hello-algo/chapter_hashing/hash_algorithm/index.html

4456 lines
262 KiB
HTML
Raw Normal View History

2023-06-16 21:22:53 +08:00
<!doctype html>
<html lang="zh" class="no-js">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width,initial-scale=1">
2023-06-22 00:23:01 +08:00
<meta name="description" content="动画图解、一键运行的数据结构与算法教程">
2023-06-16 21:22:53 +08:00
<meta name="author" content="Krahets">
<link rel="canonical" href="https://www.hello-algo.com/chapter_hashing/hash_algorithm/">
<link rel="prev" href="../hash_collision/">
<link rel="next" href="../summary/">
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<link rel="icon" href="../../assets/images/favicon.png">
2023-09-29 22:06:02 +08:00
<meta name="generator" content="mkdocs-1.5.3, mkdocs-material-9.4.1">
2023-06-16 21:22:53 +08:00
2023-08-19 22:07:40 +08:00
<title>6.3   哈希算法 - Hello 算法</title>
2023-06-16 21:22:53 +08:00
2023-09-29 22:06:02 +08:00
<link rel="stylesheet" href="../../assets/stylesheets/main.72749a73.min.css">
2023-06-16 21:22:53 +08:00
2023-09-24 17:12:06 +08:00
<link rel="stylesheet" href="../../assets/stylesheets/palette.a5377069.min.css">
2023-06-16 21:22:53 +08:00
2023-09-24 17:12:06 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<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>
2023-09-22 13:08:10 +08:00
<link href="../../assets/stylesheets/glightbox.min.css" rel="stylesheet"/><style>
html.glightbox-open { overflow: initial; height: 100%; }
.gslide-title { margin-top: 0px; user-select: text; }
.gslide-desc { color: #666; user-select: text; }
.gslide-image img { background: white; }
.gscrollbar-fixer { padding-right: 15px; }
.gdesc-inner { font-size: 0.75rem; }
body[data-md-color-scheme="slate"] .gdesc-inner { background: var(--md-default-bg-color);}
body[data-md-color-scheme="slate"] .gslide-title { color: var(--md-default-fg-color);}
body[data-md-color-scheme="slate"] .gslide-desc { color: var(--md-default-fg-color);}
</style> <script src="../../assets/javascripts/glightbox.min.js"></script></head>
2023-06-16 21:22:53 +08:00
<body dir="ltr" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="indigo">
<script>var palette=__md_get("__palette");if(palette&&"object"==typeof palette.color)for(var key of Object.keys(palette.color))document.body.setAttribute("data-md-color-"+key,palette.color[key])</script>
<input class="md-toggle" data-md-toggle="drawer" type="checkbox" id="__drawer" autocomplete="off">
<input class="md-toggle" data-md-toggle="search" type="checkbox" id="__search" autocomplete="off">
<label class="md-overlay" for="__drawer"></label>
<div data-md-component="skip">
<a href="#63" 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">
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<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">
2023-08-19 22:07:40 +08:00
6.3 &nbsp; 哈希算法
2023-06-16 21:22:53 +08:00
</span>
</div>
</div>
</div>
<form class="md-header__option" data-md-component="palette">
2023-09-24 17:12:06 +08:00
<input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="indigo" aria-label="Switch to dark mode" type="radio" name="__palette" id="__palette_1">
<label class="md-header__button md-icon" title="Switch to dark mode" for="__palette_2" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z"/></svg>
</label>
<input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="grey" data-md-color-accent="indigo" aria-label="Switch to light mode" type="radio" name="__palette" id="__palette_2">
<label class="md-header__button md-icon" title="Switch to light mode" for="__palette_1" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z"/></svg>
</label>
</form>
2023-06-16 21:22:53 +08:00
2023-10-06 13:31:31 +08:00
<div class="md-header__option">
<div class="md-select">
<button class="md-header__button md-icon" aria-label="选择当前语言">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12.87 15.07-2.54-2.51.03-.03A17.52 17.52 0 0 0 14.07 6H17V4h-7V2H8v2H1v2h11.17C11.5 7.92 10.44 9.75 9 11.35 8.07 10.32 7.3 9.19 6.69 8h-2c.73 1.63 1.73 3.17 2.98 4.56l-5.09 5.02L4 19l5-5 3.11 3.11.76-2.04M18.5 10h-2L12 22h2l1.12-3h4.75L21 22h2l-4.5-12m-2.62 7 1.62-4.33L19.12 17h-3.24Z"/></svg>
</button>
<div class="md-select__inner">
<ul class="md-select__list">
<li class="md-select__item">
<a href="/" hreflang="zh" class="md-select__link">
中文
</a>
2023-10-06 14:10:31 +08:00
</li>
2023-10-06 13:31:31 +08:00
</ul>
</div>
</div>
</div>
2023-06-16 21:22:53 +08:00
<label class="md-header__button md-icon" for="__search">
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<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">
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<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>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<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">
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<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">
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<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">
2023-09-24 17:12:06 +08:00
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 496 512"><!--! Font Awesome Free 6.4.2 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg>
2023-06-16 21:22:53 +08:00
</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">
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<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">
2023-09-24 17:12:06 +08:00
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 496 512"><!--! Font Awesome Free 6.4.2 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg>
2023-06-16 21:22:53 +08:00
</div>
<div class="md-source__repository">
krahets/hello-algo
</div>
</a>
</div>
<ul class="md-nav__list" data-md-scrollfix>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
<li class="md-nav__item md-nav__item--nested">
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-17 17:51:12 +08:00
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_1" >
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
<div class="md-nav__link md-nav__container">
<a href="../../chapter_preface/" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
第 0 章 &nbsp; 前言
2023-07-17 17:51:12 +08:00
</span>
</a>
2023-06-16 21:22:53 +08:00
2023-09-29 22:06:02 +08:00
<label class="md-nav__link " for="__nav_1">
2023-07-17 17:51:12 +08:00
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_1_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_1">
<span class="md-nav__icon md-icon"></span>
2023-08-19 22:07:40 +08:00
第 0 章 &nbsp; 前言
2023-07-17 17:51:12 +08:00
</label>
<ul class="md-nav__list" data-md-scrollfix>
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_preface/about_the_book/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
0.1 &nbsp; 关于本书
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_preface/suggestions/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
0.2 &nbsp; 如何使用本书
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_preface/summary/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
0.3 &nbsp; 小结
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
</ul>
</nav>
2023-06-16 21:22:53 +08:00
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
<li class="md-nav__item md-nav__item--nested">
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-17 17:51:12 +08:00
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_2" >
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
<div class="md-nav__link md-nav__container">
<a href="../../chapter_introduction/" class="md-nav__link ">
2023-07-19 16:10:17 +08:00
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
第 1 章 &nbsp; 初识算法
2023-07-17 17:51:12 +08:00
</span>
</a>
2023-06-16 21:22:53 +08:00
2023-09-29 22:06:02 +08:00
<label class="md-nav__link " for="__nav_2">
2023-07-17 17:51:12 +08:00
<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>
2023-08-19 22:07:40 +08:00
第 1 章 &nbsp; 初识算法
2023-07-17 17:51:12 +08:00
</label>
<ul class="md-nav__list" data-md-scrollfix>
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
1.1 &nbsp; 算法无处不在
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
1.2 &nbsp; 算法是什么
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_introduction/summary/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
1.3 &nbsp; 小结
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
</ul>
</nav>
2023-06-16 21:22:53 +08:00
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-08-24 17:47:31 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
<li class="md-nav__item md-nav__item--nested">
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-17 17:51:12 +08:00
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
<div class="md-nav__link md-nav__container">
<a href="../../chapter_computational_complexity/" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
<span class="md-ellipsis">
2023-08-28 04:36:05 +08:00
第 2 章 &nbsp; 复杂度分析
2023-07-17 17:51:12 +08:00
</span>
</a>
2023-06-16 21:22:53 +08:00
2023-09-29 22:06:02 +08:00
<label class="md-nav__link " for="__nav_3">
2023-07-17 17:51:12 +08:00
<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>
2023-08-28 04:36:05 +08:00
第 2 章 &nbsp; 复杂度分析
2023-07-17 17:51:12 +08:00
</label>
<ul class="md-nav__list" data-md-scrollfix>
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
2.1 &nbsp; 算法效率评估
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-08-24 17:47:31 +08:00
<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>
2023-08-25 02:22:36 +08:00
<span class="md-status md-status--new" title="最近添加">
</span>
2023-08-24 17:47:31 +08:00
</a>
</li>
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-24 17:47:31 +08:00
2.3 &nbsp; 时间复杂度
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-24 17:47:31 +08:00
2.4 &nbsp; 空间复杂度
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-24 17:47:31 +08:00
2.5 &nbsp; 小结
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
</ul>
</nav>
2023-06-16 21:22:53 +08:00
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
<li class="md-nav__item md-nav__item--nested">
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-17 17:51:12 +08:00
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
<div class="md-nav__link md-nav__container">
<a href="../../chapter_data_structure/" class="md-nav__link ">
2023-06-16 21:22:53 +08:00
2023-07-19 16:10:17 +08:00
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
第 3 章 &nbsp; 数据结构
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
</a>
2023-06-16 21:22:53 +08:00
2023-09-29 22:06:02 +08:00
<label class="md-nav__link " for="__nav_4">
2023-07-17 17:51:12 +08:00
<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>
2023-08-19 22:07:40 +08:00
第 3 章 &nbsp; 数据结构
2023-07-17 17:51:12 +08:00
</label>
<ul class="md-nav__list" data-md-scrollfix>
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
2023-07-17 17:51:12 +08:00
<a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
3.1 &nbsp; 数据结构分类
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
<li class="md-nav__item">
<a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
3.2 &nbsp; 基本数据类型
2023-07-17 17:51:12 +08:00
</span>
</a>
</li>
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
3.3 &nbsp; 数字编码 *
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
3.4 &nbsp; 字符编码 *
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_data_structure/summary/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
3.5 &nbsp; 小结
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
</ul>
</nav>
2023-06-16 21:22:53 +08:00
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
<li class="md-nav__item md-nav__item--nested">
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-17 17:51:12 +08:00
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
<div class="md-nav__link md-nav__container">
<a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
2023-07-19 16:10:17 +08:00
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
第 4 章 &nbsp; 数组与链表
2023-07-17 17:51:12 +08:00
</span>
</a>
2023-06-16 21:22:53 +08:00
2023-09-29 22:06:02 +08:00
<label class="md-nav__link " for="__nav_5">
2023-07-17 17:51:12 +08:00
<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>
2023-08-19 22:07:40 +08:00
第 4 章 &nbsp; 数组与链表
2023-07-17 17:51:12 +08:00
</label>
<ul class="md-nav__list" data-md-scrollfix>
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
4.1 &nbsp; 数组
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
4.2 &nbsp; 链表
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
4.3 &nbsp; 列表
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
4.4 &nbsp; 小结
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
</ul>
</nav>
2023-06-16 21:22:53 +08:00
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
<li class="md-nav__item md-nav__item--nested">
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-17 17:51:12 +08:00
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
<div class="md-nav__link md-nav__container">
<a href="../../chapter_stack_and_queue/" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
第 5 章 &nbsp; 栈与队列
2023-07-17 17:51:12 +08:00
</span>
</a>
2023-06-16 21:22:53 +08:00
2023-09-29 22:06:02 +08:00
<label class="md-nav__link " for="__nav_6">
2023-07-17 17:51:12 +08:00
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_6">
<span class="md-nav__icon md-icon"></span>
2023-08-19 22:07:40 +08:00
第 5 章 &nbsp; 栈与队列
2023-07-17 17:51:12 +08:00
</label>
<ul class="md-nav__list" data-md-scrollfix>
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
5.1 &nbsp;
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
5.2 &nbsp; 队列
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
5.3 &nbsp; 双向队列
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
5.4 &nbsp; 小结
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
</ul>
</nav>
2023-06-16 21:22:53 +08:00
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
<li class="md-nav__item md-nav__item--active md-nav__item--nested">
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-17 17:51:12 +08:00
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" checked>
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
<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="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
<span class="md-ellipsis">
2023-08-21 03:56:52 +08:00
第 6 章 &nbsp; 哈希表
2023-07-17 17:51:12 +08:00
</span>
</a>
2023-06-16 21:22:53 +08:00
2023-09-29 22:06:02 +08:00
<label class="md-nav__link " for="__nav_7">
2023-07-17 17:51:12 +08:00
<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="true">
<label class="md-nav__title" for="__nav_7">
<span class="md-nav__icon md-icon"></span>
2023-08-21 03:56:52 +08:00
第 6 章 &nbsp; 哈希表
2023-07-17 17:51:12 +08:00
</label>
<ul class="md-nav__list" data-md-scrollfix>
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../hash_map/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
6.1 &nbsp; 哈希表
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../hash_collision/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
6.2 &nbsp; 哈希冲突
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<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">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
6.3 &nbsp; 哈希算法
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
<span class="md-nav__icon md-icon"></span>
</label>
<a href="./" class="md-nav__link md-nav__link--active">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
6.3 &nbsp; 哈希算法
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</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="#631" class="md-nav__link">
2023-08-19 22:07:40 +08:00
6.3.1 &nbsp; 哈希算法的目标
2023-06-16 21:22:53 +08:00
</a>
</li>
<li class="md-nav__item">
<a href="#632" class="md-nav__link">
2023-08-19 22:07:40 +08:00
6.3.2 &nbsp; 哈希算法的设计
2023-06-16 21:22:53 +08:00
</a>
</li>
<li class="md-nav__item">
<a href="#633" class="md-nav__link">
2023-08-19 22:07:40 +08:00
6.3.3 &nbsp; 常见哈希算法
2023-06-16 21:22:53 +08:00
</a>
</li>
<li class="md-nav__item">
<a href="#634" class="md-nav__link">
2023-08-19 22:07:40 +08:00
6.3.4 &nbsp; 数据结构的哈希值
2023-06-16 21:22:53 +08:00
</a>
</li>
</ul>
</nav>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../summary/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
6.4 &nbsp; 小结
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
</ul>
</nav>
2023-06-16 21:22:53 +08:00
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
<li class="md-nav__item md-nav__item--nested">
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-17 17:51:12 +08:00
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
<div class="md-nav__link md-nav__container">
<a href="../../chapter_tree/" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
第 7 章 &nbsp;
2023-07-17 17:51:12 +08:00
</span>
</a>
2023-06-16 21:22:53 +08:00
2023-09-29 22:06:02 +08:00
<label class="md-nav__link " for="__nav_8">
2023-07-17 17:51:12 +08:00
<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>
2023-08-19 22:07:40 +08:00
第 7 章 &nbsp;
2023-07-17 17:51:12 +08:00
</label>
<ul class="md-nav__list" data-md-scrollfix>
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_tree/binary_tree/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
7.1 &nbsp; 二叉树
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
7.2 &nbsp; 二叉树遍历
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
7.3 &nbsp; 二叉树数组表示
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
7.4 &nbsp; 二叉搜索树
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_tree/avl_tree/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
7.5 &nbsp; AVL 树 *
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_tree/summary/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
7.6 &nbsp; 小结
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
</ul>
</nav>
2023-06-16 21:22:53 +08:00
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
<li class="md-nav__item md-nav__item--nested">
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-17 17:51:12 +08:00
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
<div class="md-nav__link md-nav__container">
<a href="../../chapter_heap/" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
第 8 章 &nbsp;
2023-07-17 17:51:12 +08:00
</span>
</a>
2023-09-29 22:06:02 +08:00
<label class="md-nav__link " for="__nav_9">
2023-07-17 17:51:12 +08:00
<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>
2023-08-19 22:07:40 +08:00
第 8 章 &nbsp;
2023-07-17 17:51:12 +08:00
</label>
<ul class="md-nav__list" data-md-scrollfix>
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_heap/heap/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
8.1 &nbsp;
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_heap/build_heap/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
8.2 &nbsp; 建堆操作
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_heap/top_k/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
8.3 &nbsp; Top-K 问题
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_heap/summary/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
8.4 &nbsp; 小结
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
</ul>
</nav>
2023-06-16 21:22:53 +08:00
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
<li class="md-nav__item md-nav__item--nested">
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-17 17:51:12 +08:00
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
<div class="md-nav__link md-nav__container">
<a href="../../chapter_graph/" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
第 9 章 &nbsp;
2023-07-17 17:51:12 +08:00
</span>
</a>
2023-06-16 21:22:53 +08:00
2023-09-29 22:06:02 +08:00
<label class="md-nav__link " for="__nav_10">
2023-07-17 17:51:12 +08:00
<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>
2023-08-19 22:07:40 +08:00
第 9 章 &nbsp;
2023-07-17 17:51:12 +08:00
</label>
<ul class="md-nav__list" data-md-scrollfix>
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_graph/graph/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
9.1 &nbsp;
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_graph/graph_operations/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
9.2 &nbsp; 图基础操作
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
9.3 &nbsp; 图的遍历
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_graph/summary/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
9.4 &nbsp; 小结
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
</ul>
</nav>
2023-06-16 21:22:53 +08:00
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-08-04 05:25:00 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
<li class="md-nav__item md-nav__item--nested">
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-17 17:51:12 +08:00
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
<div class="md-nav__link md-nav__container">
<a href="../../chapter_searching/" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
第 10 章 &nbsp; 搜索
2023-07-17 17:51:12 +08:00
</span>
</a>
2023-06-16 21:22:53 +08:00
2023-09-29 22:06:02 +08:00
<label class="md-nav__link " for="__nav_11">
2023-07-17 17:51:12 +08:00
<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>
2023-08-19 22:07:40 +08:00
第 10 章 &nbsp; 搜索
2023-07-17 17:51:12 +08:00
</label>
<ul class="md-nav__list" data-md-scrollfix>
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_searching/binary_search/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
10.1 &nbsp; 二分查找
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-08-04 05:25:00 +08:00
<li class="md-nav__item">
<a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
10.2 &nbsp; 二分查找插入点
2023-08-04 05:25:00 +08:00
</span>
</a>
</li>
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
10.3 &nbsp; 二分查找边界
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
10.4 &nbsp; 哈希优化策略
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
10.5 &nbsp; 重识搜索算法
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_searching/summary/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
10.6 &nbsp; 小结
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
</ul>
</nav>
2023-06-16 21:22:53 +08:00
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
<li class="md-nav__item md-nav__item--nested">
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-17 17:51:12 +08:00
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
<div class="md-nav__link md-nav__container">
<a href="../../chapter_sorting/" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
第 11 章 &nbsp; 排序
2023-07-17 17:51:12 +08:00
</span>
</a>
2023-06-16 21:22:53 +08:00
2023-09-29 22:06:02 +08:00
<label class="md-nav__link " for="__nav_12">
2023-07-17 17:51:12 +08:00
<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>
2023-08-19 22:07:40 +08:00
第 11 章 &nbsp; 排序
2023-07-17 17:51:12 +08:00
</label>
<ul class="md-nav__list" data-md-scrollfix>
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
11.1 &nbsp; 排序算法
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
11.2 &nbsp; 选择排序
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
11.3 &nbsp; 冒泡排序
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
11.4 &nbsp; 插入排序
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
11.5 &nbsp; 快速排序
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
11.6 &nbsp; 归并排序
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
11.7 &nbsp; 堆排序
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
11.8 &nbsp; 桶排序
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
11.9 &nbsp; 计数排序
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
11.10 &nbsp; 基数排序
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_sorting/summary/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
11.11 &nbsp; 小结
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
</ul>
</nav>
2023-06-16 21:22:53 +08:00
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-07-17 02:17:51 +08:00
2023-07-17 20:19:46 +08:00
2023-07-17 17:51:12 +08:00
2023-07-17 04:21:02 +08:00
2023-07-16 04:19:01 +08:00
2023-07-17 17:51:12 +08:00
<li class="md-nav__item md-nav__item--nested">
2023-07-16 04:19:01 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-17 17:51:12 +08:00
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
2023-07-16 04:19:01 +08:00
2023-07-17 17:51:12 +08:00
<div class="md-nav__link md-nav__container">
<a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
2023-07-19 16:10:17 +08:00
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
第 12 章 &nbsp; 分治
2023-07-17 17:51:12 +08:00
</span>
</a>
2023-07-16 04:19:01 +08:00
2023-09-29 22:06:02 +08:00
<label class="md-nav__link " for="__nav_13">
2023-07-17 17:51:12 +08:00
<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>
2023-08-19 22:07:40 +08:00
第 12 章 &nbsp; 分治
2023-07-17 17:51:12 +08:00
</label>
<ul class="md-nav__list" data-md-scrollfix>
2023-07-16 04:19:01 +08:00
2023-07-17 17:51:12 +08:00
2023-07-16 04:19:01 +08:00
<li class="md-nav__item">
<a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
12.1 &nbsp; 分治算法
2023-07-17 17:51:12 +08:00
</span>
2023-07-16 04:19:01 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-07-16 04:19:01 +08:00
2023-07-17 17:51:12 +08:00
2023-07-16 04:19:01 +08:00
2023-07-17 04:21:02 +08:00
<li class="md-nav__item">
<a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
12.2 &nbsp; 分治搜索策略
2023-07-17 17:51:12 +08:00
</span>
2023-07-17 04:21:02 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-07-17 04:21:02 +08:00
2023-07-17 17:51:12 +08:00
2023-07-17 04:21:02 +08:00
2023-07-16 04:19:01 +08:00
<li class="md-nav__item">
2023-07-17 02:17:51 +08:00
<a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
12.3 &nbsp; 构建树问题
2023-07-17 17:51:12 +08:00
</span>
2023-07-16 04:19:01 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-07-17 02:17:51 +08:00
2023-07-17 17:51:12 +08:00
2023-07-17 02:17:51 +08:00
<li class="md-nav__item">
<a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
12.4 &nbsp; 汉诺塔问题
2023-07-17 17:51:12 +08:00
</span>
2023-07-17 02:17:51 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-07-17 02:17:51 +08:00
2023-07-17 20:19:46 +08:00
<li class="md-nav__item">
<a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
12.5 &nbsp; 小结
2023-07-17 20:19:46 +08:00
</span>
</a>
</li>
2023-07-17 17:51:12 +08:00
</ul>
</nav>
2023-07-16 04:19:01 +08:00
</li>
2023-07-17 17:51:12 +08:00
2023-07-16 04:19:01 +08:00
2023-07-17 17:51:12 +08:00
2023-07-16 04:19:01 +08:00
2023-07-17 17:51:12 +08:00
2023-07-16 04:19:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-21 02:55:52 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
<li class="md-nav__item md-nav__item--nested">
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-17 17:51:12 +08:00
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
<div class="md-nav__link md-nav__container">
<a href="../../chapter_backtracking/" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
第 13 章 &nbsp; 回溯
2023-07-17 17:51:12 +08:00
</span>
</a>
2023-06-16 21:22:53 +08:00
2023-09-29 22:06:02 +08:00
<label class="md-nav__link " for="__nav_14">
2023-07-17 17:51:12 +08:00
<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>
2023-08-19 22:07:40 +08:00
第 13 章 &nbsp; 回溯
2023-07-17 17:51:12 +08:00
</label>
<ul class="md-nav__list" data-md-scrollfix>
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
13.1 &nbsp; 回溯算法
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
13.2 &nbsp; 全排列问题
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-06-21 02:55:52 +08:00
<li class="md-nav__item">
<a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
13.3 &nbsp; 子集和问题
2023-07-17 17:51:12 +08:00
</span>
2023-06-21 02:55:52 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-21 02:55:52 +08:00
2023-07-17 17:51:12 +08:00
2023-06-21 02:55:52 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
13.4 &nbsp; N 皇后问题
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
<li class="md-nav__item">
<a href="../../chapter_backtracking/summary/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
13.5 &nbsp; 小结
2023-07-17 17:51:12 +08:00
</span>
2023-06-22 00:23:01 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
</ul>
</nav>
2023-06-16 21:22:53 +08:00
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-07-01 22:39:28 +08:00
2023-07-17 17:51:12 +08:00
2023-07-06 00:08:29 +08:00
2023-07-17 17:51:12 +08:00
2023-07-07 21:39:04 +08:00
2023-07-17 17:51:12 +08:00
2023-07-11 19:21:38 +08:00
2023-07-17 17:51:12 +08:00
2023-07-14 02:56:32 +08:00
2023-07-17 17:51:12 +08:00
2023-07-13 05:26:03 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
<li class="md-nav__item md-nav__item--nested">
2023-06-16 21:22:53 +08:00
2023-06-30 04:33:52 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-17 17:51:12 +08:00
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
2023-06-30 04:33:52 +08:00
2023-07-17 17:51:12 +08:00
<div class="md-nav__link md-nav__container">
<a href="../../chapter_dynamic_programming/" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
第 14 章 &nbsp; 动态规划
2023-07-17 17:51:12 +08:00
</span>
</a>
2023-06-30 04:33:52 +08:00
2023-09-29 22:06:02 +08:00
<label class="md-nav__link " for="__nav_15">
2023-07-17 17:51:12 +08:00
<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>
2023-08-19 22:07:40 +08:00
第 14 章 &nbsp; 动态规划
2023-07-17 17:51:12 +08:00
</label>
<ul class="md-nav__list" data-md-scrollfix>
2023-06-30 04:33:52 +08:00
2023-07-17 17:51:12 +08:00
2023-06-30 04:33:52 +08:00
<li class="md-nav__item">
<a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
14.1 &nbsp; 初探动态规划
2023-07-17 17:51:12 +08:00
</span>
2023-07-01 22:39:28 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-07-01 22:39:28 +08:00
2023-07-17 17:51:12 +08:00
2023-07-01 22:39:28 +08:00
<li class="md-nav__item">
<a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
14.2 &nbsp; DP 问题特性
2023-07-17 17:51:12 +08:00
</span>
2023-06-30 04:33:52 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-07-06 00:08:29 +08:00
2023-07-17 17:51:12 +08:00
2023-07-06 00:08:29 +08:00
2023-07-07 21:39:04 +08:00
<li class="md-nav__item">
2023-07-09 03:02:15 +08:00
<a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
14.3 &nbsp; DP 解题思路
2023-07-17 17:51:12 +08:00
</span>
2023-07-07 21:39:04 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-07-07 21:39:04 +08:00
2023-07-17 17:51:12 +08:00
2023-07-07 21:39:04 +08:00
2023-07-06 00:08:29 +08:00
<li class="md-nav__item">
<a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
14.4 &nbsp; 0-1 背包问题
2023-07-17 17:51:12 +08:00
</span>
2023-07-06 00:08:29 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-07-11 19:21:38 +08:00
2023-07-17 17:51:12 +08:00
2023-07-11 19:21:38 +08:00
<li class="md-nav__item">
<a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
14.5 &nbsp; 完全背包问题
2023-07-17 17:51:12 +08:00
</span>
2023-07-11 19:21:38 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-07-13 05:26:03 +08:00
2023-07-17 17:51:12 +08:00
2023-07-13 05:26:03 +08:00
<li class="md-nav__item">
<a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
14.6 &nbsp; 编辑距离问题
2023-07-17 17:51:12 +08:00
</span>
2023-07-13 05:26:03 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-07-14 02:56:32 +08:00
2023-07-17 17:51:12 +08:00
2023-07-14 02:56:32 +08:00
<li class="md-nav__item">
<a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
14.7 &nbsp; 小结
2023-07-17 17:51:12 +08:00
</span>
2023-07-14 02:56:32 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-07-14 02:56:32 +08:00
2023-07-17 17:51:12 +08:00
</ul>
</nav>
2023-06-30 04:33:52 +08:00
</li>
2023-07-17 17:51:12 +08:00
2023-06-30 04:33:52 +08:00
2023-07-17 17:51:12 +08:00
2023-06-30 04:33:52 +08:00
2023-07-17 17:51:12 +08:00
2023-07-21 21:53:15 +08:00
2023-07-21 22:50:40 +08:00
2023-07-21 15:14:51 +08:00
2023-06-30 04:33:52 +08:00
2023-07-17 17:51:12 +08:00
<li class="md-nav__item md-nav__item--nested">
2023-06-30 04:33:52 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-17 17:51:12 +08:00
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
<div class="md-nav__link md-nav__container">
2023-07-20 18:24:35 +08:00
<a href="../../chapter_greedy/" class="md-nav__link ">
2023-07-17 17:51:12 +08:00
2023-07-20 18:24:35 +08:00
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
第 15 章 &nbsp; 贪心
2023-07-17 17:51:12 +08:00
</span>
</a>
2023-09-29 22:06:02 +08:00
<label class="md-nav__link " for="__nav_16">
2023-07-17 17:51:12 +08:00
<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>
2023-08-19 22:07:40 +08:00
第 15 章 &nbsp; 贪心
2023-07-20 18:24:35 +08:00
</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">
2023-08-19 22:07:40 +08:00
15.1 &nbsp; 贪心算法
2023-07-20 18:24:35 +08:00
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
15.2 &nbsp; 分数背包问题
2023-07-20 18:24:35 +08:00
</span>
</a>
</li>
2023-07-21 15:14:51 +08:00
<li class="md-nav__item">
<a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
15.3 &nbsp; 最大容量问题
2023-07-21 15:14:51 +08:00
</span>
</a>
</li>
2023-07-21 21:53:15 +08:00
<li class="md-nav__item">
<a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
15.4 &nbsp; 最大切分乘积问题
2023-07-21 21:53:15 +08:00
</span>
</a>
</li>
2023-07-21 22:50:40 +08:00
<li class="md-nav__item">
<a href="../../chapter_greedy/summary/" class="md-nav__link">
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
15.5 &nbsp; 小结
2023-07-21 22:50:40 +08:00
</span>
</a>
</li>
2023-07-20 18:24:35 +08:00
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
2023-09-29 22:06:02 +08:00
2023-07-20 18:24:35 +08:00
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
<div class="md-nav__link md-nav__container">
<a href="../../chapter_appendix/" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
第 16 章 &nbsp; 附录
2023-07-20 18:24:35 +08:00
</span>
</a>
2023-09-29 22:06:02 +08:00
<label class="md-nav__link " for="__nav_17">
2023-07-20 18:24:35 +08:00
<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>
2023-08-19 22:07:40 +08:00
第 16 章 &nbsp; 附录
2023-07-17 17:51:12 +08:00
</label>
<ul class="md-nav__list" data-md-scrollfix>
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_appendix/installation/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
16.1 &nbsp; 编程环境安装
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<li class="md-nav__item">
<a href="../../chapter_appendix/contribution/" class="md-nav__link">
2023-07-17 17:51:12 +08:00
<span class="md-ellipsis">
2023-08-19 22:07:40 +08:00
16.2 &nbsp; 一起参与创作
2023-07-17 17:51:12 +08:00
</span>
2023-06-16 21:22:53 +08:00
</a>
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
</ul>
</nav>
2023-06-16 21:22:53 +08:00
</li>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
<li class="md-nav__item md-nav__item--nested">
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-20 18:24:35 +08:00
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
<div class="md-nav__link md-nav__container">
<a href="../../chapter_reference/" class="md-nav__link ">
<span class="md-ellipsis">
参考文献
</span>
</a>
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
</div>
2023-07-20 18:24:35 +08:00
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_18">
2023-07-17 17:51:12 +08:00
<span class="md-nav__icon md-icon"></span>
参考文献
</label>
<ul class="md-nav__list" data-md-scrollfix>
</ul>
</nav>
2023-06-16 21:22:53 +08:00
</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="#631" class="md-nav__link">
2023-08-19 22:07:40 +08:00
6.3.1 &nbsp; 哈希算法的目标
2023-06-16 21:22:53 +08:00
</a>
</li>
<li class="md-nav__item">
<a href="#632" class="md-nav__link">
2023-08-19 22:07:40 +08:00
6.3.2 &nbsp; 哈希算法的设计
2023-06-16 21:22:53 +08:00
</a>
</li>
<li class="md-nav__item">
<a href="#633" class="md-nav__link">
2023-08-19 22:07:40 +08:00
6.3.3 &nbsp; 常见哈希算法
2023-06-16 21:22:53 +08:00
</a>
</li>
<li class="md-nav__item">
<a href="#634" class="md-nav__link">
2023-08-19 22:07:40 +08:00
6.3.4 &nbsp; 数据结构的哈希值
2023-06-16 21:22:53 +08:00
</a>
</li>
</ul>
</nav>
</div>
</div>
</div>
<div class="md-content" data-md-component="content">
<article class="md-content__inner md-typeset">
2023-09-21 20:44:52 +08:00
<!--
Copyright (c) 2016-2023 Martin Donath <martin.donath@squidfunk.com>
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to
deal in the Software without restriction, including without limitation the
rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
sell copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
IN THE SOFTWARE.
-->
<!-- Tags -->
<!-- Actions -->
2023-06-16 21:22:53 +08:00
<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_hashing/hash_algorithm.md" title="编辑此页" class="md-content__button md-icon">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M10 20H6V4h7v5h5v3.1l2-2V8l-6-6H6c-1.1 0-2 .9-2 2v16c0 1.1.9 2 2 2h4v-2m10.2-7c.1 0 .3.1.4.2l1.3 1.3c.2.2.2.6 0 .8l-1 1-2.1-2.1 1-1c.1-.1.2-.2.4-.2m0 3.9L14.1 23H12v-2.1l6.1-6.1 2.1 2.1Z"/></svg>
</a>
2023-09-21 20:44:52 +08:00
<!--
Hack: check whether the content contains a h1 headline. If it doesn't, the
page title (or respectively site name) is used as the main headline.
-->
<!-- Page content -->
2023-08-19 22:07:40 +08:00
<h1 id="63">6.3 &nbsp; 哈希算法<a class="headerlink" href="#63" title="Permanent link">&para;</a></h1>
2023-07-24 03:03:58 +08:00
<p>在上两节中,我们了解了哈希表的工作原理和哈希冲突的处理方法。然而无论是开放寻址还是链地址法,<strong>它们只能保证哈希表可以在发生冲突时正常工作,但无法减少哈希冲突的发生</strong></p>
2023-09-21 20:44:52 +08:00
<p>如果哈希冲突过于频繁,哈希表的性能则会急剧劣化。如图 6-8 所示,对于链地址哈希表,理想情况下键值对平均分布在各个桶中,达到最佳查询效率;最差情况下所有键值对都被存储到同一个桶中,时间复杂度退化至 <span class="arithmatex">\(O(n)\)</span></p>
2023-09-22 13:08:10 +08:00
<p><a class="glightbox" href="../hash_algorithm.assets/hash_collision_best_worst_condition.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="哈希冲突的最佳与最差情况" src="../hash_algorithm.assets/hash_collision_best_worst_condition.png" /></a></p>
2023-09-21 20:44:52 +08:00
<p align="center"> 图 6-8 &nbsp; 哈希冲突的最佳与最差情况 </p>
2023-06-16 21:22:53 +08:00
2023-07-24 03:03:58 +08:00
<p><strong>键值对的分布情况由哈希函数决定</strong>。回忆哈希函数的计算步骤,先计算哈希值,再对数组长度取模:</p>
2023-06-16 21:22:53 +08:00
<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nv">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span>hash<span class="o">(</span>key<span class="o">)</span><span class="w"> </span>%<span class="w"> </span>capacity
</code></pre></div>
2023-07-24 03:03:58 +08:00
<p>观察以上公式,当哈希表容量 <code>capacity</code> 固定时,<strong>哈希算法 <code>hash()</code> 决定了输出值</strong>,进而决定了键值对在哈希表中的分布情况。</p>
<p>这意味着,为了减小哈希冲突的发生概率,我们应当将注意力集中在哈希算法 <code>hash()</code> 的设计上。</p>
2023-08-19 22:07:40 +08:00
<h2 id="631">6.3.1 &nbsp; 哈希算法的目标<a class="headerlink" href="#631" title="Permanent link">&para;</a></h2>
2023-08-27 23:41:10 +08:00
<p>为了实现“既快又稳”的哈希表数据结构,哈希算法应包含以下特点。</p>
2023-06-16 21:22:53 +08:00
<ul>
<li><strong>确定性</strong>:对于相同的输入,哈希算法应始终产生相同的输出。这样才能确保哈希表是可靠的。</li>
<li><strong>效率高</strong>:计算哈希值的过程应该足够快。计算开销越小,哈希表的实用性越高。</li>
<li><strong>均匀分布</strong>:哈希算法应使得键值对平均分布在哈希表中。分布越平均,哈希冲突的概率就越低。</li>
</ul>
2023-08-27 23:41:10 +08:00
<p>实际上,哈希算法除了可以用于实现哈希表,还广泛应用于其他领域中。</p>
2023-06-16 21:22:53 +08:00
<ul>
<li><strong>密码存储</strong>:为了保护用户密码的安全,系统通常不会直接存储用户的明文密码,而是存储密码的哈希值。当用户输入密码时,系统会对输入的密码计算哈希值,然后与存储的哈希值进行比较。如果两者匹配,那么密码就被视为正确。</li>
<li><strong>数据完整性检查</strong>:数据发送方可以计算数据的哈希值并将其一同发送;接收方可以重新计算接收到的数据的哈希值,并与接收到的哈希值进行比较。如果两者匹配,那么数据就被视为完整的。</li>
</ul>
2023-08-27 23:41:10 +08:00
<p>对于密码学的相关应用,为了防止从哈希值推导出原始密码等逆向工程,哈希算法需要具备更高等级的安全特性。</p>
2023-06-16 21:22:53 +08:00
<ul>
2023-10-04 02:45:10 +08:00
<li><strong>单向性</strong>:无法通过哈希值反推出关于输入数据的任何信息。</li>
2023-06-16 21:22:53 +08:00
<li><strong>抗碰撞性</strong>:应当极其困难找到两个不同的输入,使得它们的哈希值相同。</li>
<li><strong>雪崩效应</strong>:输入的微小变化应当导致输出的显著且不可预测的变化。</li>
</ul>
2023-07-24 03:03:58 +08:00
<p>请注意,<strong>“均匀分布”与“抗碰撞性”是两个独立的概念</strong>,满足均匀分布不一定满足抗碰撞性。例如,在随机输入 <code>key</code> 下,哈希函数 <code>key % 100</code> 可以产生均匀分布的输出。然而该哈希算法过于简单,所有后两位相等的 <code>key</code> 的输出都相同,因此我们可以很容易地从哈希值反推出可用的 <code>key</code> ,从而破解密码。</p>
2023-08-19 22:07:40 +08:00
<h2 id="632">6.3.2 &nbsp; 哈希算法的设计<a class="headerlink" href="#632" title="Permanent link">&para;</a></h2>
2023-08-27 23:41:10 +08:00
<p>哈希算法的设计是一个需要考虑许多因素的复杂问题。然而对于某些要求不高的场景,我们也能设计一些简单的哈希算法。</p>
2023-06-16 21:22:53 +08:00
<ul>
<li><strong>加法哈希</strong>:对输入的每个字符的 ASCII 码进行相加,将得到的总和作为哈希值。</li>
<li><strong>乘法哈希</strong>:利用了乘法的不相关性,每轮乘以一个常数,将各个字符的 ASCII 码累积到哈希值中。</li>
<li><strong>异或哈希</strong>:将输入数据的每个元素通过异或操作累积到一个哈希值中。</li>
<li><strong>旋转哈希</strong>:将每个字符的 ASCII 码累积到一个哈希值中,每次累积之前都会对哈希值进行旋转操作。</li>
</ul>
2023-09-04 03:17:06 +08:00
<div class="tabbed-set tabbed-alternate" data-tabs="1:12"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Zig</label></div>
2023-06-16 21:22:53 +08:00
<div class="tabbed-content">
<div class="tabbed-block">
2023-10-06 14:10:31 +08:00
<div class="highlight"><span class="filename">simple_hash.py</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="k">def</span> <span class="nf">add_hash</span><span class="p">(</span><span class="n">key</span><span class="p">:</span> <span class="nb">str</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;加法哈希&quot;&quot;&quot;</span>
<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a> <span class="nb">hash</span> <span class="o">=</span> <span class="mi">0</span>
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a> <span class="n">modulus</span> <span class="o">=</span> <span class="mi">1000000007</span>
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a> <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">key</span><span class="p">:</span>
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a> <span class="nb">hash</span> <span class="o">+=</span> <span class="nb">ord</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a> <span class="k">return</span> <span class="nb">hash</span> <span class="o">%</span> <span class="n">modulus</span>
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a>
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="k">def</span> <span class="nf">mul_hash</span><span class="p">(</span><span class="n">key</span><span class="p">:</span> <span class="nb">str</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;乘法哈希&quot;&quot;&quot;</span>
<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a> <span class="nb">hash</span> <span class="o">=</span> <span class="mi">0</span>
<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a> <span class="n">modulus</span> <span class="o">=</span> <span class="mi">1000000007</span>
<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a> <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">key</span><span class="p">:</span>
<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a> <span class="nb">hash</span> <span class="o">=</span> <span class="mi">31</span> <span class="o">*</span> <span class="nb">hash</span> <span class="o">+</span> <span class="nb">ord</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a> <span class="k">return</span> <span class="nb">hash</span> <span class="o">%</span> <span class="n">modulus</span>
<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a>
<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="k">def</span> <span class="nf">xor_hash</span><span class="p">(</span><span class="n">key</span><span class="p">:</span> <span class="nb">str</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</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="sd">&quot;&quot;&quot;异或哈希&quot;&quot;&quot;</span>
<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a> <span class="nb">hash</span> <span class="o">=</span> <span class="mi">0</span>
<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a> <span class="n">modulus</span> <span class="o">=</span> <span class="mi">1000000007</span>
<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a> <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">key</span><span class="p">:</span>
<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a> <span class="nb">hash</span> <span class="o">^=</span> <span class="nb">ord</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a> <span class="k">return</span> <span class="nb">hash</span> <span class="o">%</span> <span class="n">modulus</span>
<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a>
<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="k">def</span> <span class="nf">rot_hash</span><span class="p">(</span><span class="n">key</span><span class="p">:</span> <span class="nb">str</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;旋转哈希&quot;&quot;&quot;</span>
<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a> <span class="nb">hash</span> <span class="o">=</span> <span class="mi">0</span>
<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a> <span class="n">modulus</span> <span class="o">=</span> <span class="mi">1000000007</span>
<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a> <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">key</span><span class="p">:</span>
<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a> <span class="nb">hash</span> <span class="o">=</span> <span class="p">(</span><span class="nb">hash</span> <span class="o">&lt;&lt;</span> <span class="mi">4</span><span class="p">)</span> <span class="o">^</span> <span class="p">(</span><span class="nb">hash</span> <span class="o">&gt;&gt;</span> <span class="mi">28</span><span class="p">)</span> <span class="o">^</span> <span class="nb">ord</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
<a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a> <span class="k">return</span> <span class="nb">hash</span> <span class="o">%</span> <span class="n">modulus</span>
2023-06-16 21:22:53 +08:00
</code></pre></div>
</div>
<div class="tabbed-block">
2023-10-06 14:10:31 +08:00
<div class="highlight"><span class="filename">simple_hash.cpp</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 加法哈希 */</span>
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">addHash</span><span class="p">(</span><span class="n">string</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w"> </span><span class="kt">long</span><span class="w"> </span><span class="kt">long</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">unsigned</span><span class="w"> </span><span class="kt">char</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">hash</span><span class="p">;</span>
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="p">}</span>
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a>
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="cm">/* 乘法哈希 */</span>
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">mulHash</span><span class="p">(</span><span class="n">string</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w"> </span><span class="kt">long</span><span class="w"> </span><span class="kt">long</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">unsigned</span><span class="w"> </span><span class="kt">char</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="mi">31</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">hash</span><span class="p">;</span>
<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="p">}</span>
<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a>
<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="cm">/* 异或哈希 */</span>
<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="kt">int</span><span class="w"> </span><span class="nf">xorHash</span><span class="p">(</span><span class="n">string</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">unsigned</span><span class="w"> </span><span class="kt">char</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">^=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">c</span><span class="p">;</span>
<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">&amp;</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="p">}</span>
<a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a>
<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a><span class="cm">/* 旋转哈希 */</span>
<a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a><span class="kt">int</span><span class="w"> </span><span class="nf">rotHash</span><span class="p">(</span><span class="n">string</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-2-33" name="__codelineno-2-33" href="#__codelineno-2-33"></a><span class="w"> </span><span class="kt">long</span><span class="w"> </span><span class="kt">long</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-2-34" name="__codelineno-2-34" href="#__codelineno-2-34"></a><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
<a id="__codelineno-2-35" name="__codelineno-2-35" href="#__codelineno-2-35"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">unsigned</span><span class="w"> </span><span class="kt">char</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-2-36" name="__codelineno-2-36" href="#__codelineno-2-36"></a><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">((</span><span class="n">hash</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="mi">28</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
<a id="__codelineno-2-37" name="__codelineno-2-37" href="#__codelineno-2-37"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-2-38" name="__codelineno-2-38" href="#__codelineno-2-38"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">hash</span><span class="p">;</span>
<a id="__codelineno-2-39" name="__codelineno-2-39" href="#__codelineno-2-39"></a><span class="p">}</span>
2023-06-16 21:22:53 +08:00
</code></pre></div>
</div>
<div class="tabbed-block">
2023-10-06 14:10:31 +08:00
<div class="highlight"><span class="filename">simple_hash.java</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 加法哈希 */</span>
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">addHash</span><span class="p">(</span><span class="n">String</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w"> </span><span class="kt">long</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</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="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="na">toCharArray</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</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="p">}</span>
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="n">hash</span><span class="p">;</span>
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="p">}</span>
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a>
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="cm">/* 乘法哈希 */</span>
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">mulHash</span><span class="p">(</span><span class="n">String</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w"> </span><span class="kt">long</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w"> </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="na">toCharArray</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="mi">31</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="n">hash</span><span class="p">;</span>
<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="p">}</span>
<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a>
<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="cm">/* 异或哈希 */</span>
<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="kt">int</span><span class="w"> </span><span class="nf">xorHash</span><span class="p">(</span><span class="n">String</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a><span class="w"> </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</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="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="na">toCharArray</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">^=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="n">c</span><span class="p">;</span>
<a id="__codelineno-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></a><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="k">return</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">&amp;</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
<a id="__codelineno-3-29" name="__codelineno-3-29" href="#__codelineno-3-29"></a><span class="p">}</span>
<a id="__codelineno-3-30" name="__codelineno-3-30" href="#__codelineno-3-30"></a>
<a id="__codelineno-3-31" name="__codelineno-3-31" href="#__codelineno-3-31"></a><span class="cm">/* 旋转哈希 */</span>
<a id="__codelineno-3-32" name="__codelineno-3-32" href="#__codelineno-3-32"></a><span class="kt">int</span><span class="w"> </span><span class="nf">rotHash</span><span class="p">(</span><span class="n">String</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-33" name="__codelineno-3-33" href="#__codelineno-3-33"></a><span class="w"> </span><span class="kt">long</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-3-34" name="__codelineno-3-34" href="#__codelineno-3-34"></a><span class="w"> </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
<a id="__codelineno-3-35" name="__codelineno-3-35" href="#__codelineno-3-35"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="na">toCharArray</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="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">((</span><span class="n">hash</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="mi">28</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
<a id="__codelineno-3-37" name="__codelineno-3-37" href="#__codelineno-3-37"></a><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><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="n">hash</span><span class="p">;</span>
<a id="__codelineno-3-39" name="__codelineno-3-39" href="#__codelineno-3-39"></a><span class="p">}</span>
2023-06-16 21:22:53 +08:00
</code></pre></div>
</div>
<div class="tabbed-block">
2023-10-06 14:10:31 +08:00
<div class="highlight"><span class="filename">simple_hash.cs</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 加法哈希 */</span>
2023-10-08 01:43:42 +08:00
<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">AddHash</span><span class="p">(</span><span class="kt">string</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
2023-10-06 14:10:31 +08:00
<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w"> </span><span class="kt">long</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1000000007</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="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</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="p">}</span>
<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">hash</span><span class="p">;</span>
<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="p">}</span>
<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a>
<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="cm">/* 乘法哈希 */</span>
2023-10-08 01:43:42 +08:00
<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">MulHash</span><span class="p">(</span><span class="kt">string</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
2023-10-06 14:10:31 +08:00
<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w"> </span><span class="kt">long</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1000000007</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="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="m">31</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">hash</span><span class="p">;</span>
<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="p">}</span>
<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a>
<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="cm">/* 异或哈希 */</span>
2023-10-08 01:43:42 +08:00
<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="kt">int</span><span class="w"> </span><span class="nf">XorHash</span><span class="p">(</span><span class="kt">string</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
2023-10-06 14:10:31 +08:00
<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1000000007</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="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">^=</span><span class="w"> </span><span class="n">c</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="k">return</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">&amp;</span><span class="w"> </span><span class="n">MODULUS</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">/* 旋转哈希 */</span>
2023-10-08 01:43:42 +08:00
<a id="__codelineno-4-32" name="__codelineno-4-32" href="#__codelineno-4-32"></a><span class="kt">int</span><span class="w"> </span><span class="nf">RotHash</span><span class="p">(</span><span class="kt">string</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
2023-10-06 14:10:31 +08:00
<a id="__codelineno-4-33" name="__codelineno-4-33" href="#__codelineno-4-33"></a><span class="w"> </span><span class="kt">long</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
<a id="__codelineno-4-34" name="__codelineno-4-34" href="#__codelineno-4-34"></a><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1000000007</span><span class="p">;</span>
<a id="__codelineno-4-35" name="__codelineno-4-35" href="#__codelineno-4-35"></a><span class="w"> </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-36" name="__codelineno-4-36" href="#__codelineno-4-36"></a><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">((</span><span class="n">hash</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="m">4</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="m">28</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
<a id="__codelineno-4-37" name="__codelineno-4-37" href="#__codelineno-4-37"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-4-38" name="__codelineno-4-38" href="#__codelineno-4-38"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">hash</span><span class="p">;</span>
<a id="__codelineno-4-39" name="__codelineno-4-39" href="#__codelineno-4-39"></a><span class="p">}</span>
2023-06-16 21:22:53 +08:00
</code></pre></div>
</div>
<div class="tabbed-block">
2023-10-06 14:10:31 +08:00
<div class="highlight"><span class="filename">simple_hash.go</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 加法哈希 */</span>
<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">addHash</span><span class="p">(</span><span class="nx">key</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="kt">int64</span>
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nx">modulus</span><span class="w"> </span><span class="kt">int64</span>
<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a>
<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w"> </span><span class="nx">modulus</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1000000007</span>
<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="p">[]</span><span class="nb">byte</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="nx">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nb">int64</span><span class="p">(</span><span class="nx">b</span><span class="p">))</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="nx">modulus</span>
<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w"> </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="k">return</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">hash</span><span class="p">)</span>
<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="p">}</span>
<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a>
<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="cm">/* 乘法哈希 */</span>
<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="kd">func</span><span class="w"> </span><span class="nx">mulHash</span><span class="p">(</span><span class="nx">key</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="kt">int64</span>
<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nx">modulus</span><span class="w"> </span><span class="kt">int64</span>
<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a>
<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w"> </span><span class="nx">modulus</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1000000007</span>
<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="p">[]</span><span class="nb">byte</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="mi">31</span><span class="o">*</span><span class="nx">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nb">int64</span><span class="p">(</span><span class="nx">b</span><span class="p">))</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="nx">modulus</span>
<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">hash</span><span class="p">)</span>
<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a><span class="p">}</span>
<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a>
<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a><span class="cm">/* 异或哈希 */</span>
<a id="__codelineno-5-26" name="__codelineno-5-26" href="#__codelineno-5-26"></a><span class="kd">func</span><span class="w"> </span><span class="nx">xorHash</span><span class="p">(</span><span class="nx">key</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-27" name="__codelineno-5-27" href="#__codelineno-5-27"></a><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-5-28" name="__codelineno-5-28" href="#__codelineno-5-28"></a><span class="w"> </span><span class="nx">modulus</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1000000007</span>
<a id="__codelineno-5-29" name="__codelineno-5-29" href="#__codelineno-5-29"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="p">[]</span><span class="nb">byte</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-30" name="__codelineno-5-30" href="#__codelineno-5-30"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="nb">int</span><span class="p">(</span><span class="nx">b</span><span class="p">))</span>
<a id="__codelineno-5-31" name="__codelineno-5-31" href="#__codelineno-5-31"></a><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="p">^=</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">b</span><span class="p">)</span>
<a id="__codelineno-5-32" name="__codelineno-5-32" href="#__codelineno-5-32"></a><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="mi">31</span><span class="o">*</span><span class="nx">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">b</span><span class="p">))</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="nx">modulus</span>
<a id="__codelineno-5-33" name="__codelineno-5-33" href="#__codelineno-5-33"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-5-34" name="__codelineno-5-34" href="#__codelineno-5-34"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">&amp;</span><span class="w"> </span><span class="nx">modulus</span>
<a id="__codelineno-5-35" name="__codelineno-5-35" href="#__codelineno-5-35"></a><span class="p">}</span>
<a id="__codelineno-5-36" name="__codelineno-5-36" href="#__codelineno-5-36"></a>
<a id="__codelineno-5-37" name="__codelineno-5-37" href="#__codelineno-5-37"></a><span class="cm">/* 旋转哈希 */</span>
<a id="__codelineno-5-38" name="__codelineno-5-38" href="#__codelineno-5-38"></a><span class="kd">func</span><span class="w"> </span><span class="nx">rotHash</span><span class="p">(</span><span class="nx">key</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-39" name="__codelineno-5-39" href="#__codelineno-5-39"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="kt">int64</span>
<a id="__codelineno-5-40" name="__codelineno-5-40" href="#__codelineno-5-40"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nx">modulus</span><span class="w"> </span><span class="kt">int64</span>
<a id="__codelineno-5-41" name="__codelineno-5-41" href="#__codelineno-5-41"></a>
<a id="__codelineno-5-42" name="__codelineno-5-42" href="#__codelineno-5-42"></a><span class="w"> </span><span class="nx">modulus</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1000000007</span>
<a id="__codelineno-5-43" name="__codelineno-5-43" href="#__codelineno-5-43"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="p">[]</span><span class="nb">byte</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-44" name="__codelineno-5-44" href="#__codelineno-5-44"></a><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">((</span><span class="nx">hash</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span><span class="w"> </span><span class="p">^</span><span class="w"> </span><span class="p">(</span><span class="nx">hash</span><span class="w"> </span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="mi">28</span><span class="p">)</span><span class="w"> </span><span class="p">^</span><span class="w"> </span><span class="nb">int64</span><span class="p">(</span><span class="nx">b</span><span class="p">))</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="nx">modulus</span>
<a id="__codelineno-5-45" name="__codelineno-5-45" href="#__codelineno-5-45"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-5-46" name="__codelineno-5-46" href="#__codelineno-5-46"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">hash</span><span class="p">)</span>
<a id="__codelineno-5-47" name="__codelineno-5-47" href="#__codelineno-5-47"></a><span class="p">}</span>
2023-06-16 21:22:53 +08:00
</code></pre></div>
</div>
<div class="tabbed-block">
2023-10-06 14:10:31 +08:00
<div class="highlight"><span class="filename">simple_hash.swift</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 加法哈希 */</span>
<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">func</span> <span class="nf">addHash</span><span class="p">(</span><span class="n">key</span><span class="p">:</span> <span class="nb">String</span><span class="p">)</span> <span class="p">-&gt;</span> <span class="nb">Int</span> <span class="p">{</span>
<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a> <span class="kd">var</span> <span class="nv">hash</span> <span class="p">=</span> <span class="mi">0</span>
<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a> <span class="kd">let</span> <span class="nv">MODULUS</span> <span class="p">=</span> <span class="mi">1_000_000_007</span>
<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a> <span class="k">for</span> <span class="n">c</span> <span class="k">in</span> <span class="n">key</span> <span class="p">{</span>
<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a> <span class="k">for</span> <span class="n">scalar</span> <span class="k">in</span> <span class="n">c</span><span class="p">.</span><span class="n">unicodeScalars</span> <span class="p">{</span>
<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a> <span class="n">hash</span> <span class="p">=</span> <span class="p">(</span><span class="n">hash</span> <span class="o">+</span> <span class="nb">Int</span><span class="p">(</span><span class="n">scalar</span><span class="p">.</span><span class="n">value</span><span class="p">))</span> <span class="o">%</span> <span class="n">MODULUS</span>
<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a> <span class="p">}</span>
<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a> <span class="p">}</span>
<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a> <span class="k">return</span> <span class="n">hash</span>
<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="p">}</span>
<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a>
<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="cm">/* 乘法哈希 */</span>
<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="kd">func</span> <span class="nf">mulHash</span><span class="p">(</span><span class="n">key</span><span class="p">:</span> <span class="nb">String</span><span class="p">)</span> <span class="p">-&gt;</span> <span class="nb">Int</span> <span class="p">{</span>
<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a> <span class="kd">var</span> <span class="nv">hash</span> <span class="p">=</span> <span class="mi">0</span>
<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a> <span class="kd">let</span> <span class="nv">MODULUS</span> <span class="p">=</span> <span class="mi">1_000_000_007</span>
<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a> <span class="k">for</span> <span class="n">c</span> <span class="k">in</span> <span class="n">key</span> <span class="p">{</span>
<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a> <span class="k">for</span> <span class="n">scalar</span> <span class="k">in</span> <span class="n">c</span><span class="p">.</span><span class="n">unicodeScalars</span> <span class="p">{</span>
<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a> <span class="n">hash</span> <span class="p">=</span> <span class="p">(</span><span class="mi">31</span> <span class="o">*</span> <span class="n">hash</span> <span class="o">+</span> <span class="nb">Int</span><span class="p">(</span><span class="n">scalar</span><span class="p">.</span><span class="n">value</span><span class="p">))</span> <span class="o">%</span> <span class="n">MODULUS</span>
<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a> <span class="p">}</span>
<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a> <span class="p">}</span>
<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a> <span class="k">return</span> <span class="n">hash</span>
<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="p">}</span>
<a id="__codelineno-6-24" name="__codelineno-6-24" href="#__codelineno-6-24"></a>
<a id="__codelineno-6-25" name="__codelineno-6-25" href="#__codelineno-6-25"></a><span class="cm">/* 异或哈希 */</span>
<a id="__codelineno-6-26" name="__codelineno-6-26" href="#__codelineno-6-26"></a><span class="kd">func</span> <span class="nf">xorHash</span><span class="p">(</span><span class="n">key</span><span class="p">:</span> <span class="nb">String</span><span class="p">)</span> <span class="p">-&gt;</span> <span class="nb">Int</span> <span class="p">{</span>
<a id="__codelineno-6-27" name="__codelineno-6-27" href="#__codelineno-6-27"></a> <span class="kd">var</span> <span class="nv">hash</span> <span class="p">=</span> <span class="mi">0</span>
<a id="__codelineno-6-28" name="__codelineno-6-28" href="#__codelineno-6-28"></a> <span class="kd">let</span> <span class="nv">MODULUS</span> <span class="p">=</span> <span class="mi">1_000_000_007</span>
<a id="__codelineno-6-29" name="__codelineno-6-29" href="#__codelineno-6-29"></a> <span class="k">for</span> <span class="n">c</span> <span class="k">in</span> <span class="n">key</span> <span class="p">{</span>
<a id="__codelineno-6-30" name="__codelineno-6-30" href="#__codelineno-6-30"></a> <span class="k">for</span> <span class="n">scalar</span> <span class="k">in</span> <span class="n">c</span><span class="p">.</span><span class="n">unicodeScalars</span> <span class="p">{</span>
<a id="__codelineno-6-31" name="__codelineno-6-31" href="#__codelineno-6-31"></a> <span class="n">hash</span> <span class="o">^=</span> <span class="nb">Int</span><span class="p">(</span><span class="n">scalar</span><span class="p">.</span><span class="n">value</span><span class="p">)</span>
<a id="__codelineno-6-32" name="__codelineno-6-32" href="#__codelineno-6-32"></a> <span class="p">}</span>
<a id="__codelineno-6-33" name="__codelineno-6-33" href="#__codelineno-6-33"></a> <span class="p">}</span>
<a id="__codelineno-6-34" name="__codelineno-6-34" href="#__codelineno-6-34"></a> <span class="k">return</span> <span class="n">hash</span> <span class="o">&amp;</span> <span class="n">MODULUS</span>
<a id="__codelineno-6-35" name="__codelineno-6-35" href="#__codelineno-6-35"></a><span class="p">}</span>
<a id="__codelineno-6-36" name="__codelineno-6-36" href="#__codelineno-6-36"></a>
<a id="__codelineno-6-37" name="__codelineno-6-37" href="#__codelineno-6-37"></a><span class="cm">/* 旋转哈希 */</span>
<a id="__codelineno-6-38" name="__codelineno-6-38" href="#__codelineno-6-38"></a><span class="kd">func</span> <span class="nf">rotHash</span><span class="p">(</span><span class="n">key</span><span class="p">:</span> <span class="nb">String</span><span class="p">)</span> <span class="p">-&gt;</span> <span class="nb">Int</span> <span class="p">{</span>
<a id="__codelineno-6-39" name="__codelineno-6-39" href="#__codelineno-6-39"></a> <span class="kd">var</span> <span class="nv">hash</span> <span class="p">=</span> <span class="mi">0</span>
<a id="__codelineno-6-40" name="__codelineno-6-40" href="#__codelineno-6-40"></a> <span class="kd">let</span> <span class="nv">MODULUS</span> <span class="p">=</span> <span class="mi">1_000_000_007</span>
<a id="__codelineno-6-41" name="__codelineno-6-41" href="#__codelineno-6-41"></a> <span class="k">for</span> <span class="n">c</span> <span class="k">in</span> <span class="n">key</span> <span class="p">{</span>
<a id="__codelineno-6-42" name="__codelineno-6-42" href="#__codelineno-6-42"></a> <span class="k">for</span> <span class="n">scalar</span> <span class="k">in</span> <span class="n">c</span><span class="p">.</span><span class="n">unicodeScalars</span> <span class="p">{</span>
<a id="__codelineno-6-43" name="__codelineno-6-43" href="#__codelineno-6-43"></a> <span class="n">hash</span> <span class="p">=</span> <span class="p">((</span><span class="n">hash</span> <span class="o">&lt;&lt;</span> <span class="mi">4</span><span class="p">)</span> <span class="o">^</span> <span class="p">(</span><span class="n">hash</span> <span class="o">&gt;&gt;</span> <span class="mi">28</span><span class="p">)</span> <span class="o">^</span> <span class="nb">Int</span><span class="p">(</span><span class="n">scalar</span><span class="p">.</span><span class="n">value</span><span class="p">))</span> <span class="o">%</span> <span class="n">MODULUS</span>
<a id="__codelineno-6-44" name="__codelineno-6-44" href="#__codelineno-6-44"></a> <span class="p">}</span>
<a id="__codelineno-6-45" name="__codelineno-6-45" href="#__codelineno-6-45"></a> <span class="p">}</span>
<a id="__codelineno-6-46" name="__codelineno-6-46" href="#__codelineno-6-46"></a> <span class="k">return</span> <span class="n">hash</span>
<a id="__codelineno-6-47" name="__codelineno-6-47" href="#__codelineno-6-47"></a><span class="p">}</span>
2023-06-16 21:22:53 +08:00
</code></pre></div>
</div>
<div class="tabbed-block">
2023-10-06 14:10:31 +08:00
<div class="highlight"><span class="filename">simple_hash.js</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 加法哈希 */</span>
<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">addHash</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1000000007</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="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="nx">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">c</span><span class="p">.</span><span class="nx">charCodeAt</span><span class="p">(</span><span class="mf">0</span><span class="p">))</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="nx">MODULUS</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="p">}</span>
<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">hash</span><span class="p">;</span>
<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="p">}</span>
<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a>
<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="cm">/* 乘法哈希 */</span>
<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">mulHash</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1000000007</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="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="mf">31</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">c</span><span class="p">.</span><span class="nx">charCodeAt</span><span class="p">(</span><span class="mf">0</span><span class="p">))</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="nx">MODULUS</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="p">}</span>
<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">hash</span><span class="p">;</span>
<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="p">}</span>
<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a>
<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="cm">/* 异或哈希 */</span>
<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="kd">function</span><span class="w"> </span><span class="nx">xorHash</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
<a id="__codelineno-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1000000007</span><span class="p">;</span>
<a id="__codelineno-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-7-26" name="__codelineno-7-26" href="#__codelineno-7-26"></a><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">^=</span><span class="w"> </span><span class="nx">c</span><span class="p">.</span><span class="nx">charCodeAt</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
<a id="__codelineno-7-27" name="__codelineno-7-27" href="#__codelineno-7-27"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-7-28" name="__codelineno-7-28" href="#__codelineno-7-28"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">&amp;</span><span class="w"> </span><span class="nx">MODULUS</span><span class="p">;</span>
<a id="__codelineno-7-29" name="__codelineno-7-29" href="#__codelineno-7-29"></a><span class="p">}</span>
<a id="__codelineno-7-30" name="__codelineno-7-30" href="#__codelineno-7-30"></a>
<a id="__codelineno-7-31" name="__codelineno-7-31" href="#__codelineno-7-31"></a><span class="cm">/* 旋转哈希 */</span>
<a id="__codelineno-7-32" name="__codelineno-7-32" href="#__codelineno-7-32"></a><span class="kd">function</span><span class="w"> </span><span class="nx">rotHash</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-7-33" name="__codelineno-7-33" href="#__codelineno-7-33"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
<a id="__codelineno-7-34" name="__codelineno-7-34" href="#__codelineno-7-34"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1000000007</span><span class="p">;</span>
<a id="__codelineno-7-35" name="__codelineno-7-35" href="#__codelineno-7-35"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-7-36" name="__codelineno-7-36" href="#__codelineno-7-36"></a><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">((</span><span class="nx">hash</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mf">4</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="p">(</span><span class="nx">hash</span><span class="w"> </span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="mf">28</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="nx">c</span><span class="p">.</span><span class="nx">charCodeAt</span><span class="p">(</span><span class="mf">0</span><span class="p">))</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="nx">MODULUS</span><span class="p">;</span>
<a id="__codelineno-7-37" name="__codelineno-7-37" href="#__codelineno-7-37"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-7-38" name="__codelineno-7-38" href="#__codelineno-7-38"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">hash</span><span class="p">;</span>
<a id="__codelineno-7-39" name="__codelineno-7-39" href="#__codelineno-7-39"></a><span class="p">}</span>
2023-06-16 21:22:53 +08:00
</code></pre></div>
</div>
<div class="tabbed-block">
2023-10-06 14:10:31 +08:00
<div class="highlight"><span class="filename">simple_hash.ts</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 加法哈希 */</span>
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">addHash</span><span class="p">(</span><span class="nx">key</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1000000007</span><span class="p">;</span>
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="nx">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">c</span><span class="p">.</span><span class="nx">charCodeAt</span><span class="p">(</span><span class="mf">0</span><span class="p">))</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="nx">MODULUS</span><span class="p">;</span>
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">hash</span><span class="p">;</span>
<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="p">}</span>
<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a>
<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="cm">/* 乘法哈希 */</span>
<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">mulHash</span><span class="p">(</span><span class="nx">key</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1000000007</span><span class="p">;</span>
<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="mf">31</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">c</span><span class="p">.</span><span class="nx">charCodeAt</span><span class="p">(</span><span class="mf">0</span><span class="p">))</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="nx">MODULUS</span><span class="p">;</span>
<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">hash</span><span class="p">;</span>
<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="p">}</span>
<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a>
<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="cm">/* 异或哈希 */</span>
<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a><span class="kd">function</span><span class="w"> </span><span class="nx">xorHash</span><span class="p">(</span><span class="nx">key</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-8-23" name="__codelineno-8-23" href="#__codelineno-8-23"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
<a id="__codelineno-8-24" name="__codelineno-8-24" href="#__codelineno-8-24"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1000000007</span><span class="p">;</span>
<a id="__codelineno-8-25" name="__codelineno-8-25" href="#__codelineno-8-25"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-8-26" name="__codelineno-8-26" href="#__codelineno-8-26"></a><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">^=</span><span class="w"> </span><span class="nx">c</span><span class="p">.</span><span class="nx">charCodeAt</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
<a id="__codelineno-8-27" name="__codelineno-8-27" href="#__codelineno-8-27"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-8-28" name="__codelineno-8-28" href="#__codelineno-8-28"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">&amp;</span><span class="w"> </span><span class="nx">MODULUS</span><span class="p">;</span>
<a id="__codelineno-8-29" name="__codelineno-8-29" href="#__codelineno-8-29"></a><span class="p">}</span>
<a id="__codelineno-8-30" name="__codelineno-8-30" href="#__codelineno-8-30"></a>
<a id="__codelineno-8-31" name="__codelineno-8-31" href="#__codelineno-8-31"></a><span class="cm">/* 旋转哈希 */</span>
<a id="__codelineno-8-32" name="__codelineno-8-32" href="#__codelineno-8-32"></a><span class="kd">function</span><span class="w"> </span><span class="nx">rotHash</span><span class="p">(</span><span class="nx">key</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-8-33" name="__codelineno-8-33" href="#__codelineno-8-33"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
<a id="__codelineno-8-34" name="__codelineno-8-34" href="#__codelineno-8-34"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1000000007</span><span class="p">;</span>
<a id="__codelineno-8-35" name="__codelineno-8-35" href="#__codelineno-8-35"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-8-36" name="__codelineno-8-36" href="#__codelineno-8-36"></a><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">((</span><span class="nx">hash</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mf">4</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="p">(</span><span class="nx">hash</span><span class="w"> </span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="mf">28</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="nx">c</span><span class="p">.</span><span class="nx">charCodeAt</span><span class="p">(</span><span class="mf">0</span><span class="p">))</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="nx">MODULUS</span><span class="p">;</span>
<a id="__codelineno-8-37" name="__codelineno-8-37" href="#__codelineno-8-37"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-8-38" name="__codelineno-8-38" href="#__codelineno-8-38"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">hash</span><span class="p">;</span>
<a id="__codelineno-8-39" name="__codelineno-8-39" href="#__codelineno-8-39"></a><span class="p">}</span>
2023-06-16 21:22:53 +08:00
</code></pre></div>
</div>
<div class="tabbed-block">
2023-10-06 14:10:31 +08:00
<div class="highlight"><span class="filename">simple_hash.dart</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 加法哈希 */</span>
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">addHash</span><span class="p">(</span><span class="kt">String</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w"> </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1000000007</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="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="n">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="n">codeUnitAt</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">MODULUS</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="p">}</span>
<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">hash</span><span class="p">;</span>
<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="p">}</span>
<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a>
<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="cm">/* 乘法哈希 */</span>
<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="kt">int</span><span class="w"> </span><span class="n">mulHash</span><span class="p">(</span><span class="kt">String</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </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="kt">int</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w"> </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1000000007</span><span class="p">;</span>
<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="n">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="m">31</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="n">codeUnitAt</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">MODULUS</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="p">}</span>
<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">hash</span><span class="p">;</span>
<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="p">}</span>
<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a>
<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="cm">/* 异或哈希 */</span>
<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="kt">int</span><span class="w"> </span><span class="n">xorHash</span><span class="p">(</span><span class="kt">String</span><span class="w"> </span><span class="n">key</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="kt">int</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a><span class="w"> </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1000000007</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="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="n">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">^=</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="n">codeUnitAt</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
<a id="__codelineno-9-27" name="__codelineno-9-27" href="#__codelineno-9-27"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-9-28" name="__codelineno-9-28" href="#__codelineno-9-28"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">&amp;</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
<a id="__codelineno-9-29" name="__codelineno-9-29" href="#__codelineno-9-29"></a><span class="p">}</span>
<a id="__codelineno-9-30" name="__codelineno-9-30" href="#__codelineno-9-30"></a>
<a id="__codelineno-9-31" name="__codelineno-9-31" href="#__codelineno-9-31"></a><span class="cm">/* 旋转哈希 */</span>
<a id="__codelineno-9-32" name="__codelineno-9-32" href="#__codelineno-9-32"></a><span class="kt">int</span><span class="w"> </span><span class="n">rotHash</span><span class="p">(</span><span class="kt">String</span><span class="w"> </span><span class="n">key</span><span class="p">)</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="kt">int</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
<a id="__codelineno-9-34" name="__codelineno-9-34" href="#__codelineno-9-34"></a><span class="w"> </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1000000007</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="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="n">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-9-36" name="__codelineno-9-36" href="#__codelineno-9-36"></a><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">((</span><span class="n">hash</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="m">4</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="m">28</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="n">codeUnitAt</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">MODULUS</span><span class="p">;</span>
<a id="__codelineno-9-37" name="__codelineno-9-37" href="#__codelineno-9-37"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-9-38" name="__codelineno-9-38" href="#__codelineno-9-38"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">hash</span><span class="p">;</span>
<a id="__codelineno-9-39" name="__codelineno-9-39" href="#__codelineno-9-39"></a><span class="p">}</span>
2023-06-16 21:22:53 +08:00
</code></pre></div>
</div>
<div class="tabbed-block">
2023-10-06 14:10:31 +08:00
<div class="highlight"><span class="filename">simple_hash.rs</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 加法哈希 */</span>
<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="k">fn</span> <span class="nf">add_hash</span><span class="p">(</span><span class="n">key</span>: <span class="kp">&amp;</span><span class="kt">str</span><span class="p">)</span><span class="w"> </span>-&gt; <span class="kt">i32</span> <span class="p">{</span>
<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0_</span><span class="k">i64</span><span class="p">;</span>
<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="n">MODULUS</span>: <span class="kt">i64</span> <span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a>
<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="n">chars</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i64</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a>
<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span>
<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="p">}</span><span class="w"> </span>
<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a>
<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="cm">/* 乘法哈希 */</span>
<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="k">fn</span> <span class="nf">mul_hash</span><span class="p">(</span><span class="n">key</span>: <span class="kp">&amp;</span><span class="kt">str</span><span class="p">)</span><span class="w"> </span>-&gt; <span class="kt">i32</span> <span class="p">{</span>
<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0_</span><span class="k">i64</span><span class="p">;</span>
<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="n">MODULUS</span>: <span class="kt">i64</span> <span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a>
<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="n">chars</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="mi">31</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i64</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a>
<a id="__codelineno-10-22" name="__codelineno-10-22" href="#__codelineno-10-22"></a><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span>
<a id="__codelineno-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="p">}</span>
<a id="__codelineno-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a>
<a id="__codelineno-10-25" name="__codelineno-10-25" href="#__codelineno-10-25"></a><span class="cm">/* 异或哈希 */</span>
<a id="__codelineno-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></a><span class="k">fn</span> <span class="nf">xor_hash</span><span class="p">(</span><span class="n">key</span>: <span class="kp">&amp;</span><span class="kt">str</span><span class="p">)</span><span class="w"> </span>-&gt; <span class="kt">i32</span> <span class="p">{</span>
<a id="__codelineno-10-27" name="__codelineno-10-27" href="#__codelineno-10-27"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0_</span><span class="k">i64</span><span class="p">;</span>
<a id="__codelineno-10-28" name="__codelineno-10-28" href="#__codelineno-10-28"></a><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="n">MODULUS</span>: <span class="kt">i64</span> <span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
<a id="__codelineno-10-29" name="__codelineno-10-29" href="#__codelineno-10-29"></a>
<a id="__codelineno-10-30" name="__codelineno-10-30" href="#__codelineno-10-30"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="n">chars</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-10-31" name="__codelineno-10-31" href="#__codelineno-10-31"></a><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">^=</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i64</span><span class="p">;</span>
<a id="__codelineno-10-32" name="__codelineno-10-32" href="#__codelineno-10-32"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-10-33" name="__codelineno-10-33" href="#__codelineno-10-33"></a>
<a id="__codelineno-10-34" name="__codelineno-10-34" href="#__codelineno-10-34"></a><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">&amp;</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">)</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span>
<a id="__codelineno-10-35" name="__codelineno-10-35" href="#__codelineno-10-35"></a><span class="p">}</span>
<a id="__codelineno-10-36" name="__codelineno-10-36" href="#__codelineno-10-36"></a>
<a id="__codelineno-10-37" name="__codelineno-10-37" href="#__codelineno-10-37"></a><span class="cm">/* 旋转哈希 */</span>
<a id="__codelineno-10-38" name="__codelineno-10-38" href="#__codelineno-10-38"></a><span class="k">fn</span> <span class="nf">rot_hash</span><span class="p">(</span><span class="n">key</span>: <span class="kp">&amp;</span><span class="kt">str</span><span class="p">)</span><span class="w"> </span>-&gt; <span class="kt">i32</span> <span class="p">{</span>
<a id="__codelineno-10-39" name="__codelineno-10-39" href="#__codelineno-10-39"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0_</span><span class="k">i64</span><span class="p">;</span>
<a id="__codelineno-10-40" name="__codelineno-10-40" href="#__codelineno-10-40"></a><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="n">MODULUS</span>: <span class="kt">i64</span> <span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
<a id="__codelineno-10-41" name="__codelineno-10-41" href="#__codelineno-10-41"></a>
<a id="__codelineno-10-42" name="__codelineno-10-42" href="#__codelineno-10-42"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="n">chars</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-10-43" name="__codelineno-10-43" href="#__codelineno-10-43"></a><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">((</span><span class="n">hash</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="mi">28</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i64</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
<a id="__codelineno-10-44" name="__codelineno-10-44" href="#__codelineno-10-44"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-10-45" name="__codelineno-10-45" href="#__codelineno-10-45"></a>
<a id="__codelineno-10-46" name="__codelineno-10-46" href="#__codelineno-10-46"></a><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span>
<a id="__codelineno-10-47" name="__codelineno-10-47" href="#__codelineno-10-47"></a><span class="p">}</span>
2023-06-16 21:22:53 +08:00
</code></pre></div>
</div>
<div class="tabbed-block">
2023-10-06 14:10:31 +08:00
<div class="highlight"><span class="filename">simple_hash.c</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 加法哈希 */</span>
<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">addHash</span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="o">*</span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w"> </span><span class="kt">long</span><span class="w"> </span><span class="kt">long</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">strlen</span><span class="p">(</span><span class="n">key</span><span class="p">);</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="kt">unsigned</span><span class="w"> </span><span class="kt">char</span><span class="p">)</span><span class="n">key</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">MODULUS</span><span class="p">;</span>
<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">hash</span><span class="p">;</span>
<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="p">}</span>
<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a>
<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="cm">/* 乘法哈希 */</span>
<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">mulHash</span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="o">*</span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w"> </span><span class="kt">long</span><span class="w"> </span><span class="kt">long</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">strlen</span><span class="p">(</span><span class="n">key</span><span class="p">);</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="mi">31</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="kt">unsigned</span><span class="w"> </span><span class="kt">char</span><span class="p">)</span><span class="n">key</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">MODULUS</span><span class="p">;</span>
<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">hash</span><span class="p">;</span>
<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="p">}</span>
<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a>
<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="cm">/* 异或哈希 */</span>
<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></a><span class="kt">int</span><span class="w"> </span><span class="nf">xorHash</span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="o">*</span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
<a id="__codelineno-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></a>
<a id="__codelineno-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">strlen</span><span class="p">(</span><span class="n">key</span><span class="p">);</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-11-27" name="__codelineno-11-27" href="#__codelineno-11-27"></a><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">^=</span><span class="w"> </span><span class="p">(</span><span class="kt">unsigned</span><span class="w"> </span><span class="kt">char</span><span class="p">)</span><span class="n">key</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
<a id="__codelineno-11-28" name="__codelineno-11-28" href="#__codelineno-11-28"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-11-29" name="__codelineno-11-29" href="#__codelineno-11-29"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">&amp;</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
<a id="__codelineno-11-30" name="__codelineno-11-30" href="#__codelineno-11-30"></a><span class="p">}</span>
<a id="__codelineno-11-31" name="__codelineno-11-31" href="#__codelineno-11-31"></a>
<a id="__codelineno-11-32" name="__codelineno-11-32" href="#__codelineno-11-32"></a><span class="cm">/* 旋转哈希 */</span>
<a id="__codelineno-11-33" name="__codelineno-11-33" href="#__codelineno-11-33"></a><span class="kt">int</span><span class="w"> </span><span class="nf">rotHash</span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="o">*</span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-11-34" name="__codelineno-11-34" href="#__codelineno-11-34"></a><span class="w"> </span><span class="kt">long</span><span class="w"> </span><span class="kt">long</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-11-35" name="__codelineno-11-35" href="#__codelineno-11-35"></a><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
<a id="__codelineno-11-36" name="__codelineno-11-36" href="#__codelineno-11-36"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">strlen</span><span class="p">(</span><span class="n">key</span><span class="p">);</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-11-37" name="__codelineno-11-37" href="#__codelineno-11-37"></a><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">((</span><span class="n">hash</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="mi">28</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="p">(</span><span class="kt">unsigned</span><span class="w"> </span><span class="kt">char</span><span class="p">)</span><span class="n">key</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">MODULUS</span><span class="p">;</span>
<a id="__codelineno-11-38" name="__codelineno-11-38" href="#__codelineno-11-38"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-11-39" name="__codelineno-11-39" href="#__codelineno-11-39"></a>
<a id="__codelineno-11-40" name="__codelineno-11-40" href="#__codelineno-11-40"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">hash</span><span class="p">;</span>
<a id="__codelineno-11-41" name="__codelineno-11-41" href="#__codelineno-11-41"></a><span class="p">}</span>
2023-06-16 21:22:53 +08:00
</code></pre></div>
</div>
2023-07-26 10:57:52 +08:00
<div class="tabbed-block">
2023-09-04 03:17:06 +08:00
<div class="highlight"><span class="filename">simple_hash.zig</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">addHash</span><span class="p">}</span>
2023-07-26 10:57:52 +08:00
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
2023-09-04 03:17:06 +08:00
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">mulHash</span><span class="p">}</span>
2023-07-26 10:57:52 +08:00
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>
2023-09-04 03:17:06 +08:00
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">xorHash</span><span class="p">}</span>
2023-07-26 10:57:52 +08:00
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a>
2023-09-04 03:17:06 +08:00
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">rotHash</span><span class="p">}</span>
2023-07-26 10:57:52 +08:00
</code></pre></div>
</div>
2023-06-16 21:22:53 +08:00
</div>
</div>
2023-07-24 03:03:58 +08:00
<p>观察发现,每种哈希算法的最后一步都是对大质数 <span class="arithmatex">\(1000000007\)</span> 取模,以确保哈希值在合适的范围内。值得思考的是,为什么要强调对质数取模,或者说对合数取模的弊端是什么?这是一个有趣的问题。</p>
2023-06-16 21:22:53 +08:00
<p>先抛出结论:<strong>当我们使用大质数作为模数时,可以最大化地保证哈希值的均匀分布</strong>。因为质数不会与其他数字存在公约数,可以减少因取模操作而产生的周期性模式,从而避免哈希冲突。</p>
2023-08-27 23:41:10 +08:00
<p>举个例子,假设我们选择合数 <span class="arithmatex">\(9\)</span> 作为模数,它可以被 <span class="arithmatex">\(3\)</span> 整除。那么所有可以被 <span class="arithmatex">\(3\)</span> 整除的 <code>key</code> 都会被映射到 <span class="arithmatex">\(0\)</span><span class="arithmatex">\(3\)</span><span class="arithmatex">\(6\)</span> 这三个哈希值。</p>
2023-06-16 21:22:53 +08:00
<div class="arithmatex">\[
\begin{aligned}
\text{modulus} &amp; = 9 \newline
2023-08-21 03:56:52 +08:00
\text{key} &amp; = \{ 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, \dots \} \newline
\text{hash} &amp; = \{ 0, 3, 6, 0, 3, 6, 0, 3, 6, 0, 3, 6,\dots \}
2023-06-16 21:22:53 +08:00
\end{aligned}
\]</div>
<p>如果输入 <code>key</code> 恰好满足这种等差数列的数据分布,那么哈希值就会出现聚堆,从而加重哈希冲突。现在,假设将 <code>modulus</code> 替换为质数 <span class="arithmatex">\(13\)</span> ,由于 <code>key</code><code>modulus</code> 之间不存在公约数,输出的哈希值的均匀性会明显提升。</p>
<div class="arithmatex">\[
\begin{aligned}
\text{modulus} &amp; = 13 \newline
2023-08-21 03:56:52 +08:00
\text{key} &amp; = \{ 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, \dots \} \newline
\text{hash} &amp; = \{ 0, 3, 6, 9, 12, 2, 5, 8, 11, 1, 4, 7, \dots \}
2023-06-16 21:22:53 +08:00
\end{aligned}
\]</div>
2023-07-24 03:03:58 +08:00
<p>值得说明的是,如果能够保证 <code>key</code> 是随机均匀分布的,那么选择质数或者合数作为模数都是可以的,它们都能输出均匀分布的哈希值。而当 <code>key</code> 的分布存在某种周期性时,对合数取模更容易出现聚集现象。</p>
<p>总而言之,我们通常选取质数作为模数,并且这个质数最好足够大,以尽可能消除周期性模式,提升哈希算法的稳健性。</p>
2023-08-19 22:07:40 +08:00
<h2 id="633">6.3.3 &nbsp; 常见哈希算法<a class="headerlink" href="#633" title="Permanent link">&para;</a></h2>
2023-06-16 21:22:53 +08:00
<p>不难发现,以上介绍的简单哈希算法都比较“脆弱”,远远没有达到哈希算法的设计目标。例如,由于加法和异或满足交换律,因此加法哈希和异或哈希无法区分内容相同但顺序不同的字符串,这可能会加剧哈希冲突,并引起一些安全问题。</p>
2023-08-27 23:41:10 +08:00
<p>在实际中,我们通常会用一些标准哈希算法,例如 MD5、SHA-1、SHA-2、SHA3 等。它们可以将任意长度的输入数据映射到恒定长度的哈希值。</p>
2023-08-31 02:30:52 +08:00
<p>近一个世纪以来,哈希算法处在不断升级与优化的过程中。一部分研究人员努力提升哈希算法的性能,另一部分研究人员和黑客则致力于寻找哈希算法的安全性问题。表 6-2 展示了在实际应用中常见的哈希算法。</p>
2023-07-24 03:03:58 +08:00
<ul>
<li>MD5 和 SHA-1 已多次被成功攻击,因此它们被各类安全应用弃用。</li>
<li>SHA-2 系列中的 SHA-256 是最安全的哈希算法之一,仍未出现成功的攻击案例,因此常被用在各类安全应用与协议中。</li>
<li>SHA-3 相较 SHA-2 的实现开销更低、计算效率更高,但目前使用覆盖度不如 SHA-2 系列。</li>
</ul>
2023-08-31 02:30:52 +08:00
<p align="center"> 表 6-2 &nbsp; 常见的哈希算法 </p>
2023-08-19 19:21:30 +08:00
<div class="center-table">
2023-06-16 21:22:53 +08:00
<table>
<thead>
<tr>
<th></th>
<th>MD5</th>
<th>SHA-1</th>
<th>SHA-2</th>
<th>SHA-3</th>
</tr>
</thead>
<tbody>
<tr>
<td>推出时间</td>
<td>1992</td>
<td>1995</td>
<td>2002</td>
<td>2008</td>
</tr>
<tr>
<td>输出长度</td>
<td>128 bits</td>
<td>160 bits</td>
<td>256 / 512 bits</td>
<td>224/256/384/512 bits</td>
</tr>
<tr>
<td>哈希冲突</td>
<td>较多</td>
<td>较多</td>
<td>很少</td>
<td>很少</td>
</tr>
<tr>
<td>安全等级</td>
<td>低,已被成功攻击</td>
<td>低,已被成功攻击</td>
<td></td>
<td></td>
</tr>
<tr>
<td>应用</td>
<td>已被弃用,仍用于数据完整性检查</td>
<td>已被弃用</td>
<td>加密货币交易验证、数字签名等</td>
<td>可用于替代 SHA-2</td>
</tr>
</tbody>
</table>
2023-08-19 19:21:30 +08:00
</div>
2023-08-19 22:07:40 +08:00
<h2 id="634">6.3.4 &nbsp; 数据结构的哈希值<a class="headerlink" href="#634" title="Permanent link">&para;</a></h2>
2023-08-27 23:41:10 +08:00
<p>我们知道,哈希表的 <code>key</code> 可以是整数、小数或字符串等数据类型。编程语言通常会为这些数据类型提供内置的哈希算法,用于计算哈希表中的桶索引。以 Python 为例,我们可以调用 <code>hash()</code> 函数来计算各种数据类型的哈希值。</p>
2023-06-16 21:22:53 +08:00
<ul>
<li>整数和布尔量的哈希值就是其本身。</li>
<li>浮点数和字符串的哈希值计算较为复杂,有兴趣的同学请自行学习。</li>
<li>元组的哈希值是对其中每一个元素进行哈希,然后将这些哈希值组合起来,得到单一的哈希值。</li>
<li>对象的哈希值基于其内存地址生成。通过重写对象的哈希方法,可实现基于内容生成哈希值。</li>
</ul>
2023-06-21 19:26:17 +08:00
<div class="admonition tip">
<p class="admonition-title">Tip</p>
<p>请注意,不同编程语言的内置哈希值计算函数的定义和方法不同。</p>
</div>
2023-09-04 03:17:06 +08:00
<div class="tabbed-set tabbed-alternate" data-tabs="2:12"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Zig</label></div>
2023-06-16 21:22:53 +08:00
<div class="tabbed-content">
<div class="tabbed-block">
2023-09-04 03:17:06 +08:00
<div class="highlight"><span class="filename">built_in_hash.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="n">num</span> <span class="o">=</span> <span class="mi">3</span>
<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="n">hash_num</span> <span class="o">=</span> <span class="nb">hash</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="c1"># 整数 3 的哈希值为 3</span>
2023-06-21 19:26:17 +08:00
<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>
2023-09-04 03:17:06 +08:00
<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="n">bol</span> <span class="o">=</span> <span class="kc">True</span>
<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a><span class="n">hash_bol</span> <span class="o">=</span> <span class="nb">hash</span><span class="p">(</span><span class="n">bol</span><span class="p">)</span>
<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a><span class="c1"># 布尔量 True 的哈希值为 1</span>
2023-06-21 19:26:17 +08:00
<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>
2023-09-04 03:17:06 +08:00
<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="n">dec</span> <span class="o">=</span> <span class="mf">3.14159</span>
<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a><span class="n">hash_dec</span> <span class="o">=</span> <span class="nb">hash</span><span class="p">(</span><span class="n">dec</span><span class="p">)</span>
<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a><span class="c1"># 小数 3.14159 的哈希值为 326484311674566659</span>
2023-06-21 19:26:17 +08:00
<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a>
2023-09-04 03:17:06 +08:00
<a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a><span class="nb">str</span> <span class="o">=</span> <span class="s2">&quot;Hello 算法&quot;</span>
<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a><span class="n">hash_str</span> <span class="o">=</span> <span class="nb">hash</span><span class="p">(</span><span class="nb">str</span><span class="p">)</span>
<a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a><span class="c1"># 字符串 Hello 算法 的哈希值为 4617003410720528961</span>
2023-06-21 19:26:17 +08:00
<a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a>
2023-09-04 03:17:06 +08:00
<a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a><span class="n">tup</span> <span class="o">=</span> <span class="p">(</span><span class="mi">12836</span><span class="p">,</span> <span class="s2">&quot;小哈&quot;</span><span class="p">)</span>
<a id="__codelineno-13-18" name="__codelineno-13-18" href="#__codelineno-13-18"></a><span class="n">hash_tup</span> <span class="o">=</span> <span class="nb">hash</span><span class="p">(</span><span class="n">tup</span><span class="p">)</span>
<a id="__codelineno-13-19" name="__codelineno-13-19" href="#__codelineno-13-19"></a><span class="c1"># 元组 (12836, &#39;小哈&#39;) 的哈希值为 1029005403108185979</span>
2023-07-26 10:57:52 +08:00
<a id="__codelineno-13-20" name="__codelineno-13-20" href="#__codelineno-13-20"></a>
2023-09-04 03:17:06 +08:00
<a id="__codelineno-13-21" name="__codelineno-13-21" href="#__codelineno-13-21"></a><span class="n">obj</span> <span class="o">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-13-22" name="__codelineno-13-22" href="#__codelineno-13-22"></a><span class="n">hash_obj</span> <span class="o">=</span> <span class="nb">hash</span><span class="p">(</span><span class="n">obj</span><span class="p">)</span>
<a id="__codelineno-13-23" name="__codelineno-13-23" href="#__codelineno-13-23"></a><span class="c1"># 节点对象 &lt;ListNode object at 0x1058fd810&gt; 的哈希值为 274267521</span>
2023-06-16 21:22:53 +08:00
</code></pre></div>
</div>
<div class="tabbed-block">
2023-07-26 10:57:52 +08:00
<div class="highlight"><span class="filename">built_in_hash.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">size_t</span><span class="w"> </span><span class="n">hashNum</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hash</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">()(</span><span class="n">num</span><span class="p">);</span>
<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="c1">// 整数 3 的哈希值为 3</span>
2023-06-16 21:22:53 +08:00
<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a>
2023-07-26 10:57:52 +08:00
<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="kt">bool</span><span class="w"> </span><span class="n">bol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">true</span><span class="p">;</span>
<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="kt">size_t</span><span class="w"> </span><span class="n">hashBol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hash</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="p">()(</span><span class="n">bol</span><span class="p">);</span>
<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="c1">// 布尔量 1 的哈希值为 1</span>
2023-06-16 21:22:53 +08:00
<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a>
2023-07-26 10:57:52 +08:00
<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="kt">double</span><span class="w"> </span><span class="n">dec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">3.14159</span><span class="p">;</span>
<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="kt">size_t</span><span class="w"> </span><span class="n">hashDec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hash</span><span class="o">&lt;</span><span class="kt">double</span><span class="o">&gt;</span><span class="p">()(</span><span class="n">dec</span><span class="p">);</span>
<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="c1">// 小数 3.14159 的哈希值为 4614256650576692846</span>
2023-06-16 21:22:53 +08:00
<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a>
2023-07-26 10:57:52 +08:00
<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="n">string</span><span class="w"> </span><span class="n">str</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;Hello 算法&quot;</span><span class="p">;</span>
<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="kt">size_t</span><span class="w"> </span><span class="n">hashStr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hash</span><span class="o">&lt;</span><span class="n">string</span><span class="o">&gt;</span><span class="p">()(</span><span class="n">str</span><span class="p">);</span>
<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="c1">// 字符串 Hello 算法 的哈希值为 15466937326284535026</span>
2023-06-16 21:22:53 +08:00
<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a>
2023-07-26 10:57:52 +08:00
<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a><span class="c1">// 在 C++ 中,内置 std:hash() 仅提供基本数据类型的哈希值计算</span>
<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="c1">// 数组、对象的哈希值计算需要自行实现</span>
2023-06-16 21:22:53 +08:00
</code></pre></div>
</div>
<div class="tabbed-block">
2023-09-04 03:17:06 +08:00
<div class="highlight"><span class="filename">built_in_hash.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashNum</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Integer</span><span class="p">.</span><span class="na">hashCode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="c1">// 整数 3 的哈希值为 3</span>
2023-07-26 10:57:52 +08:00
<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a>
2023-09-04 03:17:06 +08:00
<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="kt">boolean</span><span class="w"> </span><span class="n">bol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span>
<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashBol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Boolean</span><span class="p">.</span><span class="na">hashCode</span><span class="p">(</span><span class="n">bol</span><span class="p">);</span>
<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="c1">// 布尔量 true 的哈希值为 1231</span>
2023-07-26 10:57:52 +08:00
<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a>
2023-09-04 03:17:06 +08:00
<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="kt">double</span><span class="w"> </span><span class="n">dec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">3.14159</span><span class="p">;</span>
<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashDec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Double</span><span class="p">.</span><span class="na">hashCode</span><span class="p">(</span><span class="n">dec</span><span class="p">);</span>
<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="c1">// 小数 3.14159 的哈希值为 -1340954729</span>
2023-07-26 10:57:52 +08:00
<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a>
2023-09-04 03:17:06 +08:00
<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="n">String</span><span class="w"> </span><span class="n">str</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;Hello 算法&quot;</span><span class="p">;</span>
<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashStr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">str</span><span class="p">.</span><span class="na">hashCode</span><span class="p">();</span>
<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="c1">// 字符串 Hello 算法 的哈希值为 -727081396</span>
2023-07-26 10:57:52 +08:00
<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a>
2023-09-04 03:17:06 +08:00
<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="n">Object</span><span class="o">[]</span><span class="w"> </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="mi">12836</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小哈&quot;</span><span class="w"> </span><span class="p">};</span>
<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashTup</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">hashCode</span><span class="p">(</span><span class="n">arr</span><span class="p">);</span>
<a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a><span class="c1">// 数组 [12836, 小哈] 的哈希值为 1151158</span>
2023-07-26 10:57:52 +08:00
<a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a>
2023-09-04 03:17:06 +08:00
<a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">obj</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
<a id="__codelineno-15-22" name="__codelineno-15-22" href="#__codelineno-15-22"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashObj</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">obj</span><span class="p">.</span><span class="na">hashCode</span><span class="p">();</span>
<a id="__codelineno-15-23" name="__codelineno-15-23" href="#__codelineno-15-23"></a><span class="c1">// 节点对象 utils.ListNode@7dc5e7b4 的哈希值为 2110121908</span>
2023-06-16 21:22:53 +08:00
</code></pre></div>
</div>
<div class="tabbed-block">
2023-09-04 03:17:06 +08:00
<div class="highlight"><span class="filename">built_in_hash.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">3</span><span class="p">;</span>
<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashNum</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">.</span><span class="n">GetHashCode</span><span class="p">();</span>
<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="c1">// 整数 3 的哈希值为 3;</span>
<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a>
<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="kt">bool</span><span class="w"> </span><span class="n">bol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">true</span><span class="p">;</span>
<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashBol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">bol</span><span class="p">.</span><span class="n">GetHashCode</span><span class="p">();</span>
<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="c1">// 布尔量 true 的哈希值为 1;</span>
<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a>
<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="kt">double</span><span class="w"> </span><span class="n">dec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">3.14159</span><span class="p">;</span>
<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashDec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dec</span><span class="p">.</span><span class="n">GetHashCode</span><span class="p">();</span>
<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="c1">// 小数 3.14159 的哈希值为 -1340954729;</span>
<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a>
<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="kt">string</span><span class="w"> </span><span class="n">str</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;Hello 算法&quot;</span><span class="p">;</span>
<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashStr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">str</span><span class="p">.</span><span class="n">GetHashCode</span><span class="p">();</span>
<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="c1">// 字符串 Hello 算法 的哈希值为 -586107568;</span>
<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a>
<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="kt">object</span><span class="p">[]</span><span class="w"> </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="m">12836</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小哈&quot;</span><span class="w"> </span><span class="p">};</span>
<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashTup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">.</span><span class="n">GetHashCode</span><span class="p">();</span>
<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="c1">// 数组 [12836, 小哈] 的哈希值为 42931033;</span>
<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a>
2023-10-08 01:43:42 +08:00
<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">obj</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
2023-09-04 03:17:06 +08:00
<a id="__codelineno-16-22" name="__codelineno-16-22" href="#__codelineno-16-22"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashObj</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">obj</span><span class="p">.</span><span class="n">GetHashCode</span><span class="p">();</span>
<a id="__codelineno-16-23" name="__codelineno-16-23" href="#__codelineno-16-23"></a><span class="c1">// 节点对象 0 的哈希值为 39053774;</span>
2023-06-16 21:22:53 +08:00
</code></pre></div>
</div>
<div class="tabbed-block">
2023-09-04 03:17:06 +08:00
<div class="highlight"><span class="filename">built_in_hash.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a>
2023-06-16 21:22:53 +08:00
</code></pre></div>
</div>
<div class="tabbed-block">
2023-09-04 03:17:06 +08:00
<div class="highlight"><span class="filename">built_in_hash.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="kd">let</span> <span class="nv">num</span> <span class="p">=</span> <span class="mi">3</span>
<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">let</span> <span class="nv">hashNum</span> <span class="p">=</span> <span class="n">num</span><span class="p">.</span><span class="n">hashValue</span>
<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="c1">// 整数 3 的哈希值为 9047044699613009734</span>
<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a>
<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="kd">let</span> <span class="nv">bol</span> <span class="p">=</span> <span class="kc">true</span>
<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="kd">let</span> <span class="nv">hashBol</span> <span class="p">=</span> <span class="n">bol</span><span class="p">.</span><span class="n">hashValue</span>
<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="c1">// 布尔量 true 的哈希值为 -4431640247352757451</span>
<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a>
<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="kd">let</span> <span class="nv">dec</span> <span class="p">=</span> <span class="mf">3.14159</span>
<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="kd">let</span> <span class="nv">hashDec</span> <span class="p">=</span> <span class="n">dec</span><span class="p">.</span><span class="n">hashValue</span>
<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="c1">// 小数 3.14159 的哈希值为 -2465384235396674631</span>
<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a>
<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="kd">let</span> <span class="nv">str</span> <span class="p">=</span> <span class="s">&quot;Hello 算法&quot;</span>
<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="kd">let</span> <span class="nv">hashStr</span> <span class="p">=</span> <span class="n">str</span><span class="p">.</span><span class="n">hashValue</span>
<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a><span class="c1">// 字符串 Hello 算法 的哈希值为 -7850626797806988787</span>
<a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></a>
<a id="__codelineno-18-17" name="__codelineno-18-17" href="#__codelineno-18-17"></a><span class="kd">let</span> <span class="nv">arr</span> <span class="p">=</span> <span class="p">[</span><span class="n">AnyHashable</span><span class="p">(</span><span class="mi">12836</span><span class="p">),</span> <span class="n">AnyHashable</span><span class="p">(</span><span class="s">&quot;小哈&quot;</span><span class="p">)]</span>
<a id="__codelineno-18-18" name="__codelineno-18-18" href="#__codelineno-18-18"></a><span class="kd">let</span> <span class="nv">hashTup</span> <span class="p">=</span> <span class="n">arr</span><span class="p">.</span><span class="n">hashValue</span>
<a id="__codelineno-18-19" name="__codelineno-18-19" href="#__codelineno-18-19"></a><span class="c1">// 数组 [AnyHashable(12836), AnyHashable(&quot;小哈&quot;)] 的哈希值为 -2308633508154532996</span>
<a id="__codelineno-18-20" name="__codelineno-18-20" href="#__codelineno-18-20"></a>
<a id="__codelineno-18-21" name="__codelineno-18-21" href="#__codelineno-18-21"></a><span class="kd">let</span> <span class="nv">obj</span> <span class="p">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span> <span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-18-22" name="__codelineno-18-22" href="#__codelineno-18-22"></a><span class="kd">let</span> <span class="nv">hashObj</span> <span class="p">=</span> <span class="n">obj</span><span class="p">.</span><span class="n">hashValue</span>
<a id="__codelineno-18-23" name="__codelineno-18-23" href="#__codelineno-18-23"></a><span class="c1">// 节点对象 utils.ListNode 的哈希值为 -2434780518035996159</span>
2023-06-16 21:22:53 +08:00
</code></pre></div>
</div>
<div class="tabbed-block">
2023-09-04 03:17:06 +08:00
<div class="highlight"><span class="filename">built_in_hash.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="c1">// JavaScript 未提供内置 hash code 函数</span>
2023-06-16 21:22:53 +08:00
</code></pre></div>
</div>
<div class="tabbed-block">
2023-09-04 03:17:06 +08:00
<div class="highlight"><span class="filename">built_in_hash.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="c1">// TypeScript 未提供内置 hash code 函数</span>
2023-07-26 10:57:52 +08:00
</code></pre></div>
</div>
<div class="tabbed-block">
2023-09-04 03:17:06 +08:00
<div class="highlight"><span class="filename">built_in_hash.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="kt">int</span><span class="w"> </span><span class="kt">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">3</span><span class="p">;</span>
<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashNum</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kt">num</span><span class="p">.</span><span class="n">hashCode</span><span class="p">;</span>
<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="c1">// 整数 3 的哈希值为 34803</span>
2023-07-26 10:57:52 +08:00
<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a>
2023-09-04 03:17:06 +08:00
<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="kt">bool</span><span class="w"> </span><span class="n">bol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span>
<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashBol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">bol</span><span class="p">.</span><span class="n">hashCode</span><span class="p">;</span>
<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="c1">// 布尔值 true 的哈希值为 1231</span>
2023-07-26 10:57:52 +08:00
<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a>
2023-09-04 03:17:06 +08:00
<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="kt">double</span><span class="w"> </span><span class="n">dec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">3.14159</span><span class="p">;</span>
<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashDec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dec</span><span class="p">.</span><span class="n">hashCode</span><span class="p">;</span>
<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="c1">// 小数 3.14159 的哈希值为 2570631074981783</span>
2023-07-26 10:57:52 +08:00
<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a>
2023-09-04 03:17:06 +08:00
<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="kt">String</span><span class="w"> </span><span class="n">str</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;Hello 算法&quot;</span><span class="p">;</span>
<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashStr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">str</span><span class="p">.</span><span class="n">hashCode</span><span class="p">;</span>
<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a><span class="c1">// 字符串 Hello 算法 的哈希值为 468167534</span>
2023-07-26 10:57:52 +08:00
<a id="__codelineno-21-16" name="__codelineno-21-16" href="#__codelineno-21-16"></a>
2023-09-04 03:17:06 +08:00
<a id="__codelineno-21-17" name="__codelineno-21-17" href="#__codelineno-21-17"></a><span class="n">List</span><span class="w"> </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="m">12836</span><span class="p">,</span><span class="w"> </span><span class="s2">&quot;小哈&quot;</span><span class="p">];</span>
<a id="__codelineno-21-18" name="__codelineno-21-18" href="#__codelineno-21-18"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashArr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">.</span><span class="n">hashCode</span><span class="p">;</span>
<a id="__codelineno-21-19" name="__codelineno-21-19" href="#__codelineno-21-19"></a><span class="c1">// 数组 [12836, 小哈] 的哈希值为 976512528</span>
2023-07-26 10:57:52 +08:00
<a id="__codelineno-21-20" name="__codelineno-21-20" href="#__codelineno-21-20"></a>
2023-09-04 03:17:06 +08:00
<a id="__codelineno-21-21" name="__codelineno-21-21" href="#__codelineno-21-21"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">obj</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
<a id="__codelineno-21-22" name="__codelineno-21-22" href="#__codelineno-21-22"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashObj</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">obj</span><span class="p">.</span><span class="n">hashCode</span><span class="p">;</span>
<a id="__codelineno-21-23" name="__codelineno-21-23" href="#__codelineno-21-23"></a><span class="c1">// 节点对象 Instance of &#39;ListNode&#39; 的哈希值为 1033450432</span>
2023-07-26 10:57:52 +08:00
</code></pre></div>
</div>
<div class="tabbed-block">
2023-10-03 03:50:07 +08:00
<div class="highlight"><span class="filename">built_in_hash.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span>::<span class="n">collections</span>::<span class="n">hash_map</span>::<span class="n">DefaultHasher</span><span class="p">;</span>
<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span>::<span class="n">hash</span>::<span class="p">{</span><span class="n">Hash</span><span class="p">,</span><span class="w"> </span><span class="n">Hasher</span><span class="p">};</span>
<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a>
<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="kd">let</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">num_hasher</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">DefaultHasher</span>::<span class="n">new</span><span class="p">();</span>
<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="n">num</span><span class="p">.</span><span class="n">hash</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">num_hasher</span><span class="p">);</span>
<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="kd">let</span><span class="w"> </span><span class="n">hash_num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num_hasher</span><span class="p">.</span><span class="n">finish</span><span class="p">();</span>
<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="c1">// 整数 3 的哈希值为 568126464209439262</span>
<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a>
<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="kd">let</span><span class="w"> </span><span class="n">bol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span>
<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">bol_hasher</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">DefaultHasher</span>::<span class="n">new</span><span class="p">();</span>
<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="n">bol</span><span class="p">.</span><span class="n">hash</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">bol_hasher</span><span class="p">);</span>
<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="kd">let</span><span class="w"> </span><span class="n">hash_bol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">bol_hasher</span><span class="p">.</span><span class="n">finish</span><span class="p">();</span>
<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="c1">// 布尔量 true 的哈希值为 4952851536318644461</span>
<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a>
<a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a><span class="kd">let</span><span class="w"> </span><span class="n">dec</span>: <span class="kt">f32</span> <span class="o">=</span><span class="w"> </span><span class="mf">3.14159</span><span class="p">;</span>
<a id="__codelineno-22-17" name="__codelineno-22-17" href="#__codelineno-22-17"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">dec_hasher</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">DefaultHasher</span>::<span class="n">new</span><span class="p">();</span>
<a id="__codelineno-22-18" name="__codelineno-22-18" href="#__codelineno-22-18"></a><span class="n">dec</span><span class="p">.</span><span class="n">to_bits</span><span class="p">().</span><span class="n">hash</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">dec_hasher</span><span class="p">);</span>
<a id="__codelineno-22-19" name="__codelineno-22-19" href="#__codelineno-22-19"></a><span class="kd">let</span><span class="w"> </span><span class="n">hash_dec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dec_hasher</span><span class="p">.</span><span class="n">finish</span><span class="p">();</span>
<a id="__codelineno-22-20" name="__codelineno-22-20" href="#__codelineno-22-20"></a><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;小数 {} 的哈希值为 {}&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">dec</span><span class="p">,</span><span class="w"> </span><span class="n">hash_dec</span><span class="p">);</span>
<a id="__codelineno-22-21" name="__codelineno-22-21" href="#__codelineno-22-21"></a><span class="c1">// 小数 3.14159 的哈希值为 2566941990314602357</span>
<a id="__codelineno-22-22" name="__codelineno-22-22" href="#__codelineno-22-22"></a>
<a id="__codelineno-22-23" name="__codelineno-22-23" href="#__codelineno-22-23"></a><span class="kd">let</span><span class="w"> </span><span class="kt">str</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;Hello 算法&quot;</span><span class="p">;</span>
<a id="__codelineno-22-24" name="__codelineno-22-24" href="#__codelineno-22-24"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">str_hasher</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">DefaultHasher</span>::<span class="n">new</span><span class="p">();</span>
<a id="__codelineno-22-25" name="__codelineno-22-25" href="#__codelineno-22-25"></a><span class="kt">str</span><span class="p">.</span><span class="n">hash</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">str_hasher</span><span class="p">);</span>
<a id="__codelineno-22-26" name="__codelineno-22-26" href="#__codelineno-22-26"></a><span class="kd">let</span><span class="w"> </span><span class="n">hash_str</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">str_hasher</span><span class="p">.</span><span class="n">finish</span><span class="p">();</span>
<a id="__codelineno-22-27" name="__codelineno-22-27" href="#__codelineno-22-27"></a><span class="c1">// 字符串 Hello 算法 的哈希值为 16092673739211250988</span>
<a id="__codelineno-22-28" name="__codelineno-22-28" href="#__codelineno-22-28"></a>
<a id="__codelineno-22-29" name="__codelineno-22-29" href="#__codelineno-22-29"></a><span class="kd">let</span><span class="w"> </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="o">&amp;</span><span class="mi">12836</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="s">&quot;小哈&quot;</span><span class="p">);</span>
<a id="__codelineno-22-30" name="__codelineno-22-30" href="#__codelineno-22-30"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">tup_hasher</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">DefaultHasher</span>::<span class="n">new</span><span class="p">();</span>
<a id="__codelineno-22-31" name="__codelineno-22-31" href="#__codelineno-22-31"></a><span class="n">arr</span><span class="p">.</span><span class="n">hash</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">tup_hasher</span><span class="p">);</span>
<a id="__codelineno-22-32" name="__codelineno-22-32" href="#__codelineno-22-32"></a><span class="kd">let</span><span class="w"> </span><span class="n">hash_tup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tup_hasher</span><span class="p">.</span><span class="n">finish</span><span class="p">();</span>
<a id="__codelineno-22-33" name="__codelineno-22-33" href="#__codelineno-22-33"></a><span class="c1">// 元组 (12836, &quot;小哈&quot;) 的哈希值为 1885128010422702749</span>
<a id="__codelineno-22-34" name="__codelineno-22-34" href="#__codelineno-22-34"></a>
<a id="__codelineno-22-35" name="__codelineno-22-35" href="#__codelineno-22-35"></a><span class="kd">let</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span>::<span class="n">new</span><span class="p">(</span><span class="mi">42</span><span class="p">);</span>
<a id="__codelineno-22-36" name="__codelineno-22-36" href="#__codelineno-22-36"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">hasher</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">DefaultHasher</span>::<span class="n">new</span><span class="p">();</span>
<a id="__codelineno-22-37" name="__codelineno-22-37" href="#__codelineno-22-37"></a><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="p">.</span><span class="n">hash</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">hasher</span><span class="p">);</span>
<a id="__codelineno-22-38" name="__codelineno-22-38" href="#__codelineno-22-38"></a><span class="kd">let</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hasher</span><span class="p">.</span><span class="n">finish</span><span class="p">();</span>
<a id="__codelineno-22-39" name="__codelineno-22-39" href="#__codelineno-22-39"></a><span class="c1">// 节点对象 RefCell { value: ListNode { val: 42, next: None } } 的哈希值为15387811073369036852</span>
2023-06-16 21:22:53 +08:00
</code></pre></div>
</div>
<div class="tabbed-block">
2023-09-10 18:37:37 +08:00
<div class="highlight"><span class="filename">built_in_hash.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="c1">// C 未提供内置 hash code 函数</span>
2023-06-16 21:22:53 +08:00
</code></pre></div>
</div>
<div class="tabbed-block">
2023-09-04 03:17:06 +08:00
<div class="highlight"><span class="filename">built_in_hash.zig</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a>
2023-06-16 21:22:53 +08:00
</code></pre></div>
</div>
</div>
</div>
2023-07-24 03:03:58 +08:00
<p>在许多编程语言中,<strong>只有不可变对象才可作为哈希表的 <code>key</code></strong> 。假如我们将列表(动态数组)作为 <code>key</code> ,当列表的内容发生变化时,它的哈希值也随之改变,我们就无法在哈希表中查询到原先的 <code>value</code> 了。</p>
<p>虽然自定义对象(比如链表节点)的成员变量是可变的,但它是可哈希的。<strong>这是因为对象的哈希值通常是基于内存地址生成的</strong>,即使对象的内容发生了变化,但它的内存地址不变,哈希值仍然是不变的。</p>
<p>细心的你可能发现在不同控制台中运行程序时,输出的哈希值是不同的。<strong>这是因为 Python 解释器在每次启动时都会为字符串哈希函数加入一个随机的盐Salt</strong>。这种做法可以有效防止 HashDoS 攻击,提升哈希算法的安全性。</p>
2023-06-16 21:22:53 +08:00
2023-09-21 20:44:52 +08:00
<!-- Source file information -->
2023-06-16 21:22:53 +08:00
2023-09-21 20:44:52 +08:00
<!-- Was this page helpful? -->
2023-06-16 21:22:53 +08:00
2023-09-21 20:44:52 +08:00
<!-- Previous and next pages link -->
<nav
class="md-footer__inner md-grid"
aria-label="页脚"
>
<!-- Link to previous page -->
<a
href="../hash_collision/"
class="md-footer__link md-footer__link--prev"
aria-label="上一页: 6.2 &amp;nbsp; 哈希冲突"
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">
6.2 &nbsp; 哈希冲突
</div>
</div>
</a>
<!-- Link to next page -->
<a
href="../summary/"
class="md-footer__link md-footer__link--next"
aria-label="下一页: 6.4 &amp;nbsp; 小结"
rel="next"
>
<div class="md-footer__title">
<span class="md-footer__direction">
下一页
</span>
<div class="md-ellipsis">
6.4 &nbsp; 小结
</div>
</div>
<div class="md-footer__button md-icon">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M4 11v2h12l-5.5 5.5 1.42 1.42L19.84 12l-7.92-7.92L10.5 5.5 16 11H4Z"/></svg>
</div>
</a>
</nav>
<!-- Comment system -->
2023-10-06 13:31:31 +08:00
2023-10-09 18:19:36 +08:00
2023-10-06 13:31:31 +08:00
2023-09-22 13:41:28 +08:00
<h5 align="center" id="__comments">欢迎在评论区留下你的见解、疑惑或建议</h5>
2023-10-06 13:31:31 +08:00
2023-06-16 21:22:53 +08:00
<!-- Insert generated snippet here -->
<script
src="https://giscus.app/client.js"
data-repo="krahets/hello-algo"
data-repo-id="R_kgDOIXtSqw"
data-category="Announcements"
data-category-id="DIC_kwDOIXtSq84CSZk_"
data-mapping="pathname"
data-strict="1"
data-reactions-enabled="1"
data-emit-metadata="0"
data-input-position="top"
data-theme="preferred_color_scheme"
data-lang="zh-CN"
crossorigin="anonymous"
async
>
</script>
<!-- Synchronize Giscus theme with palette -->
<script>
var giscus = document.querySelector("script[src*=giscus]")
/* Set palette on initial load */
var palette = __md_get("__palette")
if (palette && typeof palette.color === "object") {
2023-09-12 03:15:25 +08:00
var theme = palette.color.scheme === "slate" ? "dark_dimmed" : "light"
2023-06-16 21:22:53 +08:00
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") {
2023-09-12 03:15:25 +08:00
var theme = palette.color.scheme === "slate" ? "dark_dimmed" : "light"
2023-06-16 21:22:53 +08:00
/* 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>
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
<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>
2023-10-06 13:31:31 +08:00
<footer class="md-footer">
<nav class="md-footer__inner md-grid" aria-label="页脚" >
<a href="../hash_collision/" class="md-footer__link md-footer__link--prev" aria-label="上一页: 6.2 &amp;nbsp; 哈希冲突" 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">
6.2 &nbsp; 哈希冲突
</div>
</div>
</a>
<a href="../summary/" class="md-footer__link md-footer__link--next" aria-label="下一页: 6.4 &amp;nbsp; 小结" rel="next">
<div class="md-footer__title">
<span class="md-footer__direction">
下一页
</span>
<div class="md-ellipsis">
6.4 &nbsp; 小结
</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>
2023-06-16 21:22:53 +08:00
<div class="md-footer-meta md-typeset">
<div class="md-footer-meta__inner md-grid">
<div class="md-copyright">
<div class="md-copyright__highlight">
2023-09-22 13:08:10 +08:00
Copyright &copy; 2022 - 2023 Krahets
2023-06-16 21:22:53 +08:00
</div>
</div>
<div class="md-social">
<a href="https://github.com/krahets" target="_blank" rel="noopener" title="github.com" class="md-social__link">
2023-09-24 17:12:06 +08:00
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 496 512"><!--! Font Awesome Free 6.4.2 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg>
2023-06-16 21:22:53 +08:00
</a>
<a href="https://twitter.com/krahets" target="_blank" rel="noopener" title="twitter.com" class="md-social__link">
2023-09-24 17:12:06 +08:00
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.4.2 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M459.37 151.716c.325 4.548.325 9.097.325 13.645 0 138.72-105.583 298.558-298.558 298.558-59.452 0-114.68-17.219-161.137-47.106 8.447.974 16.568 1.299 25.34 1.299 49.055 0 94.213-16.568 130.274-44.832-46.132-.975-84.792-31.188-98.112-72.772 6.498.974 12.995 1.624 19.818 1.624 9.421 0 18.843-1.3 27.614-3.573-48.081-9.747-84.143-51.98-84.143-102.985v-1.299c13.969 7.797 30.214 12.67 47.431 13.319-28.264-18.843-46.781-51.005-46.781-87.391 0-19.492 5.197-37.36 14.294-52.954 51.655 63.675 129.3 105.258 216.365 109.807-1.624-7.797-2.599-15.918-2.599-24.04 0-57.828 46.782-104.934 104.934-104.934 30.213 0 57.502 12.67 76.67 33.137 23.715-4.548 46.456-13.32 66.599-25.34-7.798 24.366-24.366 44.833-46.132 57.827 21.117-2.273 41.584-8.122 60.426-16.243-14.292 20.791-32.161 39.308-52.628 54.253z"/></svg>
2023-06-16 21:22:53 +08:00
</a>
<a href="https://leetcode.cn/u/jyd/" target="_blank" rel="noopener" title="leetcode.cn" class="md-social__link">
2023-09-24 17:12:06 +08:00
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 640 512"><!--! Font Awesome Free 6.4.2 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M392.8 1.2c-17-4.9-34.7 5-39.6 22l-128 448c-4.9 17 5 34.7 22 39.6s34.7-5 39.6-22l128-448c4.9-17-5-34.7-22-39.6zm80.6 120.1c-12.5 12.5-12.5 32.8 0 45.3l89.3 89.4-89.4 89.4c-12.5 12.5-12.5 32.8 0 45.3s32.8 12.5 45.3 0l112-112c12.5-12.5 12.5-32.8 0-45.3l-112-112c-12.5-12.5-32.8-12.5-45.3 0zm-306.7 0c-12.5-12.5-32.8-12.5-45.3 0l-112 112c-12.5 12.5-12.5 32.8 0 45.3l112 112c12.5 12.5 32.8 12.5 45.3 0s12.5-32.8 0-45.3L77.3 256l89.4-89.4c12.5-12.5 12.5-32.8 0-45.3z"/></svg>
2023-06-16 21:22:53 +08:00
</a>
</div>
</div>
</div>
</footer>
</div>
<div class="md-dialog" data-md-component="dialog">
<div class="md-dialog__inner md-typeset"></div>
</div>
2023-09-24 17:12:06 +08:00
<script id="__config" type="application/json">{"base": "../..", "features": ["content.action.edit", "content.code.annotate", "content.code.copy", "content.tabs.link", "content.tooltips", "navigation.indexes", "navigation.instant", "navigation.top", "navigation.footer", "navigation.tracking", "search.highlight", "search.share", "search.suggest", "toc.follow"], "search": "../../assets/javascripts/workers/search.a264c092.min.js", "translations": {"clipboard.copied": "\u5df2\u590d\u5236", "clipboard.copy": "\u590d\u5236", "search.result.more.one": "\u5728\u8be5\u9875\u4e0a\u8fd8\u6709 1 \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c", "search.result.more.other": "\u5728\u8be5\u9875\u4e0a\u8fd8\u6709 # \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c", "search.result.none": "\u6ca1\u6709\u627e\u5230\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c", "search.result.one": "\u627e\u5230 1 \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c", "search.result.other": "# \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c", "search.result.placeholder": "\u952e\u5165\u4ee5\u5f00\u59cb\u641c\u7d22", "search.result.term.missing": "\u7f3a\u5c11", "select.version": "\u9009\u62e9\u5f53\u524d\u7248\u672c"}}</script>
2023-06-16 21:22:53 +08:00
2023-09-29 22:06:02 +08:00
<script src="../../assets/javascripts/bundle.4e0fa4ba.min.js"></script>
2023-06-16 21:22:53 +08:00
2023-09-24 17:12:06 +08:00
<script src="../../javascripts/mathjax.js"></script>
2023-06-16 21:22:53 +08:00
2023-09-24 17:12:06 +08:00
<script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
2023-06-16 21:22:53 +08:00
2023-09-24 17:12:06 +08:00
<script src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
2023-06-16 21:22:53 +08:00
2023-09-22 13:08:10 +08:00
<script>document$.subscribe(() => {const lightbox = GLightbox({"touchNavigation": true, "loop": false, "zoomable": true, "draggable": false, "openEffect": "zoom", "closeEffect": "zoom", "slideEffect": "none"});})</script></body>
2023-06-16 21:22:53 +08:00
</html>