
<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w"> </span><span class="p">}</span>
|
|
|
<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w"> </span><span class="c1">// 选择 coins[i]</span>
|
|
|
<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
|
|
|
<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
|
|
|
<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w"> </span><span class="p">}</span>
|
|
|
<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w"> </span><span class="c1">// 若未找到可行方案，则返回 -1</span>
|
|
|
<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">amt</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="nx">count</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span>
|
|
|
<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="p">}</span>
|
|
|
</code></pre></div>
|
|
|
</div>
|
|
|
<div class="tabbed-block">
|
|
|
<div class="highlight"><span class="filename">coin_change_greedy.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 零钱兑换：贪心 */</span>
|
|
|
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">coinChangeGreedy</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w"> </span><span class="c1">// 假设 coins 列表有序</span>
|
|
|
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">length</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-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </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-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w"> </span><span class="c1">// 循环进行贪心选择，直到无剩余金额</span>
|
|
|
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w"> </span><span class="c1">// 找到小于且最接近剩余金额的硬币</span>
|
|
|
<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w"> </span><span class="k">while</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">0</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">coins</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">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">;</span>
|
|
|
<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w"> </span><span class="p">}</span>
|
|
|
<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w"> </span><span class="c1">// 选择 coins[i]</span>
|
|
|
<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
|
|
|
<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
|
|
<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w"> </span><span class="p">}</span>
|
|
|
<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w"> </span><span class="c1">// 若未找到可行方案，则返回 -1</span>
|
|
|
<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">amt</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">count</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">;</span>
|
|
|
<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="p">}</span>
|
|
|
</code></pre></div>
|
|
|
</div>
|
|
|
<div class="tabbed-block">
|
|
|
<div class="highlight"><span class="filename">coin_change_greedy.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 零钱兑换：贪心 */</span>
|
|
|
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span> <span class="nf">coin_change_greedy</span><span class="p">(</span><span class="n">coins</span>: <span class="kp">&</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">amt</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">i32</span> <span class="p">{</span>
|
|
|
<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w"> </span><span class="c1">// 假设 coins 列表有序</span>
|
|
|
<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">len</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-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
|
|
<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w"> </span><span class="c1">// 循环进行贪心选择，直到无剩余金额</span>
|
|
|
<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="n">amt</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-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w"> </span><span class="c1">// 找到小于且最接近剩余金额的硬币</span>
|
|
|
<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w"> </span><span class="k">while</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="o">&&</span><span class="w"> </span><span class="n">coins</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">amt</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><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-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w"> </span><span class="p">}</span>
|
|
|
<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w"> </span><span class="c1">// 选择 coins[i]</span>
|
|
|
<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
|
|
|
<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w"> </span><span class="n">count</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-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w"> </span><span class="p">}</span>
|
|
|
<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w"> </span><span class="c1">// 若未找到可行方案，则返回 -1</span>
|
|
|
<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">amt</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-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w"> </span><span class="n">count</span>
|
|
|
<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
|
|
|
<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="w"> </span><span class="p">}</span>
|
|
|
<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="p">}</span>
|
|
|
</code></pre></div>
|
|
|
</div>
|
|
|
<div class="tabbed-block">
|
|
|
<div class="highlight"><span class="filename">coin_change_greedy.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 零钱兑换：贪心 */</span>
|
|
|
<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">coinChangeGreedy</span><span class="p">(</span><span class="kt">int</span><span class="o">*</span><span class="w"> </span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w"> </span><span class="c1">// 假设 coins 列表有序</span>
|
|
|
<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </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-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
|
|
<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w"> </span><span class="c1">// 循环进行贪心选择，直到无剩余金额</span>
|
|
|
<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w"> </span><span class="c1">// 找到小于且最接近剩余金额的硬币</span>
|
|
|
<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w"> </span><span class="k">while</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">0</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">coins</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">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">;</span>
|
|
|
<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w"> </span><span class="p">}</span>
|
|
|
<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w"> </span><span class="c1">// 选择 coins[i]</span>
|
|
|
<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
|
|
|
<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
|
|
<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w"> </span><span class="p">}</span>
|
|
|
<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w"> </span><span class="c1">// 若未找到可行方案，则返回 -1</span>
|
|
|
<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">amt</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">count</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-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="p">}</span>
|
|
|
</code></pre></div>
|
|
|
</div>
|
|
|
<div class="tabbed-block">
|
|
|
<div class="highlight"><span class="filename">coin_change_greedy.zig</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coinChangeGreedy</span><span class="p">}</span>
|
|
|
</code></pre></div>
|
|
|
</div>
|
|
|
</div>
|
|
|
</div>
|
|
|
<h2 id="1511">15.1.1 贪心优点与局限性<a class="headerlink" href="#1511" title="Permanent link">¶</a></h2>
|
|
|
<p><strong>贪心算法不仅操作直接、实现简单，而且通常效率也很高</strong>。在以上代码中，记硬币最小面值为 <span class="arithmatex">\(\min(coins)\)</span> ，则贪心选择最多循环 <span class="arithmatex">\(amt / \min(coins)\)</span> 次，时间复杂度为 <span class="arithmatex">\(O(amt / \min(coins))\)</span> 。这比动态规划解法的时间复杂度 <span class="arithmatex">\(O(n \times amt)\)</span> 提升了一个数量级。</p>
|
|
|
<p>然而，<strong>对于某些硬币面值组合，贪心算法并不能找到最优解</strong>。图 15-2 给出了两个示例。</p>
|
|
|
<ul>
|
|
|
<li><strong>正例 <span class="arithmatex">\(coins = [1, 5, 10, 20, 50, 100]\)</span></strong>：在该硬币组合下，给定任意 <span class="arithmatex">\(amt\)</span> ，贪心算法都可以找出最优解。</li>
|
|
|
<li><strong>反例 <span class="arithmatex">\(coins = [1, 20, 50]\)</span></strong>：假设 <span class="arithmatex">\(amt = 60\)</span> ，贪心算法只能找到 <span class="arithmatex">\(50 + 1 \times 10\)</span> 的兑换组合，共计 <span class="arithmatex">\(11\)</span> 枚硬币，但动态规划可以找到最优解 <span class="arithmatex">\(20 + 20 + 20\)</span> ，仅需 <span class="arithmatex">\(3\)</span> 枚硬币。</li>
|
|
|
<li><strong>反例 <span class="arithmatex">\(coins = [1, 49, 50]\)</span></strong>：假设 <span class="arithmatex">\(amt = 98\)</span> ，贪心算法只能找到 <span class="arithmatex">\(50 + 1 \times 48\)</span> 的兑换组合，共计 <span class="arithmatex">\(49\)</span> 枚硬币，但动态规划可以找到最优解 <span class="arithmatex">\(49 + 49\)</span> ，仅需 <span class="arithmatex">\(2\)</span> 枚硬币。</li>
|
|
|
</ul>
|
|
|
<p><a class="glightbox" href="../greedy_algorithm.assets/coin_change_greedy_vs_dp.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="贪心无法找出最优解的示例" src="../greedy_algorithm.assets/coin_change_greedy_vs_dp.png" /></a></p>
|
|
|
<p align="center"> 图 15-2 贪心无法找出最优解的示例 </p>
|
|
|
|
|
|
<p>也就是说，对于零钱兑换问题，贪心算法无法保证找到全局最优解，并且有可能找到非常差的解。它更适合用动态规划解决。</p>
|
|
|
<p>一般情况下，贪心算法适用于以下两类问题。</p>
|
|
|
<ol>
|
|
|
<li><strong>可以保证找到最优解</strong>：贪心算法在这种情况下往往是最优选择，因为它往往比回溯、动态规划更高效。</li>
|
|
|
<li><strong>可以找到近似最优解</strong>：贪心算法在这种情况下也是可用的。对于很多复杂问题来说，寻找全局最优解是非常困难的，能以较高效率找到次优解也是非常不错的。</li>
|
|
|
</ol>
|
|
|
<h2 id="1512">15.1.2 贪心算法特性<a class="headerlink" href="#1512" title="Permanent link">¶</a></h2>
|
|
|
<p>那么问题来了，什么样的问题适合用贪心算法求解呢？或者说，贪心算法在什么情况下可以保证找到最优解？</p>
|
|
|
<p>相较于动态规划，贪心算法的使用条件更加苛刻，其主要关注问题的两个性质。</p>
|
|
|
<ul>
|
|
|
<li><strong>贪心选择性质</strong>：只有当局部最优选择始终可以导致全局最优解时，贪心算法才能保证得到最优解。</li>
|
|
|
<li><strong>最优子结构</strong>：原问题的最优解包含子问题的最优解。</li>
|
|
|
</ul>
|
|
|
<p>最优子结构已经在动态规划章节中介绍过，不再赘述。值得注意的是，一些问题的最优子结构并不明显，但仍然可使用贪心算法解决。</p>
|
|
|
<p>我们主要探究贪心选择性质的判断方法。虽然它的描述看上去比较简单，<strong>但实际上对于许多问题，证明贪心选择性质不是一件易事</strong>。</p>
|
|
|
<p>例如零钱兑换问题，我们虽然能够容易地举出反例，对贪心选择性质进行证伪，但证实的难度较大。如果问：<strong>满足什么条件的硬币组合可以使用贪心算法求解</strong>？我们往往只能凭借直觉或举例子来给出一个模棱两可的答案，而难以给出严谨的数学证明。</p>
|
|
|
<div class="admonition quote">
|
|
|
<p class="admonition-title">Quote</p>
|
|
|
<p>有一篇论文给出了一个 <span class="arithmatex">\(O(n^3)\)</span> 时间复杂度的算法，用于判断一个硬币组合是否可以使用贪心算法找出任何金额的最优解。</p>
|
|
|
<p>Pearson, David. A polynomial-time algorithm for the change-making problem. Operations Research Letters 33.3 (2005): 231-234.</p>
|
|
|
</div>
|
|
|
<h2 id="1513">15.1.3 贪心解题步骤<a class="headerlink" href="#1513" title="Permanent link">¶</a></h2>
|
|
|
<p>贪心问题的解决流程大体可分为以下三步。</p>
|
|
|
<ol>
|
|
|
<li><strong>问题分析</strong>：梳理与理解问题特性，包括状态定义、优化目标和约束条件等。这一步在回溯和动态规划中都有涉及。</li>
|
|
|
<li><strong>确定贪心策略</strong>：确定如何在每一步中做出贪心选择。这个策略能够在每一步减小问题的规模，并最终能解决整个问题。</li>
|
|
|
<li><strong>正确性证明</strong>：通常需要证明问题具有贪心选择性质和最优子结构。这个步骤可能需要使用到数学证明，例如归纳法或反证法等。</li>
|
|
|
</ol>
|
|
|
<p>确定贪心策略是求解问题的核心步骤，但实施起来可能并不容易，主要包含以下原因。</p>
|
|
|
<ul>
|
|
|
<li><strong>不同问题的贪心策略的差异较大</strong>。对于许多问题来说，贪心策略都比较浅显，我们通过一些大概的思考与尝试就能得出。而对于一些复杂问题，贪心策略可能非常隐蔽，这种情况就非常考验个人的解题经验与算法能力了。</li>
|
|
|
<li><strong>某些贪心策略具有较强的迷惑性</strong>。当我们满怀信心设计好贪心策略，写出解题代码并提交运行，很可能发现部分测试样例无法通过。这是因为设计的贪心策略只是“部分正确”的，上文介绍的零钱兑换就是个典型案例。</li>
|
|
|
</ul>
|
|
|
<p>为了保证正确性，我们应该对贪心策略进行严谨的数学证明，<strong>通常需要用到反证法或数学归纳法</strong>。</p>
|
|
|
<p>然而，正确性证明也很可能不是一件易事。如若没有头绪，我们通常会选择面向测试用例进行 Debug ，一步步修改与验证贪心策略。</p>
|
|
|
<h2 id="1514">15.1.4 贪心典型例题<a class="headerlink" href="#1514" title="Permanent link">¶</a></h2>
|
|
|
<p>贪心算法常常应用在满足贪心选择性质和最优子结构的优化问题中，以下列举了一些典型的贪心算法问题。</p>
|
|
|
<ul>
|
|
|
<li><strong>硬币找零问题</strong>：在某些硬币组合下，贪心算法总是可以得到最优解。</li>
|
|
|
<li><strong>区间调度问题</strong>：假设你有一些任务，每个任务在一段时间内进行，你的目标是完成尽可能多的任务。如果每次都选择结束时间最早的任务，那么贪心算法就可以得到最优解。</li>
|
|
|
<li><strong>分数背包问题</strong>：给定一组物品和一个载重量，你的目标是选择一组物品，使得总重量不超过载重量，且总价值最大。如果每次都选择性价比最高（价值 / 重量）的物品，那么贪心算法在一些情况下可以得到最优解。</li>
|
|
|
<li><strong>股票买卖问题</strong>：给定一组股票的历史价格，你可以进行多次买卖，但如果你已经持有股票，那么在卖出之前不能再买，目标是获取最大利润。</li>
|
|
|
<li><strong>霍夫曼编码</strong>：霍夫曼编码是一种用于无损数据压缩的贪心算法。通过构建霍夫曼树，每次选择出现频率最小的两个节点合并，最后得到的霍夫曼树的带权路径长度（即编码长度）最小。</li>
|
|
|
<li><strong>Dijkstra 算法</strong>：它是一种解决给定源顶点到其余各顶点的最短路径问题的贪心算法。</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 15 章 &nbsp; 贪心"
|
|
|
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 15 章 贪心
|
|
|
</div>
|
|
|
</div>
|
|
|
</a>
|
|
|
|
|
|
|
|
|
<!-- Link to next page -->
|
|
|
|
|
|
|
|
|
<a
|
|
|
href="../fractional_knapsack_problem/"
|
|
|
class="md-footer__link md-footer__link--next"
|
|
|
aria-label="下一页: 15.2 &nbsp; 分数背包问题"
|
|
|
rel="next"
|
|
|
>
|
|
|
<div class="md-footer__title">
|
|
|
<span class="md-footer__direction">
|
|
|
下一页
|
|
|
</span>
|
|
|
<div class="md-ellipsis">
|
|
|
15.2 分数背包问题
|
|
|
</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、疑惑或建议</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>
|
|
|
|
|
|
</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>
|
|
|
|
|
|
<!--
|
|
|
Copyright (c) 2016-2023 Martin Donath <martin.donath@squidfunk.com>
|
|
|
|
|
|
Permission is hereby granted, free of charge, to any person obtaining a copy
|
|
|
of this software and associated documentation files (the "Software"), to
|
|
|
deal in the Software without restriction, including without limitation the
|
|
|
rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
|
|
|
sell copies of the Software, and to permit persons to whom the Software is
|
|
|
furnished to do so, subject to the following conditions:
|
|
|
|
|
|
The above copyright notice and this permission notice shall be included in
|
|
|
all copies or substantial portions of the Software.
|
|
|
|
|
|
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
|
|
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
|
|
FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
|
|
|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
|
|
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
|
|
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
|
|
|
IN THE SOFTWARE.
|
|
|
-->
|
|
|
|
|
|
<!-- Footer -->
|
|
|
<footer class="md-footer">
|
|
|
<!-- Further information -->
|
|
|
<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 - 2023 Krahets
|
|
|
</div>
|
|
|
|
|
|
|
|
|
Made with
|
|
|
<a href="https://squidfunk.github.io/mkdocs-material/" target="_blank" rel="noopener">
|
|
|
Material for MkDocs
|
|
|
</a>
|
|
|
|
|
|
</div>
|
|
|
|
|
|
<!-- Social links -->
|
|
|
|
|
|
<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 6.4.2 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 6.4.2 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 6.4.2 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.instant", "navigation.top", "navigation.footer", "navigation.tracking", "search.highlight", "search.share", "search.suggest", "toc.follow"], "search": "../../assets/javascripts/workers/search.a264c092.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.726fbb30.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> |
