|
|
|
|
|
<!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="一本动画图解、能运行、可提问的数据结构与算法入门书">
|
|
|
|
|
|
|
|
|
<meta name="author" content="Krahets">
|
|
|
|
|
|
|
|
|
<link rel="canonical" href="https://www.hello-algo.com/chapter_sorting/merge_sort/">
|
|
|
|
|
|
|
|
|
<link rel="prev" href="../quick_sort/">
|
|
|
|
|
|
|
|
|
<link rel="next" href="../bucket_sort/">
|
|
|
|
|
|
<link rel="icon" href="../../assets/images/favicon.png">
|
|
|
<meta name="generator" content="mkdocs-1.4.2, mkdocs-material-9.1.6">
|
|
|
|
|
|
|
|
|
|
|
|
<title>11.5. 归并排序 - Hello 算法</title>
|
|
|
|
|
|
|
|
|
|
|
|
<link rel="stylesheet" href="../../assets/stylesheets/main.ded33207.min.css">
|
|
|
|
|
|
|
|
|
<link rel="stylesheet" href="../../assets/stylesheets/palette.a0c5b2b5.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>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
</head>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<body dir="ltr" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="">
|
|
|
|
|
|
|
|
|
|
|
|
<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="#115" 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">
|
|
|
|
|
|
11.5. 归并排序
|
|
|
|
|
|
</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="" 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="M12 7a5 5 0 0 1 5 5 5 5 0 0 1-5 5 5 5 0 0 1-5-5 5 5 0 0 1 5-5m0 2a3 3 0 0 0-3 3 3 3 0 0 0 3 3 3 3 0 0 0 3-3 3 3 0 0 0-3-3m0-7 2.39 3.42C13.65 5.15 12.84 5 12 5c-.84 0-1.65.15-2.39.42L12 2M3.34 7l4.16-.35A7.2 7.2 0 0 0 5.94 8.5c-.44.74-.69 1.5-.83 2.29L3.34 7m.02 10 1.76-3.77a7.131 7.131 0 0 0 2.38 4.14L3.36 17M20.65 7l-1.77 3.79a7.023 7.023 0 0 0-2.38-4.15l4.15.36m-.01 10-4.14.36c.59-.51 1.12-1.14 1.54-1.86.42-.73.69-1.5.83-2.29L20.64 17M12 22l-2.41-3.44c.74.27 1.55.44 2.41.44.82 0 1.63-.17 2.37-.44L12 22Z"/></svg>
|
|
|
</label>
|
|
|
|
|
|
|
|
|
|
|
|
<input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="" data-md-color-accent="" 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="m17.75 4.09-2.53 1.94.91 3.06-2.63-1.81-2.63 1.81.91-3.06-2.53-1.94L12.44 4l1.06-3 1.06 3 3.19.09m3.5 6.91-1.64 1.25.59 1.98-1.7-1.17-1.7 1.17.59-1.98L15.75 11l2.06-.05L18.5 9l.69 1.95 2.06.05m-2.28 4.95c.83-.08 1.72 1.1 1.19 1.85-.32.45-.66.87-1.08 1.27C15.17 23 8.84 23 4.94 19.07c-3.91-3.9-3.91-10.24 0-14.14.4-.4.82-.76 1.27-1.08.75-.53 1.93.36 1.85 1.19-.27 2.86.69 5.83 2.89 8.02a9.96 9.96 0 0 0 8.02 2.89m-1.64 2.02a12.08 12.08 0 0 1-7.8-3.47c-2.17-2.19-3.33-5-3.49-7.82-2.81 3.14-2.7 7.96.31 10.98 3.02 3.01 7.84 3.12 10.98.31Z"/></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 6.4.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 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 6.4.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 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--section md-nav__item--nested">
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_1" >
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<label class="md-nav__link" for="__nav_1" id="__nav_1_label" tabindex="0">
|
|
|
0. 写在前面
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
|
|
|
|
|
<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>
|
|
|
0. 写在前面
|
|
|
</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">
|
|
|
0.1. 关于本书
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_preface/suggestions/" class="md-nav__link">
|
|
|
0.2. 如何使用本书
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_preface/summary/" class="md-nav__link">
|
|
|
0.3. 小结
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
</ul>
|
|
|
</nav>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_2" >
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<label class="md-nav__link" for="__nav_2" id="__nav_2_label" tabindex="0">
|
|
|
1. 引言
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
|
|
|
|
|
<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>
|
|
|
1. 引言
|
|
|
</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">
|
|
|
1.1. 算法无处不在
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
|
|
|
1.2. 算法是什么
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_introduction/summary/" class="md-nav__link">
|
|
|
1.3. 小结
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
</ul>
|
|
|
</nav>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<label class="md-nav__link" for="__nav_3" id="__nav_3_label" tabindex="0">
|
|
|
2. 复杂度分析
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
|
|
|
|
|
<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>
|
|
|
2. 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">
|
|
|
2.1. 算法效率评估
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
|
|
|
2.2. 时间复杂度
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
|
|
|
2.3. 空间复杂度
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
|
|
|
2.4. 小结
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
</ul>
|
|
|
</nav>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<label class="md-nav__link" for="__nav_4" id="__nav_4_label" tabindex="0">
|
|
|
3. 数据结构简介
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
|
|
|
|
|
<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>
|
|
|
3. 数据结构简介
|
|
|
</label>
|
|
|
<ul class="md-nav__list" data-md-scrollfix>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_data_structure/data_and_memory/" class="md-nav__link">
|
|
|
3.1. 基本数据类型
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
|
|
|
3.2. 数据结构分类
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_data_structure/summary/" class="md-nav__link">
|
|
|
3.3. 小结
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
</ul>
|
|
|
</nav>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<label class="md-nav__link" for="__nav_5" id="__nav_5_label" tabindex="0">
|
|
|
4. 数组与链表
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
|
|
|
|
|
<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>
|
|
|
4. 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">
|
|
|
4.1. 数组
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
|
|
|
4.2. 链表
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
|
|
|
4.3. 列表
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
|
|
|
4.4. 小结
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
</ul>
|
|
|
</nav>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<label class="md-nav__link" for="__nav_6" id="__nav_6_label" tabindex="0">
|
|
|
5. 栈与队列
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
|
|
|
|
|
<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>
|
|
|
5. 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">
|
|
|
5.1. 栈
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
|
|
|
5.2. 队列
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
|
|
|
5.3. 双向队列
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
|
|
|
5.4. 小结
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
</ul>
|
|
|
</nav>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<label class="md-nav__link" for="__nav_7" id="__nav_7_label" tabindex="0">
|
|
|
6. 二分查找
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
|
|
|
|
|
<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>
|
|
|
6. 二分查找
|
|
|
</label>
|
|
|
<ul class="md-nav__list" data-md-scrollfix>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_binary_search/binary_search/" class="md-nav__link">
|
|
|
6.1. 二分查找
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
</ul>
|
|
|
</nav>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<label class="md-nav__link" for="__nav_8" id="__nav_8_label" tabindex="0">
|
|
|
7. 散列表
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
|
|
|
|
|
<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>
|
|
|
7. 散列表
|
|
|
</label>
|
|
|
<ul class="md-nav__list" data-md-scrollfix>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_hashing/hash_map/" class="md-nav__link">
|
|
|
7.1. 哈希表
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
|
|
|
7.2. 哈希冲突处理
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_hashing/summary/" class="md-nav__link">
|
|
|
7.3. 小结
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
</ul>
|
|
|
</nav>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<label class="md-nav__link" for="__nav_9" id="__nav_9_label" tabindex="0">
|
|
|
8. 树
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
|
|
|
|
|
<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>
|
|
|
8. 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">
|
|
|
8.1. 二叉树
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
|
|
|
8.2. 二叉树遍历
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
|
|
|
8.3. 二叉树数组表示
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
|
|
|
8.4. 二叉搜索树
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_tree/avl_tree/" class="md-nav__link">
|
|
|
8.5. AVL 树 *
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_tree/summary/" class="md-nav__link">
|
|
|
8.6. 小结
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
</ul>
|
|
|
</nav>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<label class="md-nav__link" for="__nav_10" id="__nav_10_label" tabindex="0">
|
|
|
9. 堆
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
|
|
|
|
|
<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>
|
|
|
9. 堆
|
|
|
</label>
|
|
|
<ul class="md-nav__list" data-md-scrollfix>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_heap/heap/" class="md-nav__link">
|
|
|
9.1. 堆
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_heap/build_heap/" class="md-nav__link">
|
|
|
9.2. 建堆操作 *
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_heap/summary/" class="md-nav__link">
|
|
|
9.3. 小结
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
</ul>
|
|
|
</nav>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<label class="md-nav__link" for="__nav_11" id="__nav_11_label" tabindex="0">
|
|
|
10. 图
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
|
|
|
|
|
<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>
|
|
|
10. 图
|
|
|
</label>
|
|
|
<ul class="md-nav__list" data-md-scrollfix>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_graph/graph/" class="md-nav__link">
|
|
|
10.1. 图
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_graph/graph_operations/" class="md-nav__link">
|
|
|
10.2. 图基础操作
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
|
|
|
10.3. 图的遍历
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_graph/summary/" class="md-nav__link">
|
|
|
10.4. 小结
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
</ul>
|
|
|
</nav>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item md-nav__item--active md-nav__item--section md-nav__item--nested">
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" checked>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<label class="md-nav__link" for="__nav_12" id="__nav_12_label" tabindex="0">
|
|
|
11. 排序算法
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
|
|
|
|
|
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="true">
|
|
|
<label class="md-nav__title" for="__nav_12">
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
11. 排序算法
|
|
|
</label>
|
|
|
<ul class="md-nav__list" data-md-scrollfix>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../sorting_algorithm/" class="md-nav__link">
|
|
|
11.1. 排序算法
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../bubble_sort/" class="md-nav__link">
|
|
|
11.2. 冒泡排序
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../insertion_sort/" class="md-nav__link">
|
|
|
11.3. 插入排序
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../quick_sort/" class="md-nav__link">
|
|
|
11.4. 快速排序
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item md-nav__item--active">
|
|
|
|
|
|
<input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<label class="md-nav__link md-nav__link--active" for="__toc">
|
|
|
11.5. 归并排序
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
|
|
|
|
|
<a href="./" class="md-nav__link md-nav__link--active">
|
|
|
11.5. 归并排序
|
|
|
</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="#1151" class="md-nav__link">
|
|
|
11.5.1. 算法流程
|
|
|
</a>
|
|
|
|
|
|
</li>
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="#1152" class="md-nav__link">
|
|
|
11.5.2. 算法特性
|
|
|
</a>
|
|
|
|
|
|
</li>
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="#1153" class="md-nav__link">
|
|
|
11.5.3. 链表排序 *
|
|
|
</a>
|
|
|
|
|
|
</li>
|
|
|
|
|
|
</ul>
|
|
|
|
|
|
</nav>
|
|
|
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../bucket_sort/" class="md-nav__link">
|
|
|
11.6. 桶排序
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../counting_sort/" class="md-nav__link">
|
|
|
11.7. 计数排序
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../radix_sort/" class="md-nav__link">
|
|
|
11.8. 基数排序
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../summary/" class="md-nav__link">
|
|
|
11.9. 小结
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
</ul>
|
|
|
</nav>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<label class="md-nav__link" for="__nav_13" id="__nav_13_label" tabindex="0">
|
|
|
12. 搜索算法
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
|
|
|
|
|
<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>
|
|
|
12. 搜索算法
|
|
|
</label>
|
|
|
<ul class="md-nav__list" data-md-scrollfix>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
|
|
|
12.1. 搜索算法（New）
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
|
|
|
12.2. 哈希优化策略
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_searching/summary/" class="md-nav__link">
|
|
|
12.3. 小结
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
</ul>
|
|
|
</nav>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<label class="md-nav__link" for="__nav_14" id="__nav_14_label" tabindex="0">
|
|
|
13. 回溯算法
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
|
|
|
|
|
<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>
|
|
|
13. 回溯算法
|
|
|
</label>
|
|
|
<ul class="md-nav__list" data-md-scrollfix>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
|
|
|
13.1. 回溯算法（New）
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
|
|
|
13.2. 全排列问题（New）
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
|
|
|
13.3. N 皇后问题（New）
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
</ul>
|
|
|
</nav>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<label class="md-nav__link" for="__nav_15" id="__nav_15_label" tabindex="0">
|
|
|
14. 附录
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
|
|
|
|
|
<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>
|
|
|
14. 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">
|
|
|
14.1. 编程环境安装
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_appendix/contribution/" class="md-nav__link">
|
|
|
14.2. 一起参与创作
|
|
|
</a>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
</ul>
|
|
|
</nav>
|
|
|
</li>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<div class="md-nav__link md-nav__link--index ">
|
|
|
<a href="../../chapter_reference/">参考文献</a>
|
|
|
|
|
|
</div>
|
|
|
|
|
|
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
|
|
|
<label class="md-nav__title" for="__nav_16">
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
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="#1151" class="md-nav__link">
|
|
|
11.5.1. 算法流程
|
|
|
</a>
|
|
|
|
|
|
</li>
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="#1152" class="md-nav__link">
|
|
|
11.5.2. 算法特性
|
|
|
</a>
|
|
|
|
|
|
</li>
|
|
|
|
|
|
<li class="md-nav__item">
|
|
|
<a href="#1153" class="md-nav__link">
|
|
|
11.5.3. 链表排序 *
|
|
|
</a>
|
|
|
|
|
|
</li>
|
|
|
|
|
|
</ul>
|
|
|
|
|
|
</nav>
|
|
|
</div>
|
|
|
</div>
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
|
|
<div class="md-content" data-md-component="content">
|
|
|
<article class="md-content__inner md-typeset">
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_sorting/merge_sort.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>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<h1 id="115">11.5. 归并排序<a class="headerlink" href="#115" title="Permanent link">¶</a></h1>
|
|
|
<p>「归并排序 Merge Sort」基于分治思想实现排序，包含“划分”和“合并”两个阶段：</p>
|
|
|
<ol>
|
|
|
<li><strong>划分阶段</strong>：通过递归不断地将数组从中点处分开，将长数组的排序问题转换为短数组的排序问题；</li>
|
|
|
<li><strong>合并阶段</strong>：当子数组长度为 1 时终止划分，开始合并，持续地将左右两个较短的有序数组合并为一个较长的有序数组，直至结束；</li>
|
|
|
</ol>
|
|
|
<p><img alt="归并排序的划分与合并阶段" src="../merge_sort.assets/merge_sort_overview.png" /></p>
|
|
|
<p align="center"> Fig. 归并排序的划分与合并阶段 </p>
|
|
|
|
|
|
<h2 id="1151">11.5.1. 算法流程<a class="headerlink" href="#1151" title="Permanent link">¶</a></h2>
|
|
|
<p>“划分阶段”从顶至底递归地将数组从中点切为两个子数组，直至长度为 1 ；</p>
|
|
|
<ol>
|
|
|
<li>计算数组中点 <code>mid</code> ，递归划分左子数组（区间 <code>[left, mid]</code> ）和右子数组（区间 <code>[mid + 1, right]</code> ）；</li>
|
|
|
<li>递归执行步骤 <code>1.</code> ，直至子数组区间长度为 1 时，终止递归划分；</li>
|
|
|
</ol>
|
|
|
<p>“合并阶段”从底至顶地将左子数组和右子数组合并为一个有序数组。需要注意的是，从长度为 1 的子数组开始合并，合并阶段中的每个子数组都是有序的。</p>
|
|
|
<div class="tabbed-set tabbed-alternate" data-tabs="1:10"><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" /><div class="tabbed-labels"><label for="__tabbed_1_1"><1></label><label for="__tabbed_1_2"><2></label><label for="__tabbed_1_3"><3></label><label for="__tabbed_1_4"><4></label><label for="__tabbed_1_5"><5></label><label for="__tabbed_1_6"><6></label><label for="__tabbed_1_7"><7></label><label for="__tabbed_1_8"><8></label><label for="__tabbed_1_9"><9></label><label for="__tabbed_1_10"><10></label></div>
|
|
|
<div class="tabbed-content">
|
|
|
<div class="tabbed-block">
|
|
|
<p><img alt="归并排序步骤" src="../merge_sort.assets/merge_sort_step1.png" /></p>
|
|
|
</div>
|
|
|
<div class="tabbed-block">
|
|
|
<p><img alt="merge_sort_step2" src="../merge_sort.assets/merge_sort_step2.png" /></p>
|
|
|
</div>
|
|
|
<div class="tabbed-block">
|
|
|
<p><img alt="merge_sort_step3" src="../merge_sort.assets/merge_sort_step3.png" /></p>
|
|
|
</div>
|
|
|
<div class="tabbed-block">
|
|
|
<p><img alt="merge_sort_step4" src="../merge_sort.assets/merge_sort_step4.png" /></p>
|
|
|
</div>
|
|
|
<div class="tabbed-block">
|
|
|
<p><img alt="merge_sort_step5" src="../merge_sort.assets/merge_sort_step5.png" /></p>
|
|
|
</div>
|
|
|
<div class="tabbed-block">
|
|
|
<p><img alt="merge_sort_step6" src="../merge_sort.assets/merge_sort_step6.png" /></p>
|
|
|
</div>
|
|
|
<div class="tabbed-block">
|
|
|
<p><img alt="merge_sort_step7" src="../merge_sort.assets/merge_sort_step7.png" /></p>
|
|
|
</div>
|
|
|
<div class="tabbed-block">
|
|
|
<p><img alt="merge_sort_step8" src="../merge_sort.assets/merge_sort_step8.png" /></p>
|
|
|
</div>
|
|
|
<div class="tabbed-block">
|
|
|
<p><img alt="merge_sort_step9" src="../merge_sort.assets/merge_sort_step9.png" /></p>
|
|
|
</div>
|
|
|
<div class="tabbed-block">
|
|
|
<p><img alt="merge_sort_step10" src="../merge_sort.assets/merge_sort_step10.png" /></p>
|
|
|
</div>
|
|
|
</div>
|
|
|
</div>
|
|
|
<p>观察发现，归并排序的递归顺序与二叉树的后序遍历相同，具体来看：</p>
|
|
|
<ul>
|
|
|
<li><strong>后序遍历</strong>：先递归左子树，再递归右子树，最后处理根节点。</li>
|
|
|
<li><strong>归并排序</strong>：先递归左子数组，再递归右子数组，最后处理合并。</li>
|
|
|
</ul>
|
|
|
<div class="tabbed-set tabbed-alternate" data-tabs="2:10"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Java</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Python</label><label for="__tabbed_2_4">Go</label><label for="__tabbed_2_5">JavaScript</label><label for="__tabbed_2_6">TypeScript</label><label for="__tabbed_2_7">C</label><label for="__tabbed_2_8">C#</label><label for="__tabbed_2_9">Swift</label><label for="__tabbed_2_10">Zig</label></div>
|
|
|
<div class="tabbed-content">
|
|
|
<div class="tabbed-block">
|
|
|
<div class="highlight"><span class="filename">merge_sort.java</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="cm">/* 合并左子数组和右子数组 */</span>
|
|
|
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="c1">// 左子数组区间 [left, mid]</span>
|
|
|
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="c1">// 右子数组区间 [mid + 1, right]</span>
|
|
|
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="kt">void</span><span class="w"> </span><span class="nf">merge</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="w"> </span><span class="c1">// 初始化辅助数组</span>
|
|
|
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Arrays</span><span class="p">.</span><span class="na">copyOfRange</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">right</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-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="w"> </span><span class="c1">// 左子数组的起始索引和结束索引</span>
|
|
|
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">leftStart</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">leftEnd</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">;</span>
|
|
|
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="w"> </span><span class="c1">// 右子数组的起始索引和结束索引</span>
|
|
|
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">rightStart</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">rightEnd</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">;</span>
|
|
|
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a><span class="w"> </span><span class="c1">// i, j 分别指向左子数组、右子数组的首元素</span>
|
|
|
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></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">leftStart</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rightStart</span><span class="p">;</span>
|
|
|
<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a><span class="w"> </span><span class="c1">// 通过覆盖原数组 nums 来合并左子数组和右子数组</span>
|
|
|
<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">right</span><span class="p">;</span><span class="w"> </span><span class="n">k</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a><span class="w"> </span><span class="c1">// 若“左子数组已全部合并完”，则选取右子数组元素，并且 j++</span>
|
|
|
<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a><span class="w"> </span><span class="k">if</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="n">leftEnd</span><span class="p">)</span>
|
|
|
<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">k</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="o">[</span><span class="n">j</span><span class="o">++]</span><span class="p">;</span>
|
|
|
<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a><span class="w"> </span><span class="c1">// 否则，若“右子数组已全部合并完”或“左子数组元素 <= 右子数组元素”，则选取左子数组元素，并且 i++</span>
|
|
|
<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">rightEnd</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">tmp</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">tmp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">)</span>
|
|
|
<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">k</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="o">[</span><span class="n">i</span><span class="o">++]</span><span class="p">;</span>
|
|
|
<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a><span class="w"> </span><span class="c1">// 否则，若“左右子数组都未全部合并完”且“左子数组元素 > 右子数组元素”，则选取右子数组元素，并且 j++</span>
|
|
|
<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a><span class="w"> </span><span class="k">else</span>
|
|
|
<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">k</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="o">[</span><span class="n">j</span><span class="o">++]</span><span class="p">;</span>
|
|
|
<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a><span class="w"> </span><span class="p">}</span>
|
|
|
<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a><span class="p">}</span>
|
|
|
<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a>
|
|
|
<a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a><span class="cm">/* 归并排序 */</span>
|
|
|
<a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a><span class="kt">void</span><span class="w"> </span><span class="nf">mergeSort</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a><span class="w"> </span><span class="c1">// 终止条件</span>
|
|
|
<a id="__codelineno-0-30" name="__codelineno-0-30" href="#__codelineno-0-30"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
|
|
|
<a id="__codelineno-0-31" name="__codelineno-0-31" href="#__codelineno-0-31"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span><span class="w"> </span><span class="c1">// 当子数组长度为 1 时终止递归</span>
|
|
|
<a id="__codelineno-0-32" name="__codelineno-0-32" href="#__codelineno-0-32"></a><span class="w"> </span><span class="c1">// 划分阶段</span>
|
|
|
<a id="__codelineno-0-33" name="__codelineno-0-33" href="#__codelineno-0-33"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 计算中点</span>
|
|
|
<a id="__codelineno-0-34" name="__codelineno-0-34" href="#__codelineno-0-34"></a><span class="w"> </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">);</span><span class="w"> </span><span class="c1">// 递归左子数组</span>
|
|
|
<a id="__codelineno-0-35" name="__codelineno-0-35" href="#__codelineno-0-35"></a><span class="w"> </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 递归右子数组</span>
|
|
|
<a id="__codelineno-0-36" name="__codelineno-0-36" href="#__codelineno-0-36"></a><span class="w"> </span><span class="c1">// 合并阶段</span>
|
|
|
<a id="__codelineno-0-37" name="__codelineno-0-37" href="#__codelineno-0-37"></a><span class="w"> </span><span class="n">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
|
|
|
<a id="__codelineno-0-38" name="__codelineno-0-38" href="#__codelineno-0-38"></a><span class="p">}</span>
|
|
|
</code></pre></div>
|
|
|
</div>
|
|
|
<div class="tabbed-block">
|
|
|
<div class="highlight"><span class="filename">merge_sort.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 合并左子数组和右子数组 */</span>
|
|
|
<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="c1">// 左子数组区间 [left, mid]</span>
|
|
|
<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="c1">// 右子数组区间 [mid + 1, right]</span>
|
|
|
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="kt">void</span><span class="w"> </span><span class="nf">merge</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">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </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="c1">// 初始化辅助数组</span>
|
|
|
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w"> </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="n">tmp</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">begin</span><span class="p">()</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">begin</span><span class="p">()</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">right</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-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w"> </span><span class="c1">// 左子数组的起始索引和结束索引</span>
|
|
|
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">leftStart</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">leftEnd</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">;</span>
|
|
|
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w"> </span><span class="c1">// 右子数组的起始索引和结束索引</span>
|
|
|
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">rightStart</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">rightEnd</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">;</span>
|
|
|
<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w"> </span><span class="c1">// i, j 分别指向左子数组、右子数组的首元素</span>
|
|
|
<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></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">leftStart</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rightStart</span><span class="p">;</span>
|
|
|
<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w"> </span><span class="c1">// 通过覆盖原数组 nums 来合并左子数组和右子数组</span>
|
|
|
<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">right</span><span class="p">;</span><span class="w"> </span><span class="n">k</span><span class="o">++</span><span class="p">)</span><span class="w"> </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="c1">// 若“左子数组已全部合并完”，则选取右子数组元素，并且 j++</span>
|
|
|
<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w"> </span><span class="k">if</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="n">leftEnd</span><span class="p">)</span>
|
|
|
<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">j</span><span class="o">++</span><span class="p">];</span>
|
|
|
<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w"> </span><span class="c1">// 否则，若“右子数组已全部合并完”或“左子数组元素 <= 右子数组元素”，则选取左子数组元素，并且 i++</span>
|
|
|
<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">rightEnd</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">tmp</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">tmp</span><span class="p">[</span><span class="n">j</span><span class="p">])</span>
|
|
|
<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">i</span><span class="o">++</span><span class="p">];</span>
|
|
|
<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w"> </span><span class="c1">// 否则，若“左右子数组都未全部合并完”且“左子数组元素 > 右子数组元素”，则选取右子数组元素，并且 j++</span>
|
|
|
<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="w"> </span><span class="k">else</span>
|
|
|
<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">j</span><span class="o">++</span><span class="p">];</span>
|
|
|
<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="w"> </span><span class="p">}</span>
|
|
|
<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="p">}</span>
|
|
|
<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a>
|
|
|
<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a><span class="cm">/* 归并排序 */</span>
|
|
|
<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="kt">void</span><span class="w"> </span><span class="nf">mergeSort</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">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="w"> </span><span class="c1">// 终止条件</span>
|
|
|
<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
|
|
|
<a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span><span class="w"> </span><span class="c1">// 当子数组长度为 1 时终止递归</span>
|
|
|
<a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a><span class="w"> </span><span class="c1">// 划分阶段</span>
|
|
|
<a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 计算中点</span>
|
|
|
<a id="__codelineno-1-34" name="__codelineno-1-34" href="#__codelineno-1-34"></a><span class="w"> </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">);</span><span class="w"> </span><span class="c1">// 递归左子数组</span>
|
|
|
<a id="__codelineno-1-35" name="__codelineno-1-35" href="#__codelineno-1-35"></a><span class="w"> </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 递归右子数组</span>
|
|
|
<a id="__codelineno-1-36" name="__codelineno-1-36" href="#__codelineno-1-36"></a><span class="w"> </span><span class="c1">// 合并阶段</span>
|
|
|
<a id="__codelineno-1-37" name="__codelineno-1-37" href="#__codelineno-1-37"></a><span class="w"> </span><span class="n">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
|
|
|
<a id="__codelineno-1-38" name="__codelineno-1-38" href="#__codelineno-1-38"></a><span class="p">}</span>
|
|
|
</code></pre></div>
|
|
|
</div>
|
|
|
<div class="tabbed-block">
|
|
|
<div class="highlight"><span class="filename">merge_sort.py</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="k">def</span> <span class="nf">merge</span><span class="p">(</span><span class="n">nums</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">left</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">mid</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">right</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-></span> <span class="kc">None</span><span class="p">:</span>
|
|
|
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="w"> </span><span class="sd">"""合并左子数组和右子数组"""</span>
|
|
|
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a> <span class="c1"># 左子数组区间 [left, mid]</span>
|
|
|
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a> <span class="c1"># 右子数组区间 [mid + 1, right]</span>
|
|
|
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a> <span class="c1"># 初始化辅助数组</span>
|
|
|
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a> <span class="n">tmp</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">left</span> <span class="p">:</span> <span class="n">right</span> <span class="o">+</span> <span class="mi">1</span><span class="p">])</span>
|
|
|
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a> <span class="c1"># 左子数组的起始索引和结束索引</span>
|
|
|
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a> <span class="n">left_start</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span>
|
|
|
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a> <span class="n">left_end</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">mid</span> <span class="o">-</span> <span class="n">left</span>
|
|
|
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a> <span class="c1"># 右子数组的起始索引和结束索引</span>
|
|
|
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a> <span class="n">right_start</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">mid</span> <span class="o">+</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">left</span>
|
|
|
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a> <span class="n">right_end</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">right</span> <span class="o">-</span> <span class="n">left</span>
|
|
|
<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a> <span class="c1"># i, j 分别指向左子数组、右子数组的首元素</span>
|
|
|
<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">left_start</span>
|
|
|
<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a> <span class="n">j</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">right_start</span>
|
|
|
<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a> <span class="c1"># 通过覆盖原数组 nums 来合并左子数组和右子数组</span>
|
|
|
<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a> <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">left</span><span class="p">,</span> <span class="n">right</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="c1"># 若“左子数组已全部合并完”，则选取右子数组元素，并且 j++</span>
|
|
|
<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a> <span class="k">if</span> <span class="n">i</span> <span class="o">></span> <span class="n">left_end</span><span class="p">:</span>
|
|
|
<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a> <span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">tmp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
|
|
|
<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a> <span class="n">j</span> <span class="o">+=</span> <span class="mi">1</span>
|
|
|
<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a> <span class="c1"># 否则，若“右子数组已全部合并完”或“左子数组元素 <= 右子数组元素”，则选取左子数组元素，并且 i++</span>
|
|
|
<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a> <span class="k">elif</span> <span class="n">j</span> <span class="o">></span> <span class="n">right_end</span> <span class="ow">or</span> <span class="n">tmp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o"><=</span> <span class="n">tmp</span><span class="p">[</span><span class="n">j</span><span class="p">]:</span>
|
|
|
<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a> <span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">tmp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
|
|
|
<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a> <span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
|
|
|
<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a> <span class="c1"># 否则，若“左右子数组都未全部合并完”且“左子数组元素 > 右子数组元素”，则选取右子数组元素，并且 j++</span>
|
|
|
<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a> <span class="k">else</span><span class="p">:</span>
|
|
|
<a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a> <span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">tmp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
|
|
|
<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a> <span class="n">j</span> <span class="o">+=</span> <span class="mi">1</span>
|
|
|
<a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a>
|
|
|
<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a><span class="k">def</span> <span class="nf">merge_sort</span><span class="p">(</span><span class="n">nums</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">left</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">right</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-></span> <span class="kc">None</span><span class="p">:</span>
|
|
|
<a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a><span class="w"> </span><span class="sd">"""归并排序"""</span>
|
|
|
<a id="__codelineno-2-33" name="__codelineno-2-33" href="#__codelineno-2-33"></a> <span class="c1"># 终止条件</span>
|
|
|
<a id="__codelineno-2-34" name="__codelineno-2-34" href="#__codelineno-2-34"></a> <span class="k">if</span> <span class="n">left</span> <span class="o">>=</span> <span class="n">right</span><span class="p">:</span>
|
|
|
<a id="__codelineno-2-35" name="__codelineno-2-35" href="#__codelineno-2-35"></a> <span class="k">return</span> <span class="c1"># 当子数组长度为 1 时终止递归</span>
|
|
|
<a id="__codelineno-2-36" name="__codelineno-2-36" href="#__codelineno-2-36"></a> <span class="c1"># 划分阶段</span>
|
|
|
<a id="__codelineno-2-37" name="__codelineno-2-37" href="#__codelineno-2-37"></a> <span class="n">mid</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="p">(</span><span class="n">left</span> <span class="o">+</span> <span class="n">right</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span> <span class="c1"># 计算中点</span>
|
|
|
<a id="__codelineno-2-38" name="__codelineno-2-38" href="#__codelineno-2-38"></a> <span class="n">merge_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">left</span><span class="p">,</span> <span class="n">mid</span><span class="p">)</span> <span class="c1"># 递归左子数组</span>
|
|
|
<a id="__codelineno-2-39" name="__codelineno-2-39" href="#__codelineno-2-39"></a> <span class="n">merge_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">mid</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">right</span><span class="p">)</span> <span class="c1"># 递归右子数组</span>
|
|
|
<a id="__codelineno-2-40" name="__codelineno-2-40" href="#__codelineno-2-40"></a> <span class="c1"># 合并阶段</span>
|
|
|
<a id="__codelineno-2-41" name="__codelineno-2-41" href="#__codelineno-2-41"></a> <span class="n">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">left</span><span class="p">,</span> <span class="n">mid</span><span class="p">,</span> <span class="n">right</span><span class="p">)</span>
|
|
|
</code></pre></div>
|
|
|
</div>
|
|
|
<div class="tabbed-block">
|
|
|
<div class="highlight"><span class="filename">merge_sort.go</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 合并左子数组和右子数组 */</span>
|
|
|
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="c1">// 左子数组区间 [left, mid]</span>
|
|
|
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="c1">// 右子数组区间 [mid + 1, right]</span>
|
|
|
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="kd">func</span><span class="w"> </span><span class="nx">merge</span><span class="p">(</span><span class="nx">nums</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">left</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w"> </span><span class="c1">// 初始化辅助数组 借助 copy 模块</span>
|
|
|
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="o">-</span><span class="nx">left</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
|
|
|
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></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="o">:=</span><span class="w"> </span><span class="nx">left</span><span class="p">;</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">right</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</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="nx">tmp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="nx">left</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span>
|
|
|
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><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="c1">// 左子数组的起始索引和结束索引</span>
|
|
|
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w"> </span><span class="nx">leftStart</span><span class="p">,</span><span class="w"> </span><span class="nx">leftEnd</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">left</span><span class="o">-</span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="o">-</span><span class="nx">left</span>
|
|
|
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w"> </span><span class="c1">// 右子数组的起始索引和结束索引</span>
|
|
|
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w"> </span><span class="nx">rightStart</span><span class="p">,</span><span class="w"> </span><span class="nx">rightEnd</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">mid</span><span class="o">+</span><span class="mi">1</span><span class="o">-</span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="o">-</span><span class="nx">left</span>
|
|
|
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w"> </span><span class="c1">// i, j 分别指向左子数组、右子数组的首元素</span>
|
|
|
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">leftStart</span><span class="p">,</span><span class="w"> </span><span class="nx">rightStart</span>
|
|
|
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w"> </span><span class="c1">// 通过覆盖原数组 nums 来合并左子数组和右子数组</span>
|
|
|
<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">k</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">left</span><span class="p">;</span><span class="w"> </span><span class="nx">k</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="nx">right</span><span class="p">;</span><span class="w"> </span><span class="nx">k</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w"> </span><span class="c1">// 若“左子数组已全部合并完”，则选取右子数组元素，并且 j++</span>
|
|
|
<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">></span><span class="w"> </span><span class="nx">leftEnd</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">k</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span>
|
|
|
<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="w"> </span><span class="nx">j</span><span class="o">++</span>
|
|
|
<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="w"> </span><span class="c1">// 否则，若“右子数组已全部合并完”或“左子数组元素 <= 右子数组元素”，则选取左子数组元素，并且 i++</span>
|
|
|
<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">></span><span class="w"> </span><span class="nx">rightEnd</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">tmp</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">tmp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">k</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span>
|
|
|
<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="w"> </span><span class="nx">i</span><span class="o">++</span>
|
|
|
<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="w"> </span><span class="c1">// 否则，若“左右子数组都未全部合并完”且“左子数组元素 > 右子数组元素”，则选取右子数组元素，并且 j++</span>
|
|
|
<a id="__codelineno-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></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-3-28" name="__codelineno-3-28" href="#__codelineno-3-28"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">k</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span>
|
|
|
<a id="__codelineno-3-29" name="__codelineno-3-29" href="#__codelineno-3-29"></a><span class="w"> </span><span class="nx">j</span><span class="o">++</span>
|
|
|
<a id="__codelineno-3-30" name="__codelineno-3-30" href="#__codelineno-3-30"></a><span class="w"> </span><span class="p">}</span>
|
|
|
<a id="__codelineno-3-31" name="__codelineno-3-31" href="#__codelineno-3-31"></a><span class="w"> </span><span class="p">}</span>
|
|
|
<a id="__codelineno-3-32" name="__codelineno-3-32" href="#__codelineno-3-32"></a><span class="p">}</span>
|
|
|
<a id="__codelineno-3-33" name="__codelineno-3-33" href="#__codelineno-3-33"></a>
|
|
|
<a id="__codelineno-3-34" name="__codelineno-3-34" href="#__codelineno-3-34"></a><span class="cm">/* 归并排序 */</span>
|
|
|
<a id="__codelineno-3-35" name="__codelineno-3-35" href="#__codelineno-3-35"></a><span class="kd">func</span><span class="w"> </span><span class="nx">mergeSort</span><span class="p">(</span><span class="nx">nums</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">left</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-3-36" name="__codelineno-3-36" href="#__codelineno-3-36"></a><span class="w"> </span><span class="c1">// 终止条件</span>
|
|
|
<a id="__codelineno-3-37" name="__codelineno-3-37" href="#__codelineno-3-37"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">left</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-3-38" name="__codelineno-3-38" href="#__codelineno-3-38"></a><span class="w"> </span><span class="k">return</span>
|
|
|
<a id="__codelineno-3-39" name="__codelineno-3-39" href="#__codelineno-3-39"></a><span class="w"> </span><span class="p">}</span>
|
|
|
<a id="__codelineno-3-40" name="__codelineno-3-40" href="#__codelineno-3-40"></a><span class="w"> </span><span class="c1">// 划分阶段</span>
|
|
|
<a id="__codelineno-3-41" name="__codelineno-3-41" href="#__codelineno-3-41"></a><span class="w"> </span><span class="nx">mid</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="p">(</span><span class="nx">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span>
|
|
|
<a id="__codelineno-3-42" name="__codelineno-3-42" href="#__codelineno-3-42"></a><span class="w"> </span><span class="nx">mergeSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="p">)</span>
|
|
|
<a id="__codelineno-3-43" name="__codelineno-3-43" href="#__codelineno-3-43"></a><span class="w"> </span><span class="nx">mergeSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span>
|
|
|
<a id="__codelineno-3-44" name="__codelineno-3-44" href="#__codelineno-3-44"></a><span class="w"> </span><span class="c1">// 合并阶段</span>
|
|
|
<a id="__codelineno-3-45" name="__codelineno-3-45" href="#__codelineno-3-45"></a><span class="w"> </span><span class="nx">merge</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span>
|
|
|
<a id="__codelineno-3-46" name="__codelineno-3-46" href="#__codelineno-3-46"></a><span class="p">}</span>
|
|
|
</code></pre></div>
|
|
|
</div>
|
|
|
<div class="tabbed-block">
|
|
|
<div class="highlight"><span class="filename">merge_sort.js</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 合并左子数组和右子数组 */</span>
|
|
|
<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="c1">// 左子数组区间 [left, mid]</span>
|
|
|
<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="c1">// 右子数组区间 [mid + 1, right]</span>
|
|
|
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="kd">function</span><span class="w"> </span><span class="nx">merge</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w"> </span><span class="c1">// 初始化辅助数组</span>
|
|
|
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">slice</span><span class="p">(</span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">right</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-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w"> </span><span class="c1">// 左子数组的起始索引和结束索引</span>
|
|
|
<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">leftStart</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">left</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span>
|
|
|
<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w"> </span><span class="nx">leftEnd</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">mid</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">left</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="c1">// 右子数组的起始索引和结束索引</span>
|
|
|
<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">rightStart</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">left</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="nx">rightEnd</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">left</span><span class="p">;</span>
|
|
|
<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w"> </span><span class="c1">// i, j 分别指向左子数组、右子数组的首元素</span>
|
|
|
<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></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">leftStart</span><span class="p">,</span>
|
|
|
<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">rightStart</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">// 通过覆盖原数组 nums 来合并左子数组和右子数组</span>
|
|
|
<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">left</span><span class="p">;</span><span class="w"> </span><span class="nx">k</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="nx">right</span><span class="p">;</span><span class="w"> </span><span class="nx">k</span><span class="o">++</span><span class="p">)</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">if</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="nx">leftEnd</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w"> </span><span class="c1">// 若“左子数组已全部合并完”，则选取右子数组元素，并且 j++</span>
|
|
|
<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">j</span><span class="o">++</span><span class="p">];</span>
|
|
|
<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="nx">rightEnd</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">tmp</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">tmp</span><span class="p">[</span><span class="nx">j</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w"> </span><span class="c1">// 否则，若“右子数组已全部合并完”或“左子数组元素 <= 右子数组元素”，则选取左子数组元素，并且 i++</span>
|
|
|
<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">i</span><span class="o">++</span><span class="p">];</span>
|
|
|
<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></a><span class="w"> </span><span class="c1">// 否则，若“左右子数组都未全部合并完”且“左子数组元素 > 右子数组元素”，则选取右子数组元素，并且 j++</span>
|
|
|
<a id="__codelineno-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">j</span><span class="o">++</span><span class="p">];</span>
|
|
|
<a id="__codelineno-4-27" name="__codelineno-4-27" href="#__codelineno-4-27"></a><span class="w"> </span><span class="p">}</span>
|
|
|
<a id="__codelineno-4-28" name="__codelineno-4-28" href="#__codelineno-4-28"></a><span class="w"> </span><span class="p">}</span>
|
|
|
<a id="__codelineno-4-29" name="__codelineno-4-29" href="#__codelineno-4-29"></a><span class="p">}</span>
|
|
|
<a id="__codelineno-4-30" name="__codelineno-4-30" href="#__codelineno-4-30"></a>
|
|
|
<a id="__codelineno-4-31" name="__codelineno-4-31" href="#__codelineno-4-31"></a><span class="cm">/* 归并排序 */</span>
|
|
|
<a id="__codelineno-4-32" name="__codelineno-4-32" href="#__codelineno-4-32"></a><span class="kd">function</span><span class="w"> </span><span class="nx">mergeSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-4-33" name="__codelineno-4-33" href="#__codelineno-4-33"></a><span class="w"> </span><span class="c1">// 终止条件</span>
|
|
|
<a id="__codelineno-4-34" name="__codelineno-4-34" href="#__codelineno-4-34"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">left</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span><span class="w"> </span><span class="c1">// 当子数组长度为 1 时终止递归</span>
|
|
|
<a id="__codelineno-4-35" name="__codelineno-4-35" href="#__codelineno-4-35"></a><span class="w"> </span><span class="c1">// 划分阶段</span>
|
|
|
<a id="__codelineno-4-36" name="__codelineno-4-36" href="#__codelineno-4-36"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">mid</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">((</span><span class="nx">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// 计算中点</span>
|
|
|
<a id="__codelineno-4-37" name="__codelineno-4-37" href="#__codelineno-4-37"></a><span class="w"> </span><span class="nx">mergeSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="p">);</span><span class="w"> </span><span class="c1">// 递归左子数组</span>
|
|
|
<a id="__codelineno-4-38" name="__codelineno-4-38" href="#__codelineno-4-38"></a><span class="w"> </span><span class="nx">mergeSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 递归右子数组</span>
|
|
|
<a id="__codelineno-4-39" name="__codelineno-4-39" href="#__codelineno-4-39"></a><span class="w"> </span><span class="c1">// 合并阶段</span>
|
|
|
<a id="__codelineno-4-40" name="__codelineno-4-40" href="#__codelineno-4-40"></a><span class="w"> </span><span class="nx">merge</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">);</span>
|
|
|
<a id="__codelineno-4-41" name="__codelineno-4-41" href="#__codelineno-4-41"></a><span class="p">}</span>
|
|
|
</code></pre></div>
|
|
|
</div>
|
|
|
<div class="tabbed-block">
|
|
|
<div class="highlight"><span class="filename">merge_sort.ts</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 合并左子数组和右子数组 */</span>
|
|
|
<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="c1">// 左子数组区间 [left, mid]</span>
|
|
|
<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="c1">// 右子数组区间 [mid + 1, right]</span>
|
|
|
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="kd">function</span><span class="w"> </span><span class="nx">merge</span><span class="p">(</span><span class="nx">nums</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">left</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">mid</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">right</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w"> </span><span class="c1">// 初始化辅助数组</span>
|
|
|
<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">slice</span><span class="p">(</span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">right</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-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w"> </span><span class="c1">// 左子数组的起始索引和结束索引</span>
|
|
|
<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">leftStart</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">left</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span>
|
|
|
<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w"> </span><span class="nx">leftEnd</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">mid</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">left</span><span class="p">;</span>
|
|
|
<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w"> </span><span class="c1">// 右子数组的起始索引和结束索引</span>
|
|
|
<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">rightStart</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span>
|
|
|
<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w"> </span><span class="nx">rightEnd</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">left</span><span class="p">;</span>
|
|
|
<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w"> </span><span class="c1">// i, j 分别指向左子数组、右子数组的首元素</span>
|
|
|
<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></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">leftStart</span><span class="p">,</span>
|
|
|
<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">rightStart</span><span class="p">;</span>
|
|
|
<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w"> </span><span class="c1">// 通过覆盖原数组 nums 来合并左子数组和右子数组</span>
|
|
|
<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">left</span><span class="p">;</span><span class="w"> </span><span class="nx">k</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="nx">right</span><span class="p">;</span><span class="w"> </span><span class="nx">k</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w"> </span><span class="k">if</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="nx">leftEnd</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="w"> </span><span class="c1">// 若“左子数组已全部合并完”，则选取右子数组元素，并且 j++</span>
|
|
|
<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">j</span><span class="o">++</span><span class="p">];</span>
|
|
|
<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="w"> </span><span class="c1">// 否则，若“右子数组已全部合并完”或“左子数组元素 <= 右子数组元素”，则选取左子数组元素，并且 i++</span>
|
|
|
<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="nx">rightEnd</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">tmp</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">tmp</span><span class="p">[</span><span class="nx">j</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">i</span><span class="o">++</span><span class="p">];</span>
|
|
|
<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a><span class="w"> </span><span class="c1">// 否则，若“左右子数组都未全部合并完”且“左子数组元素 > 右子数组元素”，则选取右子数组元素，并且 j++</span>
|
|
|
<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></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-5-26" name="__codelineno-5-26" href="#__codelineno-5-26"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">j</span><span class="o">++</span><span class="p">];</span>
|
|
|
<a id="__codelineno-5-27" name="__codelineno-5-27" href="#__codelineno-5-27"></a><span class="w"> </span><span class="p">}</span>
|
|
|
<a id="__codelineno-5-28" name="__codelineno-5-28" href="#__codelineno-5-28"></a><span class="w"> </span><span class="p">}</span>
|
|
|
<a id="__codelineno-5-29" name="__codelineno-5-29" href="#__codelineno-5-29"></a><span class="p">}</span>
|
|
|
<a id="__codelineno-5-30" name="__codelineno-5-30" href="#__codelineno-5-30"></a>
|
|
|
<a id="__codelineno-5-31" name="__codelineno-5-31" href="#__codelineno-5-31"></a><span class="cm">/* 归并排序 */</span>
|
|
|
<a id="__codelineno-5-32" name="__codelineno-5-32" href="#__codelineno-5-32"></a><span class="kd">function</span><span class="w"> </span><span class="nx">mergeSort</span><span class="p">(</span><span class="nx">nums</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">left</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">right</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-5-33" name="__codelineno-5-33" href="#__codelineno-5-33"></a><span class="w"> </span><span class="c1">// 终止条件</span>
|
|
|
<a id="__codelineno-5-34" name="__codelineno-5-34" href="#__codelineno-5-34"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">left</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span><span class="w"> </span><span class="c1">// 当子数组长度为 1 时终止递归</span>
|
|
|
<a id="__codelineno-5-35" name="__codelineno-5-35" href="#__codelineno-5-35"></a><span class="w"> </span><span class="c1">// 划分阶段</span>
|
|
|
<a id="__codelineno-5-36" name="__codelineno-5-36" href="#__codelineno-5-36"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">mid</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">((</span><span class="nx">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// 计算中点</span>
|
|
|
<a id="__codelineno-5-37" name="__codelineno-5-37" href="#__codelineno-5-37"></a><span class="w"> </span><span class="nx">mergeSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="p">);</span><span class="w"> </span><span class="c1">// 递归左子数组</span>
|
|
|
<a id="__codelineno-5-38" name="__codelineno-5-38" href="#__codelineno-5-38"></a><span class="w"> </span><span class="nx">mergeSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 递归右子数组</span>
|
|
|
<a id="__codelineno-5-39" name="__codelineno-5-39" href="#__codelineno-5-39"></a><span class="w"> </span><span class="c1">// 合并阶段</span>
|
|
|
<a id="__codelineno-5-40" name="__codelineno-5-40" href="#__codelineno-5-40"></a><span class="w"> </span><span class="nx">merge</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">);</span>
|
|
|
<a id="__codelineno-5-41" name="__codelineno-5-41" href="#__codelineno-5-41"></a><span class="p">}</span>
|
|
|
</code></pre></div>
|
|
|
</div>
|
|
|
<div class="tabbed-block">
|
|
|
<div class="highlight"><span class="filename">merge_sort.c</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 合并左子数组和右子数组 */</span>
|
|
|
<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="c1">// 左子数组区间 [left, mid]</span>
|
|
|
<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="c1">// 右子数组区间 [mid + 1, right]</span>
|
|
|
<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="kt">void</span><span class="w"> </span><span class="nf">merge</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </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="kt">int</span><span class="w"> </span><span class="n">index</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">// 初始化辅助数组</span>
|
|
|
<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">right</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</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="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">index</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">index</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">index</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="p">}</span>
|
|
|
<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w"> </span><span class="c1">// 左子数组的起始索引和结束索引</span>
|
|
|
<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">leftStart</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">leftEnd</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">;</span>
|
|
|
<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w"> </span><span class="c1">// 右子数组的起始索引和结束索引</span>
|
|
|
<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">rightStart</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">rightEnd</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</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="c1">// i, j 分别指向左子数组、右子数组的首元素</span>
|
|
|
<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></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">leftStart</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rightStart</span><span class="p">;</span>
|
|
|
<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="w"> </span><span class="c1">// 通过覆盖原数组 nums 来合并左子数组和右子数组</span>
|
|
|
<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">right</span><span class="p">;</span><span class="w"> </span><span class="n">k</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w"> </span><span class="c1">// 若“左子数组已全部合并完”，则选取右子数组元素，并且 j++</span>
|
|
|
<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="w"> </span><span class="k">if</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="n">leftEnd</span><span class="p">)</span>
|
|
|
<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">j</span><span class="o">++</span><span class="p">];</span>
|
|
|
<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="w"> </span><span class="c1">// 否则，若“右子数组已全部合并完”或“左子数组元素 <= 右子数组元素”，则选取左子数组元素，并且 i++</span>
|
|
|
<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">rightEnd</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">tmp</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">tmp</span><span class="p">[</span><span class="n">j</span><span class="p">])</span>
|
|
|
<a id="__codelineno-6-24" name="__codelineno-6-24" href="#__codelineno-6-24"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">i</span><span class="o">++</span><span class="p">];</span>
|
|
|
<a id="__codelineno-6-25" name="__codelineno-6-25" href="#__codelineno-6-25"></a><span class="w"> </span><span class="c1">// 否则，若“左右子数组都未全部合并完”且“左子数组元素 > 右子数组元素”，则选取右子数组元素，并且 j++</span>
|
|
|
<a id="__codelineno-6-26" name="__codelineno-6-26" href="#__codelineno-6-26"></a><span class="w"> </span><span class="k">else</span>
|
|
|
<a id="__codelineno-6-27" name="__codelineno-6-27" href="#__codelineno-6-27"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">j</span><span class="o">++</span><span class="p">];</span>
|
|
|
<a id="__codelineno-6-28" name="__codelineno-6-28" href="#__codelineno-6-28"></a><span class="w"> </span><span class="p">}</span>
|
|
|
<a id="__codelineno-6-29" name="__codelineno-6-29" href="#__codelineno-6-29"></a><span class="p">}</span>
|
|
|
<a id="__codelineno-6-30" name="__codelineno-6-30" href="#__codelineno-6-30"></a>
|
|
|
<a id="__codelineno-6-31" name="__codelineno-6-31" href="#__codelineno-6-31"></a><span class="cm">/* 归并排序 */</span>
|
|
|
<a id="__codelineno-6-32" name="__codelineno-6-32" href="#__codelineno-6-32"></a><span class="kt">void</span><span class="w"> </span><span class="nf">mergeSort</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-6-33" name="__codelineno-6-33" href="#__codelineno-6-33"></a><span class="w"> </span><span class="c1">// 终止条件</span>
|
|
|
<a id="__codelineno-6-34" name="__codelineno-6-34" href="#__codelineno-6-34"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
|
|
|
<a id="__codelineno-6-35" name="__codelineno-6-35" href="#__codelineno-6-35"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span><span class="w"> </span><span class="c1">// 当子数组长度为 1 时终止递归</span>
|
|
|
<a id="__codelineno-6-36" name="__codelineno-6-36" href="#__codelineno-6-36"></a><span class="w"> </span><span class="c1">// 划分阶段</span>
|
|
|
<a id="__codelineno-6-37" name="__codelineno-6-37" href="#__codelineno-6-37"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 计算中点</span>
|
|
|
<a id="__codelineno-6-38" name="__codelineno-6-38" href="#__codelineno-6-38"></a><span class="w"> </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">);</span><span class="w"> </span><span class="c1">// 递归左子数组</span>
|
|
|
<a id="__codelineno-6-39" name="__codelineno-6-39" href="#__codelineno-6-39"></a><span class="w"> </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 递归右子数组</span>
|
|
|
<a id="__codelineno-6-40" name="__codelineno-6-40" href="#__codelineno-6-40"></a><span class="w"> </span><span class="c1">// 合并阶段</span>
|
|
|
<a id="__codelineno-6-41" name="__codelineno-6-41" href="#__codelineno-6-41"></a><span class="w"> </span><span class="n">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
|
|
|
<a id="__codelineno-6-42" name="__codelineno-6-42" href="#__codelineno-6-42"></a><span class="p">}</span>
|
|
|
</code></pre></div>
|
|
|
</div>
|
|
|
<div class="tabbed-block">
|
|
|
<div class="highlight"><span class="filename">merge_sort.cs</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 合并左子数组和右子数组 */</span>
|
|
|
<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="c1">// 左子数组区间 [left, mid]</span>
|
|
|
<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="c1">// 右子数组区间 [mid + 1, right]</span>
|
|
|
<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="k">void</span><span class="w"> </span><span class="nf">merge</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </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="c1">// 初始化辅助数组</span>
|
|
|
<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">..(</span><span class="n">right</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-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w"> </span><span class="c1">// 左子数组的起始索引和结束索引 </span>
|
|
|
<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">leftStart</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">leftEnd</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">;</span>
|
|
|
<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w"> </span><span class="c1">// 右子数组的起始索引和结束索引 </span>
|
|
|
<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">rightStart</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">rightEnd</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">;</span>
|
|
|
<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w"> </span><span class="c1">// i, j 分别指向左子数组、右子数组的首元素</span>
|
|
|
<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></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">leftStart</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rightStart</span><span class="p">;</span>
|
|
|
<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w"> </span><span class="c1">// 通过覆盖原数组 nums 来合并左子数组和右子数组</span>
|
|
|
<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">right</span><span class="p">;</span><span class="w"> </span><span class="n">k</span><span class="o">++</span><span class="p">)</span><span class="w"> </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="c1">// 若“左子数组已全部合并完”，则选取右子数组元素，并且 j++</span>
|
|
|
<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w"> </span><span class="k">if</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="n">leftEnd</span><span class="p">)</span>
|
|
|
<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">j</span><span class="o">++</span><span class="p">];</span>
|
|
|
<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w"> </span><span class="c1">// 否则，若“右子数组已全部合并完”或“左子数组元素 <= 右子数组元素”，则选取左子数组元素，并且 i++</span>
|
|
|
<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="nf">if</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">rightEnd</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">tmp</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">tmp</span><span class="p">[</span><span class="n">j</span><span class="p">])</span>
|
|
|
<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">i</span><span class="o">++</span><span class="p">];</span>
|
|
|
<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="w"> </span><span class="c1">// 否则，若“左右子数组都未全部合并完”且“左子数组元素 > 右子数组元素”，则选取右子数组元素，并且 j++</span>
|
|
|
<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="w"> </span><span class="k">else</span>
|
|
|
<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">j</span><span class="o">++</span><span class="p">];</span>
|
|
|
<a id="__codelineno-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></a><span class="w"> </span><span class="p">}</span>
|
|
|
<a id="__codelineno-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a><span class="p">}</span>
|
|
|
<a id="__codelineno-7-26" name="__codelineno-7-26" href="#__codelineno-7-26"></a>
|
|
|
<a id="__codelineno-7-27" name="__codelineno-7-27" href="#__codelineno-7-27"></a><span class="cm">/* 归并排序 */</span>
|
|
|
<a id="__codelineno-7-28" name="__codelineno-7-28" href="#__codelineno-7-28"></a><span class="k">void</span><span class="w"> </span><span class="nf">mergeSort</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-7-29" name="__codelineno-7-29" href="#__codelineno-7-29"></a><span class="w"> </span><span class="c1">// 终止条件</span>
|
|
|
<a id="__codelineno-7-30" name="__codelineno-7-30" href="#__codelineno-7-30"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span><span class="w"> </span><span class="c1">// 当子数组长度为 1 时终止递归</span>
|
|
|
<a id="__codelineno-7-31" name="__codelineno-7-31" href="#__codelineno-7-31"></a><span class="w"> </span><span class="c1">// 划分阶段</span>
|
|
|
<a id="__codelineno-7-32" name="__codelineno-7-32" href="#__codelineno-7-32"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 计算中点</span>
|
|
|
<a id="__codelineno-7-33" name="__codelineno-7-33" href="#__codelineno-7-33"></a><span class="w"> </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">);</span><span class="w"> </span><span class="c1">// 递归左子数组</span>
|
|
|
<a id="__codelineno-7-34" name="__codelineno-7-34" href="#__codelineno-7-34"></a><span class="w"> </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 递归右子数组</span>
|
|
|
<a id="__codelineno-7-35" name="__codelineno-7-35" href="#__codelineno-7-35"></a><span class="w"> </span><span class="c1">// 合并阶段</span>
|
|
|
<a id="__codelineno-7-36" name="__codelineno-7-36" href="#__codelineno-7-36"></a><span class="w"> </span><span class="n">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
|
|
|
<a id="__codelineno-7-37" name="__codelineno-7-37" href="#__codelineno-7-37"></a><span class="p">}</span>
|
|
|
</code></pre></div>
|
|
|
</div>
|
|
|
<div class="tabbed-block">
|
|
|
<div class="highlight"><span class="filename">merge_sort.swift</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 合并左子数组和右子数组 */</span>
|
|
|
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="c1">// 左子数组区间 [left, mid]</span>
|
|
|
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="c1">// 右子数组区间 [mid + 1, right]</span>
|
|
|
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="kd">func</span> <span class="nf">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="kr">inout</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="kr">left</span><span class="p">:</span> <span class="nb">Int</span><span class="p">,</span> <span class="n">mid</span><span class="p">:</span> <span class="nb">Int</span><span class="p">,</span> <span class="kr">right</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
|
|
|
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a> <span class="c1">// 初始化辅助数组</span>
|
|
|
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a> <span class="kd">let</span> <span class="nv">tmp</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="kr">left</span> <span class="p">..</span><span class="o"><</span> <span class="p">(</span><span class="kr">right</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)])</span>
|
|
|
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a> <span class="c1">// 左子数组的起始索引和结束索引</span>
|
|
|
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a> <span class="kd">let</span> <span class="nv">leftStart</span> <span class="p">=</span> <span class="kr">left</span> <span class="o">-</span> <span class="kr">left</span>
|
|
|
<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a> <span class="kd">let</span> <span class="nv">leftEnd</span> <span class="p">=</span> <span class="n">mid</span> <span class="o">-</span> <span class="kr">left</span>
|
|
|
<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a> <span class="c1">// 右子数组的起始索引和结束索引</span>
|
|
|
<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a> <span class="kd">let</span> <span class="nv">rightStart</span> <span class="p">=</span> <span class="n">mid</span> <span class="o">+</span> <span class="mi">1</span> <span class="o">-</span> <span class="kr">left</span>
|
|
|
<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a> <span class="kd">let</span> <span class="nv">rightEnd</span> <span class="p">=</span> <span class="kr">right</span> <span class="o">-</span> <span class="kr">left</span>
|
|
|
<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a> <span class="c1">// i, j 分别指向左子数组、右子数组的首元素</span>
|
|
|
<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a> <span class="kd">var</span> <span class="nv">i</span> <span class="p">=</span> <span class="n">leftStart</span>
|
|
|
<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a> <span class="kd">var</span> <span class="nv">j</span> <span class="p">=</span> <span class="n">rightStart</span>
|
|
|
<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a> <span class="c1">// 通过覆盖原数组 nums 来合并左子数组和右子数组</span>
|
|
|
<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a> <span class="k">for</span> <span class="n">k</span> <span class="k">in</span> <span class="kr">left</span> <span class="p">...</span> <span class="kr">right</span> <span class="p">{</span>
|
|
|
<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a> <span class="c1">// 若“左子数组已全部合并完”，则选取右子数组元素，并且 j++</span>
|
|
|
<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a> <span class="k">if</span> <span class="n">i</span> <span class="o">></span> <span class="n">leftEnd</span> <span class="p">{</span>
|
|
|
<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a> <span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="p">=</span> <span class="n">tmp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
|
|
|
<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a> <span class="n">j</span> <span class="o">+=</span> <span class="mi">1</span>
|
|
|
<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a> <span class="p">}</span>
|
|
|
<a id="__codelineno-8-23" name="__codelineno-8-23" href="#__codelineno-8-23"></a> <span class="c1">// 否则，若“右子数组已全部合并完”或“左子数组元素 <= 右子数组元素”，则选取左子数组元素，并且 i++</span>
|
|
|
<a id="__codelineno-8-24" name="__codelineno-8-24" href="#__codelineno-8-24"></a> <span class="k">else</span> <span class="k">if</span> <span class="n">j</span> <span class="o">></span> <span class="n">rightEnd</span> <span class="o">||</span> <span class="n">tmp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o"><=</span> <span class="n">tmp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="p">{</span>
|
|
|
<a id="__codelineno-8-25" name="__codelineno-8-25" href="#__codelineno-8-25"></a> <span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="p">=</span> <span class="n">tmp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
|
|
|
<a id="__codelineno-8-26" name="__codelineno-8-26" href="#__codelineno-8-26"></a> <span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
|
|
|
<a id="__codelineno-8-27" name="__codelineno-8-27" href="#__codelineno-8-27"></a> <span class="p">}</span>
|
|
|
<a id="__codelineno-8-28" name="__codelineno-8-28" href="#__codelineno-8-28"></a> <span class="c1">// 否则，若“左右子数组都未全部合并完”且“左子数组元素 > 右子数组元素”，则选取右子数组元素，并且 j++</span>
|
|
|
<a id="__codelineno-8-29" name="__codelineno-8-29" href="#__codelineno-8-29"></a> <span class="k">else</span> <span class="p">{</span>
|
|
|
<a id="__codelineno-8-30" name="__codelineno-8-30" href="#__codelineno-8-30"></a> <span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="p">=</span> <span class="n">tmp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
|
|
|
<a id="__codelineno-8-31" name="__codelineno-8-31" href="#__codelineno-8-31"></a> <span class="n">j</span> <span class="o">+=</span> <span class="mi">1</span>
|
|
|
<a id="__codelineno-8-32" name="__codelineno-8-32" href="#__codelineno-8-32"></a> <span class="p">}</span>
|
|
|
<a id="__codelineno-8-33" name="__codelineno-8-33" href="#__codelineno-8-33"></a> <span class="p">}</span>
|
|
|
<a id="__codelineno-8-34" name="__codelineno-8-34" href="#__codelineno-8-34"></a><span class="p">}</span>
|
|
|
<a id="__codelineno-8-35" name="__codelineno-8-35" href="#__codelineno-8-35"></a>
|
|
|
<a id="__codelineno-8-36" name="__codelineno-8-36" href="#__codelineno-8-36"></a><span class="cm">/* 归并排序 */</span>
|
|
|
<a id="__codelineno-8-37" name="__codelineno-8-37" href="#__codelineno-8-37"></a><span class="kd">func</span> <span class="nf">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="kr">inout</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="kr">left</span><span class="p">:</span> <span class="nb">Int</span><span class="p">,</span> <span class="kr">right</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
|
|
|
<a id="__codelineno-8-38" name="__codelineno-8-38" href="#__codelineno-8-38"></a> <span class="c1">// 终止条件</span>
|
|
|
<a id="__codelineno-8-39" name="__codelineno-8-39" href="#__codelineno-8-39"></a> <span class="k">if</span> <span class="kr">left</span> <span class="o">>=</span> <span class="kr">right</span> <span class="p">{</span> <span class="c1">// 当子数组长度为 1 时终止递归</span>
|
|
|
<a id="__codelineno-8-40" name="__codelineno-8-40" href="#__codelineno-8-40"></a> <span class="k">return</span>
|
|
|
<a id="__codelineno-8-41" name="__codelineno-8-41" href="#__codelineno-8-41"></a> <span class="p">}</span>
|
|
|
<a id="__codelineno-8-42" name="__codelineno-8-42" href="#__codelineno-8-42"></a> <span class="c1">// 划分阶段</span>
|
|
|
<a id="__codelineno-8-43" name="__codelineno-8-43" href="#__codelineno-8-43"></a> <span class="kd">let</span> <span class="nv">mid</span> <span class="p">=</span> <span class="p">(</span><span class="kr">left</span> <span class="o">+</span> <span class="kr">right</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span> <span class="c1">// 计算中点</span>
|
|
|
<a id="__codelineno-8-44" name="__codelineno-8-44" href="#__codelineno-8-44"></a> <span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="p">&</span><span class="n">nums</span><span class="p">,</span> <span class="kr">left</span><span class="p">:</span> <span class="kr">left</span><span class="p">,</span> <span class="kr">right</span><span class="p">:</span> <span class="n">mid</span><span class="p">)</span> <span class="c1">// 递归左子数组</span>
|
|
|
<a id="__codelineno-8-45" name="__codelineno-8-45" href="#__codelineno-8-45"></a> <span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="p">&</span><span class="n">nums</span><span class="p">,</span> <span class="kr">left</span><span class="p">:</span> <span class="n">mid</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="kr">right</span><span class="p">:</span> <span class="kr">right</span><span class="p">)</span> <span class="c1">// 递归右子数组</span>
|
|
|
<a id="__codelineno-8-46" name="__codelineno-8-46" href="#__codelineno-8-46"></a> <span class="c1">// 合并阶段</span>
|
|
|
<a id="__codelineno-8-47" name="__codelineno-8-47" href="#__codelineno-8-47"></a> <span class="n">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="p">&</span><span class="n">nums</span><span class="p">,</span> <span class="kr">left</span><span class="p">:</span> <span class="kr">left</span><span class="p">,</span> <span class="n">mid</span><span class="p">:</span> <span class="n">mid</span><span class="p">,</span> <span class="kr">right</span><span class="p">:</span> <span class="kr">right</span><span class="p">)</span>
|
|
|
<a id="__codelineno-8-48" name="__codelineno-8-48" href="#__codelineno-8-48"></a><span class="p">}</span>
|
|
|
</code></pre></div>
|
|
|
</div>
|
|
|
<div class="tabbed-block">
|
|
|
<div class="highlight"><span class="filename">merge_sort.zig</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="c1">// 合并左子数组和右子数组</span>
|
|
|
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="c1">// 左子数组区间 [left, mid]</span>
|
|
|
<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="c1">// 右子数组区间 [mid + 1, right]</span>
|
|
|
<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="k">fn</span><span class="w"> </span><span class="n">merge</span><span class="p">(</span><span class="n">nums</span><span class="o">:</span><span class="w"> </span><span class="p">[]</span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="o">!</span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w"> </span><span class="c1">// 初始化辅助数组</span>
|
|
|
<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">mem_arena</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">.</span><span class="n">heap</span><span class="p">.</span><span class="n">ArenaAllocator</span><span class="p">.</span><span class="n">init</span><span class="p">(</span><span class="n">std</span><span class="p">.</span><span class="n">heap</span><span class="p">.</span><span class="n">page_allocator</span><span class="p">);</span>
|
|
|
<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w"> </span><span class="k">defer</span><span class="w"> </span><span class="n">mem_arena</span><span class="p">.</span><span class="n">deinit</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="kr">const</span><span class="w"> </span><span class="n">mem_allocator</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mem_arena</span><span class="p">.</span><span class="n">allocator</span><span class="p">();</span>
|
|
|
<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">mem_allocator</span><span class="p">.</span><span class="n">alloc</span><span class="p">(</span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</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">std</span><span class="p">.</span><span class="n">mem</span><span class="p">.</span><span class="n">copy</span><span class="p">(</span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">tmp</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">..</span><span class="n">right</span><span class="o">+</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="c1">// 左子数组的起始索引和结束索引 </span>
|
|
|
<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">leftStart</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">;</span>
|
|
|
<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">leftEnd</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</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="c1">// 右子数组的起始索引和结束索引 </span>
|
|
|
<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">rightStart</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</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="kr">var</span><span class="w"> </span><span class="n">rightEnd</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">;</span>
|
|
|
<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w"> </span><span class="c1">// i, j 分别指向左子数组、右子数组的首元素</span>
|
|
|
<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftStart</span><span class="p">;</span>
|
|
|
<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rightStart</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="c1">// 通过覆盖原数组 nums 来合并左子数组和右子数组</span>
|
|
|
<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">;</span>
|
|
|
<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">k</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="n">k</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="w"> </span><span class="c1">// 若“左子数组已全部合并完”，则选取右子数组元素，并且 j++</span>
|
|
|
<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a><span class="w"> </span><span class="k">if</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="n">leftEnd</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
|
|
|
<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a><span class="w"> </span><span class="n">j</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-9-27" name="__codelineno-9-27" href="#__codelineno-9-27"></a><span class="w"> </span><span class="c1">// 否则，若“右子数组已全部合并完”或“左子数组元素 <= 右子数组元素”，则选取左子数组元素，并且 i++</span>
|
|
|
<a id="__codelineno-9-28" name="__codelineno-9-28" href="#__codelineno-9-28"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">rightEnd</span><span class="w"> </span><span class="k">or</span><span class="w"> </span><span class="n">tmp</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">tmp</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-9-29" name="__codelineno-9-29" href="#__codelineno-9-29"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
|
|
|
<a id="__codelineno-9-30" name="__codelineno-9-30" href="#__codelineno-9-30"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
|
|
<a id="__codelineno-9-31" name="__codelineno-9-31" href="#__codelineno-9-31"></a><span class="w"> </span><span class="c1">// 否则，若“左右子数组都未全部合并完”且“左子数组元素 > 右子数组元素”，则选取右子数组元素，并且 j++</span>
|
|
|
<a id="__codelineno-9-32" name="__codelineno-9-32" href="#__codelineno-9-32"></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-9-33" name="__codelineno-9-33" href="#__codelineno-9-33"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
|
|
|
<a id="__codelineno-9-34" name="__codelineno-9-34" href="#__codelineno-9-34"></a><span class="w"> </span><span class="n">j</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-9-35" name="__codelineno-9-35" href="#__codelineno-9-35"></a><span class="w"> </span><span class="p">}</span>
|
|
|
<a id="__codelineno-9-36" name="__codelineno-9-36" href="#__codelineno-9-36"></a><span class="w"> </span><span class="p">}</span>
|
|
|
<a id="__codelineno-9-37" name="__codelineno-9-37" href="#__codelineno-9-37"></a><span class="p">}</span>
|
|
|
<a id="__codelineno-9-38" name="__codelineno-9-38" href="#__codelineno-9-38"></a>
|
|
|
<a id="__codelineno-9-39" name="__codelineno-9-39" href="#__codelineno-9-39"></a><span class="c1">// 归并排序</span>
|
|
|
<a id="__codelineno-9-40" name="__codelineno-9-40" href="#__codelineno-9-40"></a><span class="k">fn</span><span class="w"> </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="o">:</span><span class="w"> </span><span class="p">[]</span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="o">!</span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-9-41" name="__codelineno-9-41" href="#__codelineno-9-41"></a><span class="w"> </span><span class="c1">// 终止条件</span>
|
|
|
<a id="__codelineno-9-42" name="__codelineno-9-42" href="#__codelineno-9-42"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span><span class="w"> </span><span class="c1">// 当子数组长度为 1 时终止递归</span>
|
|
|
<a id="__codelineno-9-43" name="__codelineno-9-43" href="#__codelineno-9-43"></a><span class="w"> </span><span class="c1">// 划分阶段</span>
|
|
|
<a id="__codelineno-9-44" name="__codelineno-9-44" href="#__codelineno-9-44"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 计算中点</span>
|
|
|
<a id="__codelineno-9-45" name="__codelineno-9-45" href="#__codelineno-9-45"></a><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">);</span><span class="w"> </span><span class="c1">// 递归左子数组</span>
|
|
|
<a id="__codelineno-9-46" name="__codelineno-9-46" href="#__codelineno-9-46"></a><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 递归右子数组</span>
|
|
|
<a id="__codelineno-9-47" name="__codelineno-9-47" href="#__codelineno-9-47"></a><span class="w"> </span><span class="c1">// 合并阶段</span>
|
|
|
<a id="__codelineno-9-48" name="__codelineno-9-48" href="#__codelineno-9-48"></a><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
|
|
|
<a id="__codelineno-9-49" name="__codelineno-9-49" href="#__codelineno-9-49"></a><span class="p">}</span>
|
|
|
</code></pre></div>
|
|
|
</div>
|
|
|
</div>
|
|
|
</div>
|
|
|
<p>合并方法 <code>merge()</code> 代码中的难点包括：</p>
|
|
|
<ul>
|
|
|
<li><strong>在阅读代码时，需要特别注意各个变量的含义</strong>。<code>nums</code> 的待合并区间为 <code>[left, right]</code> ，但由于 <code>tmp</code> 仅复制了 <code>nums</code> 该区间的元素，因此 <code>tmp</code> 对应区间为 <code>[0, right - left]</code> 。</li>
|
|
|
<li>在比较 <code>tmp[i]</code> 和 <code>tmp[j]</code> 的大小时，<strong>还需考虑子数组遍历完成后的索引越界问题</strong>，即 <code>i > leftEnd</code> 和 <code>j > rightEnd</code> 的情况。索引越界的优先级是最高的，如果左子数组已经被合并完了，那么不需要继续比较，直接合并右子数组元素即可。</li>
|
|
|
</ul>
|
|
|
<h2 id="1152">11.5.2. 算法特性<a class="headerlink" href="#1152" title="Permanent link">¶</a></h2>
|
|
|
<p><strong>时间复杂度 <span class="arithmatex">\(O(n \log n)\)</span></strong> ：划分产生高度为 <span class="arithmatex">\(\log n\)</span> 的递归树，每层合并的总操作数量为 <span class="arithmatex">\(n\)</span> ，因此总体时间复杂度为 <span class="arithmatex">\(O(n \log n)\)</span> 。</p>
|
|
|
<p><strong>空间复杂度 <span class="arithmatex">\(O(n)\)</span></strong> ：递归深度为 <span class="arithmatex">\(\log n\)</span> ，使用 <span class="arithmatex">\(O(\log n)\)</span> 大小的栈帧空间；合并操作需要借助辅助数组实现，使用 <span class="arithmatex">\(O(n)\)</span> 大小的额外空间；因此是“非原地排序”。</p>
|
|
|
<p>在合并过程中，相等元素的次序保持不变，因此归并排序是“稳定排序”。</p>
|
|
|
<h2 id="1153">11.5.3. 链表排序 *<a class="headerlink" href="#1153" title="Permanent link">¶</a></h2>
|
|
|
<p>归并排序在排序链表时具有显著优势，空间复杂度可以优化至 <span class="arithmatex">\(O(1)\)</span> ，原因如下：</p>
|
|
|
<ul>
|
|
|
<li>由于链表仅需改变指针就可实现节点的增删操作，因此合并阶段（将两个短有序链表合并为一个长有序链表）无需创建辅助链表。</li>
|
|
|
<li>通过使用“迭代划分”替代“递归划分”，可省去递归使用的栈帧空间；</li>
|
|
|
</ul>
|
|
|
<p>具体实现细节比较复杂，有兴趣的同学可以查阅相关资料进行学习。</p>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<h2 id="__comments">评论</h2>
|
|
|
<!-- 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="bottom"
|
|
|
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" : "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" : "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>
|
|
|
|
|
|
<footer class="md-footer">
|
|
|
|
|
|
|
|
|
|
|
|
<nav class="md-footer__inner md-grid" aria-label="页脚" >
|
|
|
|
|
|
|
|
|
<a href="../quick_sort/" class="md-footer__link md-footer__link--prev" aria-label="上一页: 11.4. &nbsp; 快速排序" 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">
|
|
|
11.4. 快速排序
|
|
|
</div>
|
|
|
</div>
|
|
|
</a>
|
|
|
|
|
|
|
|
|
|
|
|
<a href="../bucket_sort/" class="md-footer__link md-footer__link--next" aria-label="下一页: 11.6. &nbsp; 桶排序" rel="next">
|
|
|
<div class="md-footer__title">
|
|
|
<span class="md-footer__direction">
|
|
|
下一页
|
|
|
</span>
|
|
|
<div class="md-ellipsis">
|
|
|
11.6. 桶排序
|
|
|
</div>
|
|
|
</div>
|
|
|
<div class="md-footer__button md-icon">
|
|
|
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M4 11v2h12l-5.5 5.5 1.42 1.42L19.84 12l-7.92-7.92L10.5 5.5 16 11H4Z"/></svg>
|
|
|
</div>
|
|
|
</a>
|
|
|
|
|
|
</nav>
|
|
|
|
|
|
|
|
|
<div class="md-footer-meta md-typeset">
|
|
|
<div class="md-footer-meta__inner md-grid">
|
|
|
<div class="md-copyright">
|
|
|
|
|
|
<div class="md-copyright__highlight">
|
|
|
Copyright © 2023 Krahets
|
|
|
</div>
|
|
|
|
|
|
|
|
|
</div>
|
|
|
|
|
|
<div class="md-social">
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<a href="https://github.com/krahets" target="_blank" rel="noopener" title="github.com" class="md-social__link">
|
|
|
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 496 512"><!--! Font Awesome Free 6.4.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 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 6.4.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 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 6.4.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 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.sections", "navigation.top", "navigation.footer", "navigation.tracking", "search.highlight", "search.share", "search.suggest", "toc.follow"], "search": "../../assets/javascripts/workers/search.208ed371.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.51198bba.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>
|
|
|
|
|
|
|
|
|
</body>
|
|
|
</html> |
