xinyin025/hello-algo
1
0
Fork 0
mirror of https://github.com/krahets/hello-algo.git synced 2026-07-21 19:06:11 +00:00
Code Issues Packages Projects Releases Wiki Activity
Files
858a7888ea5daf2183ffd41d2987f467eaadc456
hello-algo/chapter_array_and_linkedlist/exercises/index.html
T
krahets 858a7888ea deploy
2026-07-19 07:20:12 +08:00

5317 lines
100 KiB
HTML
Raw Blame History

This file contains ambiguous Unicode characters
This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.
<!doctype html>
<html lang="zh" class="no-js">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width,initial-scale=1">
<meta name="description" content="动画图解、一键运行的数据结构与算法教程">
<meta name="author" content="krahets">
<link rel="canonical" href="https://www.hello-algo.com/chapter_array_and_linkedlist/exercises/">
<link rel="prev" href="../summary/">
<link rel="next" href="../../chapter_stack_and_queue/">
<link rel="alternate" href="/chapter_array_and_linkedlist/exercises/" hreflang="zh">
<link rel="alternate" href="/zh-hant/chapter_array_and_linkedlist/exercises/" hreflang="zh-Hant">
<link rel="alternate" href="/en/chapter_array_and_linkedlist/exercises/" hreflang="en">
<link rel="alternate" href="/ja/chapter_array_and_linkedlist/exercises/" hreflang="ja">
<link rel="alternate" href="/ru/chapter_array_and_linkedlist/exercises/" hreflang="ru">
<link rel="icon" href="../../assets/images/favicon.png">
<meta name="generator" content="zensical-0.0.29">
<title>4.6 练习 - Hello 算法</title>
<link rel="stylesheet" href="../../assets/stylesheets/modern/main.6f2fbb28.min.css">
<link rel="stylesheet" href="../../assets/stylesheets/modern/palette.dfe2e883.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,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
<style>:root{--md-text-font:"Noto Sans SC";--md-code-font:"JetBrains Mono"}</style>
<link rel="stylesheet" href="../../stylesheets/extra.css">
<link rel="stylesheet" href="../../stylesheets/animation_player.css">
<script>__md_scope=new URL("../..",location),__md_hash=e=>[...e].reduce(((e,t)=>(e<<5)-e+t.charCodeAt(0)),0),__md_get=(e,t=localStorage,a=__md_scope)=>JSON.parse(t.getItem(("__palette"===e?"/":a.pathname)+"."+e)),__md_set=(e,t,a=localStorage,_=__md_scope)=>{try{a.setItem(("__palette"===e?"/":_.pathname)+"."+e,JSON.stringify(t))}catch(e){}},document.documentElement.setAttribute("data-platform",navigator.platform)</script>
</head>
<body dir="ltr" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="teal">
<input class="md-toggle" data-md-toggle="drawer" type="checkbox" id="__drawer" autocomplete="off">
<input class="md-toggle" data-md-toggle="search" type="checkbox" id="__search" autocomplete="off">
<label class="md-overlay" for="__drawer" aria-label="导航栏"></label>
<div data-md-component="skip">
<a href="#46" class="md-skip">
跳转至
</a>
</div>
<div data-md-component="announce">
<aside class="md-banner">
<div class="md-banner__inner md-grid md-typeset">
<div class="banner-svg">
<svg xmlns="http://www.w3.org/2000/svg"
viewBox="0 0 512 512"><!--!Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free Copyright 2024 Fonticons, Inc.-->
<path
d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
</svg>
<span>纸质书已发行，详情请见<a href="/chapter_paperbook/">这里</a></span>
</div>
</div>
</aside>
</div>
<header class="md-header md-header--shadow" data-md-component="header">
<nav class="md-header__inner md-grid" aria-label="页眉">
<a href="../.." title="Hello 算法" class="md-header__button md-logo" aria-label="Hello 算法" data-md-component="logo">
<img src="../../assets/images/logo.svg" alt="Hello 算法">
</a>
<label class="md-header__button md-icon" for="__drawer" aria-label="导航栏">
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-menu" viewBox="0 0 24 24"><path d="M4 5h16M4 12h16M4 19h16"/></svg>
</label>
<div class="md-header__title" data-md-component="header-title">
<div class="md-header__ellipsis">
<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">
4.6 &nbsp; 练习
</span>
</div>
</div>
</div>
<form class="md-header__option" data-md-component="palette">
<input class="md-option" data-md-color-media="none" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="teal" aria-label="深色模式" type="radio" name="__palette" id="__palette_0">
<label class="md-header__button md-icon" title="深色模式" for="__palette_1" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07zm-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13zm-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87zM19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35zm4.33-2.7 1.15-2.77 2.2 2.54zm1.15-4.96-1.14-2.78 3.34.24zM9.63 18.93l2.77 1.15-2.53 2.19z"/></svg>
</label>
<input class="md-option" data-md-color-media="none" data-md-color-scheme="slate" data-md-color-primary="black" data-md-color-accent="teal" aria-label="浅色模式" type="radio" name="__palette" id="__palette_1">
<label class="md-header__button md-icon" title="浅色模式" for="__palette_0" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07zm-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13zm-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87zM19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35zm4.33-2.7 1.15-2.77 2.2 2.54zm1.15-4.96-1.14-2.78 3.34.24zM9.63 18.93l2.77 1.15-2.53 2.19z"/></svg>
</label>
</form>
<script>var palette=__md_get("__palette");if(palette&&palette.color){if("(prefers-color-scheme)"===palette.color.media){var media=matchMedia("(prefers-color-scheme: light)"),input=document.querySelector(media.matches?"[data-md-color-media='(prefers-color-scheme: light)']":"[data-md-color-media='(prefers-color-scheme: dark)']");palette.color.media=input.getAttribute("data-md-color-media"),palette.color.scheme=input.getAttribute("data-md-color-scheme"),palette.color.primary=input.getAttribute("data-md-color-primary"),palette.color.accent=input.getAttribute("data-md-color-accent")}for(var[key,value]of Object.entries(palette.color))document.body.setAttribute("data-md-color-"+key,value)}</script>
<div class="md-header__option">
<div class="md-select">
<button class="md-header__button md-icon" aria-label="选择当前语言">
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-languages" viewBox="0 0 24 24"><path d="m5 8 6 6M4 14l6-6 2-3M2 5h12M7 2h1M22 22l-5-10-5 10M14 18h6"/></svg>
</button>
<div class="md-select__inner">
<ul class="md-select__list">
<li class="md-select__item">
<a href="/chapter_array_and_linkedlist/exercises/" hreflang="zh" class="md-select__link">
简体中文
</a>
</li>
<li class="md-select__item">
<a href="/zh-hant/chapter_array_and_linkedlist/exercises/" hreflang="zh-Hant" class="md-select__link">
繁體中文
</a>
</li>
<li class="md-select__item">
<a href="/en/chapter_array_and_linkedlist/exercises/" hreflang="en" class="md-select__link">
English
</a>
</li>
<li class="md-select__item">
<a href="/ja/chapter_array_and_linkedlist/exercises/" hreflang="ja" class="md-select__link">
日本語
</a>
</li>
<li class="md-select__item">
<a href="/ru/chapter_array_and_linkedlist/exercises/" hreflang="ru" class="md-select__link">
Русский
</a>
</li>
</ul>
</div>
</div>
</div>
<label class="md-header__button md-icon" for="__search" aria-label="查找">
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-search" viewBox="0 0 24 24"><path d="m21 21-4.34-4.34"/><circle cx="11" cy="11" r="8"/></svg>
</label>
<div class="md-search" data-md-component="search" role="dialog" aria-label="查找">
<button type="button" class="md-search__button">
查找
</button>
</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 0 512 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path fill="currentColor" d="M173.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6m-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3m44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9M252.8 8C114.1 8 8 113.3 8 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C436.2 457.8 504 362.9 504 252 504 113.3 391.5 8 252.8 8M105.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1m-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7m32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1m-11.4-14.7c-1.6 1-1.6 3.6 0 5.9s4.3 3.3 5.6 2.3c1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2"/></svg>
</div>
<div class="md-source__repository">
krahets/hello-algo
</div>
</a>
</div>
</nav>
</header>
<div class="md-container" data-md-component="container">
<main class="md-main" data-md-component="main">
<div class="md-main__inner md-grid">
<div class="md-sidebar md-sidebar--primary" data-md-component="sidebar" data-md-type="navigation" >
<div class="md-sidebar__scrollwrap">
<div class="md-sidebar__inner">
<nav class="md-nav md-nav--primary" aria-label="导航栏" data-md-level="0">
<label class="md-nav__title" for="__drawer">
<a href="../.." title="Hello 算法" class="md-nav__button md-logo" aria-label="Hello 算法" data-md-component="logo">
<img src="../../assets/images/logo.svg" alt="Hello 算法">
</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 0 512 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path fill="currentColor" d="M173.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6m-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3m44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9M252.8 8C114.1 8 8 113.3 8 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C436.2 457.8 504 362.9 504 252 504 113.3 391.5 8 252.8 8M105.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1m-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7m32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1m-11.4-14.7c-1.6 1-1.6 3.6 0 5.9s4.3 3.3 5.6 2.3c1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2"/></svg>
</div>
<div class="md-source__repository">
krahets/hello-algo
</div>
</a>
</div>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_1" >
<div class="md-nav__link md-nav__container">
<a href="../../chapter_hello_algo/" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m13.13 22.19-1.63-3.83c1.57-.58 3.04-1.36 4.4-2.27zM5.64 12.5l-3.83-1.63 6.1-2.77C7 9.46 6.22 10.93 5.64 12.5M19.22 4c.28 0 .53 0 .74.05.17 1.39-.02 4.25-3.3 7.53-1.7 1.71-3.73 3.02-6.01 3.89l-2.15-2.1c.92-2.31 2.23-4.34 3.92-6.03C15.18 4.58 17.64 4 19.22 4m0-2c-1.98 0-4.98.69-8.22 3.93-2.19 2.19-3.5 4.6-4.35 6.71-.28.75-.09 1.57.46 2.13l2.13 2.12c.38.38.89.61 1.42.61.23 0 .47-.06.7-.15A19.1 19.1 0 0 0 18.07 13c5.66-5.66 3.54-10.61 3.54-10.61S20.7 2 19.22 2m-4.68 7.46c-.78-.78-.78-2.05 0-2.83s2.05-.78 2.83 0c.77.78.78 2.05 0 2.83s-2.05.78-2.83 0m-5.66 7.07-1.41-1.41zM6.24 22l3.64-3.64c-.34-.09-.67-.24-.97-.45L4.83 22zM2 22h1.41l4.77-4.76-1.42-1.41L2 20.59zm0-2.83 4.09-4.08c-.21-.3-.36-.62-.45-.97L2 17.76z"/></svg>
<span class="md-ellipsis">
序
</span>
</a>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_1_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_1">
<span class="md-nav__icon md-icon"></span>
序
</label>
<ul class="md-nav__list" data-md-scrollfix>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_2" >
<div class="md-nav__link md-nav__container">
<a href="../../chapter_preface/" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13zm18 0h-8V6h8zm-7-9.5h6V11h-6zm0 2.5h6v1.5h-6zm0 2.5h6V16h-6z"/></svg>
<span class="md-ellipsis">
第 0 章 &nbsp; 前言
</span>
</a>
<label class="md-nav__link " for="__nav_2" id="__nav_2_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_2">
<span class="md-nav__icon md-icon"></span>
第 0 章 &nbsp; 前言
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter_preface/about_the_book/" class="md-nav__link">
<span class="md-ellipsis">
0.1 &nbsp; 关于本书
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_preface/suggestions/" class="md-nav__link">
<span class="md-ellipsis">
0.2 &nbsp; 如何使用本书
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_preface/summary/" class="md-nav__link">
<span class="md-ellipsis">
0.3 &nbsp; 小结
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
<div class="md-nav__link md-nav__container">
<a href="../../chapter_introduction/" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14zM6.2 7.7h5v1.5h-5zm6.8 8.1h5v1.5h-5zm0-2.6h5v1.5h-5zM8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2zm6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9z"/></svg>
<span class="md-ellipsis">
第 1 章 &nbsp; 初识算法
</span>
</a>
<label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_3">
<span class="md-nav__icon md-icon"></span>
第 1 章 &nbsp; 初识算法
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
<span class="md-ellipsis">
1.1 &nbsp; 算法无处不在
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
<span class="md-ellipsis">
1.2 &nbsp; 算法是什么
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_introduction/summary/" class="md-nav__link">
<span class="md-ellipsis">
1.3 &nbsp; 小结
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
<div class="md-nav__link md-nav__container">
<a href="../../chapter_computational_complexity/" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4zm10 14.5-4-4-4 4V20h8zm-4-5 4-4V4H8v3.5zM10 6h4v.75l-2 2-2-2z"/></svg>
<span class="md-ellipsis">
第 2 章 &nbsp; 复杂度分析
</span>
</a>
<label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_4">
<span class="md-nav__icon md-icon"></span>
第 2 章 &nbsp; 复杂度分析
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
<span class="md-ellipsis">
2.1 &nbsp; 算法效率评估
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
<span class="md-ellipsis">
2.2 &nbsp; 迭代与递归
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
<span class="md-ellipsis">
2.3 &nbsp; 时间复杂度
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
<span class="md-ellipsis">
2.4 &nbsp; 空间复杂度
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
<span class="md-ellipsis">
2.5 &nbsp; 小结
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_computational_complexity/exercises/" class="md-nav__link">
<span class="md-ellipsis">
2.6 &nbsp; 练习
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
<div class="md-nav__link md-nav__container">
<a href="../../chapter_data_structure/" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8zm-2 2H5v4h4zM12 2l5.5 9h-11zm0 3.86L10.08 9h3.84zM17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5"/></svg>
<span class="md-ellipsis">
第 3 章 &nbsp; 数据结构
</span>
</a>
<label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_5">
<span class="md-nav__icon md-icon"></span>
第 3 章 &nbsp; 数据结构
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
<span class="md-ellipsis">
3.1 &nbsp; 数据结构分类
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
<span class="md-ellipsis">
3.2 &nbsp; 基本数据类型
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
<span class="md-ellipsis">
3.3 &nbsp; 数字编码 *
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
<span class="md-ellipsis">
3.4 &nbsp; 字符编码 *
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_data_structure/summary/" class="md-nav__link">
<span class="md-ellipsis">
3.5 &nbsp; 小结
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_data_structure/exercises/" class="md-nav__link">
<span class="md-ellipsis">
3.6 &nbsp; 练习
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--active md-nav__item--nested">
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" checked>
<div class="md-nav__link md-nav__container">
<a href="../" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5zm4 2v2H5V7zm-2 6v-2h2v2zm0 2h2v2H5zm13 2H9v-2h9zm0-4H9v-2h9zm0-4H9V7h9z"/></svg>
<span class="md-ellipsis">
第 4 章 &nbsp; 数组与链表
</span>
</a>
<label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="true">
<label class="md-nav__title" for="__nav_6">
<span class="md-nav__icon md-icon"></span>
第 4 章 &nbsp; 数组与链表
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../array/" class="md-nav__link">
<span class="md-ellipsis">
4.1 &nbsp; 数组
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../linked_list/" class="md-nav__link">
<span class="md-ellipsis">
4.2 &nbsp; 链表
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../list/" class="md-nav__link">
<span class="md-ellipsis">
4.3 &nbsp; 列表
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../ram_and_cache/" class="md-nav__link">
<span class="md-ellipsis">
4.4 &nbsp; 内存与缓存 *
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../summary/" class="md-nav__link">
<span class="md-ellipsis">
4.5 &nbsp; 小结
</span>
</a>
</li>
<li class="md-nav__item md-nav__item--active">
<input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
<label class="md-nav__link md-nav__link--active" for="__toc">
<span class="md-ellipsis">
4.6 &nbsp; 练习
</span>
<span class="md-nav__icon md-icon"></span>
</label>
<a href="././" class="md-nav__link md-nav__link--active">
<span class="md-ellipsis">
4.6 &nbsp; 练习
</span>
</a>
<nav class="md-nav md-nav--secondary" aria-label="目录">
<label class="md-nav__title" for="__toc">
<span class="md-nav__icon md-icon"></span>
目录
</label>
<ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
<li class="md-nav__item">
<a href="#461" class="md-nav__link">
<span class="md-ellipsis">
4.6.1 &nbsp; 知识巩固
</span>
</a>
<nav class="md-nav" aria-label="4.6.1 知识巩固">
<ul class="md-nav__list">
<li class="md-nav__item">
<a href="#1" class="md-nav__link">
<span class="md-ellipsis">
1. &nbsp; 数组和链表怎样找到元素
</span>
</a>
</li>
<li class="md-nav__item">
<a href="#2" class="md-nav__link">
<span class="md-ellipsis">
2. &nbsp; 数组和链表怎样插入元素
</span>
</a>
</li>
<li class="md-nav__item">
<a href="#3" class="md-nav__link">
<span class="md-ellipsis">
3. &nbsp; 列表容量是怎样增长的
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item">
<a href="#462" class="md-nav__link">
<span class="md-ellipsis">
4.6.2 &nbsp; 编程练习
</span>
</a>
<nav class="md-nav" aria-label="4.6.2 编程练习">
<ul class="md-nav__list">
<li class="md-nav__item">
<a href="#1_1" class="md-nav__link">
<span class="md-ellipsis">
1. &nbsp; 数组表示的大整数加一
</span>
</a>
</li>
<li class="md-nav__item">
<a href="#2_1" class="md-nav__link">
<span class="md-ellipsis">
2. &nbsp; 反转单向链表
</span>
</a>
</li>
</ul>
</nav>
</li>
</ul>
</nav>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
<div class="md-nav__link md-nav__container">
<a href="../../chapter_stack_and_queue/" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38zM6.77 14.32l.37-1.76 8.79 1.85-.37 1.76zm1.16-4.21.76-1.61 8.14 3.78-.76 1.62zm2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37zm4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21zM6.59 18.41v-1.8h8.98v1.8z"/></svg>
<span class="md-ellipsis">
第 5 章 &nbsp; 栈与队列
</span>
</a>
<label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_7">
<span class="md-nav__icon md-icon"></span>
第 5 章 &nbsp; 栈与队列
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
<span class="md-ellipsis">
5.1 &nbsp; 栈
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
<span class="md-ellipsis">
5.2 &nbsp; 队列
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
<span class="md-ellipsis">
5.3 &nbsp; 双向队列
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
<span class="md-ellipsis">
5.4 &nbsp; 小结
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_stack_and_queue/exercises/" class="md-nav__link">
<span class="md-ellipsis">
5.5 &nbsp; 练习
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
<div class="md-nav__link md-nav__container">
<a href="../../chapter_hashing/" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21zm-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54zM19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2"/></svg>
<span class="md-ellipsis">
第 6 章 &nbsp; 哈希表
</span>
</a>
<label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_8">
<span class="md-nav__icon md-icon"></span>
第 6 章 &nbsp; 哈希表
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter_hashing/hash_map/" class="md-nav__link">
<span class="md-ellipsis">
6.1 &nbsp; 哈希表
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
<span class="md-ellipsis">
6.2 &nbsp; 哈希冲突
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
<span class="md-ellipsis">
6.3 &nbsp; 哈希算法
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_hashing/summary/" class="md-nav__link">
<span class="md-ellipsis">
6.4 &nbsp; 小结
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_hashing/exercises/" class="md-nav__link">
<span class="md-ellipsis">
6.5 &nbsp; 练习
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
<div class="md-nav__link md-nav__container">
<a href="../../chapter_tree/" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1"/></svg>
<span class="md-ellipsis">
第 7 章 &nbsp; 树
</span>
</a>
<label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_9">
<span class="md-nav__icon md-icon"></span>
第 7 章 &nbsp; 树
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter_tree/binary_tree/" class="md-nav__link">
<span class="md-ellipsis">
7.1 &nbsp; 二叉树
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
<span class="md-ellipsis">
7.2 &nbsp; 二叉树遍历
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
<span class="md-ellipsis">
7.3 &nbsp; 二叉树数组表示
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
<span class="md-ellipsis">
7.4 &nbsp; 二叉搜索树
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_tree/avl_tree/" class="md-nav__link">
<span class="md-ellipsis">
7.5 &nbsp; AVL 树 *
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_tree/summary/" class="md-nav__link">
<span class="md-ellipsis">
7.6 &nbsp; 小结
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_tree/exercises/" class="md-nav__link">
<span class="md-ellipsis">
7.7 &nbsp; 练习
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
<div class="md-nav__link md-nav__container">
<a href="../../chapter_heap/" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1"/></svg>
<span class="md-ellipsis">
第 8 章 &nbsp; 堆
</span>
</a>
<label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_10">
<span class="md-nav__icon md-icon"></span>
第 8 章 &nbsp; 堆
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter_heap/heap/" class="md-nav__link">
<span class="md-ellipsis">
8.1 &nbsp; 堆
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_heap/build_heap/" class="md-nav__link">
<span class="md-ellipsis">
8.2 &nbsp; 建堆操作
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_heap/top_k/" class="md-nav__link">
<span class="md-ellipsis">
8.3 &nbsp; Top-k 问题
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_heap/summary/" class="md-nav__link">
<span class="md-ellipsis">
8.4 &nbsp; 小结
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_heap/exercises/" class="md-nav__link">
<span class="md-ellipsis">
8.5 &nbsp; 练习
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
<div class="md-nav__link md-nav__container">
<a href="../../chapter_graph/" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59zM6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43s.83.16 1.12.43l4.28-2.53zM12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68s1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25zm2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24z"/></svg>
<span class="md-ellipsis">
第 9 章 &nbsp; 图
</span>
</a>
<label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_11">
<span class="md-nav__icon md-icon"></span>
第 9 章 &nbsp; 图
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter_graph/graph/" class="md-nav__link">
<span class="md-ellipsis">
9.1 &nbsp; 图
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_graph/graph_operations/" class="md-nav__link">
<span class="md-ellipsis">
9.2 &nbsp; 图基础操作
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
<span class="md-ellipsis">
9.3 &nbsp; 图的遍历
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_graph/summary/" class="md-nav__link">
<span class="md-ellipsis">
9.4 &nbsp; 小结
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_graph/exercises/" class="md-nav__link">
<span class="md-ellipsis">
9.5 &nbsp; 练习
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
<div class="md-nav__link md-nav__container">
<a href="../../chapter_searching/" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4zM3 16v-2h6v2zm0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1z"/></svg>
<span class="md-ellipsis">
第 10 章 &nbsp; 搜索
</span>
</a>
<label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_12">
<span class="md-nav__icon md-icon"></span>
第 10 章 &nbsp; 搜索
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter_searching/binary_search/" class="md-nav__link">
<span class="md-ellipsis">
10.1 &nbsp; 二分查找
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
<span class="md-ellipsis">
10.2 &nbsp; 二分查找插入点
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
<span class="md-ellipsis">
10.3 &nbsp; 二分查找边界
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
<span class="md-ellipsis">
10.4 &nbsp; 哈希优化策略
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
<span class="md-ellipsis">
10.5 &nbsp; 重识搜索算法
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_searching/summary/" class="md-nav__link">
<span class="md-ellipsis">
10.6 &nbsp; 小结
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_searching/exercises/" class="md-nav__link">
<span class="md-ellipsis">
10.7 &nbsp; 练习
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
<div class="md-nav__link md-nav__container">
<a href="../../chapter_sorting/" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2z"/></svg>
<span class="md-ellipsis">
第 11 章 &nbsp; 排序
</span>
</a>
<label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_13">
<span class="md-nav__icon md-icon"></span>
第 11 章 &nbsp; 排序
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
<span class="md-ellipsis">
11.1 &nbsp; 排序算法
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
<span class="md-ellipsis">
11.2 &nbsp; 选择排序
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
<span class="md-ellipsis">
11.3 &nbsp; 冒泡排序
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
<span class="md-ellipsis">
11.4 &nbsp; 插入排序
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
<span class="md-ellipsis">
11.5 &nbsp; 快速排序
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
<span class="md-ellipsis">
11.6 &nbsp; 归并排序
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
<span class="md-ellipsis">
11.7 &nbsp; 堆排序
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
<span class="md-ellipsis">
11.8 &nbsp; 桶排序
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
<span class="md-ellipsis">
11.9 &nbsp; 计数排序
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
<span class="md-ellipsis">
11.10 &nbsp; 基数排序
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_sorting/summary/" class="md-nav__link">
<span class="md-ellipsis">
11.11 &nbsp; 小结
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_sorting/exercises/" class="md-nav__link">
<span class="md-ellipsis">
11.12 &nbsp; 练习
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
<div class="md-nav__link md-nav__container">
<a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7zM2 9v6h5V9zm10 0v2H9v2h3v2l3-3zm5 2v2h5v-2zm0 4v2h5v-2z"/></svg>
<span class="md-ellipsis">
第 12 章 &nbsp; 分治
</span>
</a>
<label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_14">
<span class="md-nav__icon md-icon"></span>
第 12 章 &nbsp; 分治
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
<span class="md-ellipsis">
12.1 &nbsp; 分治算法
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
<span class="md-ellipsis">
12.2 &nbsp; 分治搜索策略
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
<span class="md-ellipsis">
12.3 &nbsp; 构建树问题
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
<span class="md-ellipsis">
12.4 &nbsp; 汉诺塔问题
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
<span class="md-ellipsis">
12.5 &nbsp; 小结
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_divide_and_conquer/exercises/" class="md-nav__link">
<span class="md-ellipsis">
12.6 &nbsp; 练习
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
<div class="md-nav__link md-nav__container">
<a href="../../chapter_backtracking/" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2zm-4-6H5v-2h2z"/></svg>
<span class="md-ellipsis">
第 13 章 &nbsp; 回溯
</span>
</a>
<label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_15">
<span class="md-nav__icon md-icon"></span>
第 13 章 &nbsp; 回溯
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
<span class="md-ellipsis">
13.1 &nbsp; 回溯算法
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
<span class="md-ellipsis">
13.2 &nbsp; 全排列问题
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
<span class="md-ellipsis">
13.3 &nbsp; 子集和问题
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
<span class="md-ellipsis">
13.4 &nbsp; N 皇后问题
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_backtracking/summary/" class="md-nav__link">
<span class="md-ellipsis">
13.5 &nbsp; 小结
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_backtracking/exercises/" class="md-nav__link">
<span class="md-ellipsis">
13.6 &nbsp; 练习
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
<div class="md-nav__link md-nav__container">
<a href="../../chapter_dynamic_programming/" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3zm0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4zm0 2v4h4v-4zm4 10v-4H4v4zm6-12V4h-4v4zm6-4h-4v4h4z"/></svg>
<span class="md-ellipsis">
第 14 章 &nbsp; 动态规划
</span>
</a>
<label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_16">
<span class="md-nav__icon md-icon"></span>
第 14 章 &nbsp; 动态规划
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
<span class="md-ellipsis">
14.1 &nbsp; 初探动态规划
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
<span class="md-ellipsis">
14.2 &nbsp; DP 问题特性
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
<span class="md-ellipsis">
14.3 &nbsp; DP 解题思路
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
<span class="md-ellipsis">
14.4 &nbsp; 0-1 背包问题
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
<span class="md-ellipsis">
14.5 &nbsp; 完全背包问题
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
<span class="md-ellipsis">
14.6 &nbsp; 编辑距离问题
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
<span class="md-ellipsis">
14.7 &nbsp; 小结
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_dynamic_programming/exercises/" class="md-nav__link">
<span class="md-ellipsis">
14.8 &nbsp; 练习
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
<div class="md-nav__link md-nav__container">
<a href="../../chapter_greedy/" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16z"/></svg>
<span class="md-ellipsis">
第 15 章 &nbsp; 贪心
</span>
</a>
<label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_17">
<span class="md-nav__icon md-icon"></span>
第 15 章 &nbsp; 贪心
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
<span class="md-ellipsis">
15.1 &nbsp; 贪心算法
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
<span class="md-ellipsis">
15.2 &nbsp; 分数背包问题
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
<span class="md-ellipsis">
15.3 &nbsp; 最大容量问题
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
<span class="md-ellipsis">
15.4 &nbsp; 最大切分乘积问题
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_greedy/summary/" class="md-nav__link">
<span class="md-ellipsis">
15.5 &nbsp; 小结
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_greedy/exercises/" class="md-nav__link">
<span class="md-ellipsis">
15.6 &nbsp; 练习
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
<div class="md-nav__link md-nav__container">
<a href="../../chapter_appendix/" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2zm1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4"/></svg>
<span class="md-ellipsis">
第 16 章 &nbsp; 附录
</span>
</a>
<label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_18">
<span class="md-nav__icon md-icon"></span>
第 16 章 &nbsp; 附录
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter_appendix/installation/" class="md-nav__link">
<span class="md-ellipsis">
16.1 &nbsp; 编程环境安装
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_appendix/contribution/" class="md-nav__link">
<span class="md-ellipsis">
16.2 &nbsp; 一起参与创作
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_appendix/terminology/" class="md-nav__link">
<span class="md-ellipsis">
16.3 &nbsp; 术语表
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
<div class="md-nav__link md-nav__container">
<a href="../../chapter_reference/" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3zm3 2 4 13 3-1-4-13zM5 5v13h3V5zM3 19v2h18v-2z"/></svg>
<span class="md-ellipsis">
参考文献
</span>
</a>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_19">
<span class="md-nav__icon md-icon"></span>
参考文献
</label>
<ul class="md-nav__list" data-md-scrollfix>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_20" >
<div class="md-nav__link md-nav__container">
<a href="../../chapter_paperbook/" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19 2-5 4.5v11l5-4.5zM6.5 5C4.55 5 2.45 5.4 1 6.5v14.66c0 .25.25.5.5.5.1 0 .15-.07.25-.07 1.35-.65 3.3-1.09 4.75-1.09 1.95 0 4.05.4 5.5 1.5 1.35-.85 3.8-1.5 5.5-1.5 1.65 0 3.35.31 4.75 1.06.1.05.15.03.25.03.25 0 .5-.25.5-.5V6.5c-.6-.45-1.25-.75-2-1V19c-1.1-.35-2.3-.5-3.5-.5-1.7 0-4.15.65-5.5 1.5V6.5C10.55 5.4 8.45 5 6.5 5"/></svg>
<span class="md-ellipsis">
纸质书
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_20_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_20">
<span class="md-nav__icon md-icon"></span>
纸质书
</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="#461" class="md-nav__link">
<span class="md-ellipsis">
4.6.1 &nbsp; 知识巩固
</span>
</a>
<nav class="md-nav" aria-label="4.6.1 知识巩固">
<ul class="md-nav__list">
<li class="md-nav__item">
<a href="#1" class="md-nav__link">
<span class="md-ellipsis">
1. &nbsp; 数组和链表怎样找到元素
</span>
</a>
</li>
<li class="md-nav__item">
<a href="#2" class="md-nav__link">
<span class="md-ellipsis">
2. &nbsp; 数组和链表怎样插入元素
</span>
</a>
</li>
<li class="md-nav__item">
<a href="#3" class="md-nav__link">
<span class="md-ellipsis">
3. &nbsp; 列表容量是怎样增长的
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item">
<a href="#462" class="md-nav__link">
<span class="md-ellipsis">
4.6.2 &nbsp; 编程练习
</span>
</a>
<nav class="md-nav" aria-label="4.6.2 编程练习">
<ul class="md-nav__list">
<li class="md-nav__item">
<a href="#1_1" class="md-nav__link">
<span class="md-ellipsis">
1. &nbsp; 数组表示的大整数加一
</span>
</a>
</li>
<li class="md-nav__item">
<a href="#2_1" class="md-nav__link">
<span class="md-ellipsis">
2. &nbsp; 反转单向链表
</span>
</a>
</li>
</ul>
</nav>
</li>
</ul>
</nav>
</div>
</div>
</div>
<div class="md-content" data-md-component="content">
<article class="md-content__inner md-typeset">
<!-- Tags -->
<!-- Actions -->
<!-- Actions -->
<!-- Edit button -->
<a
href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_array_and_linkedlist/exercises.md"
title="编辑此页"
class="md-content__button md-icon"
>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path fill="currentColor" d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0M88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24z"/></svg>
</a>
<!-- View button -->
<!-- Page content -->
<h1 id="46">4.6 &nbsp; 练习<a class="headerlink" href="#46" title="Permanent link">&para;</a></h1>
<h2 id="461">4.6.1 &nbsp; 知识巩固<a class="headerlink" href="#461" title="Permanent link">&para;</a></h2>
<h3 id="1">1. &nbsp; 数组和链表怎样找到元素<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
<p>数组和单向链表中都按顺序保存了 <code>[A, B, C, D, E]</code>。现在要读取第 4 个元素 <code>D</code>：</p>
<!-- numbered-subquestions -->
<ol>
<li>数组可以直接使用哪个索引？</li>
<li>单向链表从头节点 <code>A</code> 开始，要沿着 <code>next</code> 依次经过哪些节点？</li>
<li>当要读取的元素位置越来越靠后时，两种结构所需的步骤会怎样变化？哪一种更适合反复按位置读取？为什么？</li>
</ol>
<details class="success">
<summary>参考答案</summary>
<ol>
<li>
<p>若索引从 0 开始，第 4 个元素的索引是 3，数组可直接读取 <code>arr[3]</code>。</p>
</li>
<li>
<p>单向链表必须从头开始，访问路径为 <code>A → B → C → D</code>，需要沿 <code>next</code> 前进 3 次。</p>
</li>
<li>
<p>数组可以根据首地址和索引直接定位元素，按位置访问的时间复杂度为 <span class="arithmatex">\(O(1)\)</span>。
单向链表访问第 <span class="arithmatex">\(k\)</span> 个节点时，必须从头节点开始，沿着 <code>next</code> 前进 <span class="arithmatex">\(k-1\)</span> 次，
最坏需要 <span class="arithmatex">\(O(n)\)</span> 时间。</p>
<p>这里只比较按位置读取，不表示链表在所有操作上都更慢。</p>
</li>
</ol>
</details>
<h3 id="2">2. &nbsp; 数组和链表怎样插入元素<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
<p>数组和单向链表中都保存了 <code>A、B、C、D</code>。现在要在 <code>B</code> 后面插入 <code>X</code>：</p>
<ul>
<li>数组容量为 5，当前状态是 <code>[A, B, C, D, _]</code>；</li>
<li>链表为 <code>A → B → C → D</code>，并且已经拿到了指向节点 <code>B</code> 的引用。</li>
</ul>
<!-- numbered-subquestions -->
<ol>
<li>数组需要移动哪些元素？写出插入后的数组。</li>
<li>链表应按什么顺序修改 <code>X.next</code> 和 <code>B.next</code>？写出插入后的链表。</li>
<li>为什么比较插入效率时，要特别说明“已经拿到了节点 B 的引用”？</li>
</ol>
<details class="success">
<summary>参考答案</summary>
<ol>
<li>
<p>数组要先把 <code>D</code> 向右移动一格，再把 <code>C</code> 向右移动一格，最后把 <code>X</code> 放入索引 2，
得到 <code>[A, B, X, C, D]</code>。</p>
</li>
<li>
<p><code>B.next</code> 原本指向 <code>C</code>。应先令 <code>X.next = B.next</code>，让 <code>X</code> 指向 <code>C</code>；
再令 <code>B.next = X</code>。结果为 <code>A → B → X → C → D</code>。
如果先覆盖 <code>B.next</code> 又没有保存原来的连接，就可能找不到 <code>C</code>。</p>
</li>
<li>
<p>已知 <code>B</code> 的位置后，链表插入只需修改两个连接，可以在 <span class="arithmatex">\(O(1)\)</span> 时间完成。
如果还要从头查找 <code>B</code>，查找过程本身可能需要 <span class="arithmatex">\(O(n)\)</span> 时间。</p>
</li>
</ol>
</details>
<h3 id="3">3. &nbsp; 列表容量是怎样增长的<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
<p>一个基于数组实现的列表当前内容为 <code>[A, B, C]</code>，长度 <code>size = 3</code>，容量 <code>capacity = 4</code>。
规定容量不足时，新数组的容量扩大为原来的 2 倍。</p>
<!-- numbered-subquestions -->
<ol>
<li>追加 <code>D</code> 后，列表的长度和容量分别是多少？是否需要扩容？</li>
<li>接着追加 <code>E</code> 时，容量会变为多少？需要复制几个原有元素？</li>
<li>底层数组的长度不可变，为什么列表的容量看起来却可以增长？</li>
</ol>
<details class="success">
<summary>参考答案</summary>
<ol>
<li>
<p><code>D</code> 可以放入最后一个空位。此时内容为 <code>[A, B, C, D]</code>，
<code>size = 4</code>、<code>capacity = 4</code>，不需要扩容。</p>
</li>
<li>
<p>再追加 <code>E</code> 时已经没有空位，需要创建容量为 8 的新数组，
将 <code>A、B、C、D</code> 共 4 个原有元素复制过去，再加入 <code>E</code>。
此时 <code>size = 5</code>、<code>capacity = 8</code>。</p>
</li>
<li>
<p>原来的数组本身没有变长。列表创建了一个更大的新数组，复制原有元素，
再改用新数组作为底层存储，因此对使用者来说容量增长了。</p>
</li>
</ol>
</details>
<h2 id="462">4.6.2 &nbsp; 编程练习<a class="headerlink" href="#462" title="Permanent link">&para;</a></h2>
<h3 id="1_1">1. &nbsp; 数组表示的大整数加一<a class="headerlink" href="#1_1" title="Permanent link">&para;</a></h3>
<p>数组 <code>digits</code> 从左到右保存一个非负整数的各位数字，例如 <code>[3, 0, 8]</code> 表示 308。
数字 0 用 <code>[0]</code> 表示；其他输入的第一位均不为 0。</p>
<p>请模拟一次十进制竖式加法，将这个整数增加 1，并把结果仍按相同的数组形式返回。
可以直接修改 <code>digits</code>；若最前面产生新的进位，可以返回一个更长的数组。</p>
<details class="tip">
<summary>解题提示</summary>
<ol>
<li>像做竖式加法一样，从数组最后一位开始</li>
<li>当前位小于 9 时加一后即可立即返回</li>
<li>当前位等于 9 时把它改成 0；若所有位都是 9，需要在最前面补 1</li>
</ol>
</details>
<p><a class="rounded-button exercise-button" href="https://leetcode.cn/problems/plus-one/" rel="noopener noreferrer" target="_blank">LeetCode</a></p>
<h3 id="2_1">2. &nbsp; 反转单向链表<a class="headerlink" href="#2_1" title="Permanent link">&para;</a></h3>
<p>给定一个单向链表的头节点 <code>head</code>。每个节点包含一个值和指向下一节点的 <code>next</code>。</p>
<p>请使用迭代方法反转所有节点之间的连接，并返回反转后的头节点。
要求不创建新的链表节点。</p>
<details class="tip">
<summary>解题提示</summary>
<ol>
<li>先在纸上画出三个相连的节点和 prev、cur 两个指针</li>
<li>改写 cur.next 前，必须先用 nxt 保存原来的下一个节点</li>
<li>反转 cur.next 后，令 prev = cur，再令 cur = nxt，继续处理原链表中的下一个节点</li>
</ol>
</details>
<p><a class="rounded-button exercise-button" href="https://leetcode.cn/problems/reverse-linked-list/" rel="noopener noreferrer" target="_blank">LeetCode</a> <a class="rounded-button exercise-button" href="https://leetcode.cn/problems/reverse-linked-list/solutions/2361282/206-fan-zhuan-lian-biao-shuang-zhi-zhen-r1jel/" rel="noopener noreferrer" target="_blank">题目解析</a></p>
<!-- Source file information -->
<!-- Was this page helpful? -->
<!-- Previous and next pages link -->
<nav
class="md-footer__inner md-grid"
aria-label="页脚"
>
<!-- Link to previous page -->
<a
href="../summary/"
class="md-footer__link md-footer__link--prev"
aria-label="上一页: 4.5 &amp;nbsp; 小结"
rel="prev"
>
<div class="md-footer__button md-icon">
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-arrow-left" viewBox="0 0 24 24"><path d="m12 19-7-7 7-7M19 12H5"/></svg>
</div>
<div class="md-footer__title">
<span class="md-footer__direction">
上一页
</span>
<div class="md-ellipsis">
4.5 &nbsp; 小结
</div>
</div>
</a>
<!-- Link to next page -->
<a
href="../../chapter_stack_and_queue/"
class="md-footer__link md-footer__link--next"
aria-label="下一页: 第 5 章 &amp;nbsp; 栈与队列"
rel="next"
>
<div class="md-footer__title">
<span class="md-footer__direction">
下一页
</span>
<div class="md-ellipsis">
第 5 章 &nbsp; 栈与队列
</div>
</div>
<div class="md-footer__button md-icon">
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-arrow-right" viewBox="0 0 24 24"><path d="M5 12h14M12 5l7 7-7 7"/></svg>
</div>
</a>
</nav>
<!-- Comment system -->
<!-- Check-in button above comments -->
<h5 align="center" id="__comments">欢迎在评论区留下你的见解、问题或建议</h5>
<!-- Insert generated snippet here -->
<script
src="https://giscus.app/client.js"
data-repo="krahets/hello-algo"
data-repo-id="R_kgDOIXtSqw"
data-category="Announcements"
data-category-id="DIC_kwDOIXtSq84CSZk_"
data-mapping="pathname"
data-strict="1"
data-reactions-enabled="1"
data-emit-metadata="1"
data-input-position="top"
data-theme="light"
data-lang="zh-CN"
crossorigin="anonymous"
async
>
</script>
<!-- Synchronize Giscus theme with palette -->
<script>
var giscus = document.querySelector("script[src*=giscus]")
function getGiscusTheme() {
var palette = __md_get("__palette")
var isDark = palette && typeof palette.color === "object" && palette.color.scheme === "slate"
return isDark ? "noborder_dark" : "light"
}
/* Set palette on initial load */
giscus.setAttribute("data-theme", getGiscusTheme())
/* Register event handlers after documented loaded */
document.addEventListener("DOMContentLoaded", function() {
var ref = document.querySelector("[data-md-component=palette]")
if (!ref) return
ref.addEventListener("change", function() {
var theme = getGiscusTheme()
/* Instruct Giscus to change theme */
var frame = document.querySelector(".giscus-frame")
if (!frame) return
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 labels=set.querySelector(".tabbed-labels");for(var tab of tabs)for(var label of labels.getElementsByTagName("label"))if(label.innerText.trim()===tab){var input=document.getElementById(label.htmlFor);input.checked=!0;continue e}}</script>
<script>var target=document.getElementById(location.hash.slice(1));target&&target.name&&(target.checked=target.name.startsWith("__tabbed_"))</script>
</div>
</main>
<footer class="md-footer">
<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 &copy; 2026 krahets<br>The website content is licensed under <a href="https://creativecommons.org/licenses/by-nc-sa/4.0/">CC BY-NC-SA 4.0</a>
</div>
</div>
<div class="md-social">
<a href="https://github.com/krahets" target="_blank" rel="noopener" title="github.com" class="md-social__link">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path fill="currentColor" d="M173.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6m-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3m44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9M252.8 8C114.1 8 8 113.3 8 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C436.2 457.8 504 362.9 504 252 504 113.3 391.5 8 252.8 8M105.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1m-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7m32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1m-11.4-14.7c-1.6 1-1.6 3.6 0 5.9s4.3 3.3 5.6 2.3c1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2"/></svg>
</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 0 448 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path fill="currentColor" d="M357.2 48h70.6L273.6 224.2 455 464H313L201.7 318.6 74.5 464H3.8l164.9-188.5L-5.2 48h145.6l100.5 132.9zm-24.8 373.8h39.1L119.1 88h-42z"/></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 0 576 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path fill="currentColor" d="M360.8 1.2c-17-4.9-34.7 5-39.6 22l-128 448c-4.9 17 5 34.7 22 39.6s34.7-5 39.6-22l128-448c4.9-17-5-34.7-22-39.6m64.6 136.1c-12.5 12.5-12.5 32.8 0 45.3l73.4 73.4-73.4 73.4c-12.5 12.5-12.5 32.8 0 45.3s32.8 12.5 45.3 0l96-96c12.5-12.5 12.5-32.8 0-45.3l-96-96c-12.5-12.5-32.8-12.5-45.3 0zm-274.7 0c-12.5-12.5-32.8-12.5-45.3 0l-96 96c-12.5 12.5-12.5 32.8 0 45.3l96 96c12.5 12.5 32.8 12.5 45.3 0s12.5-32.8 0-45.3L77.3 256l73.3-73.4c12.5-12.5 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">{"annotate":null,"base":"../../","features":["content.action.edit","content.code.annotate","content.code.copy","content.tabs.link","content.tooltips","navigation.indexes","navigation.tracking","search.highlight","search.share","search.suggest","toc.follow"],"search":"../../assets/javascripts/workers/search.e2d2d235.min.js","tags":null,"translations":{"clipboard.copied":"已复制","clipboard.copy":"复制","search.result.more.one":"在该页上还有 1 个符合条件的结果","search.result.more.other":"在该页上还有 # 个符合条件的结果","search.result.none":"没有找到符合条件的结果","search.result.one":"找到 1 个符合条件的结果","search.result.other":"# 个符合条件的结果","search.result.placeholder":"键入以开始搜索","search.result.term.missing":"缺少","select.version":"选择当前版本"},"version":null}</script>
<script src="../../assets/javascripts/bundle.c2b142ea.min.js"></script>
<script src="../../javascripts/mathjax.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/3.2.2/es5/tex-mml-chtml.min.js"></script>
<script src="../../javascripts/animation_player.js"></script>
</body>
</html>
Reference in New Issue View Git Blame Copy Permalink