1843 lines
76 KiB
HTML
1843 lines
76 KiB
HTML
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<!doctype html>
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<html lang="zh" class="no-js">
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<head>
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<meta name="viewport" content="width=device-width,initial-scale=1">
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<meta name="description" content="Your first book to learn Data Structure And Algorithm.">
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<meta name="author" content="Krahets">
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<link rel="canonical" href="https://www.hello-algo.com/chapter_hashing/hash_map/">
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<title>哈希表（HashMap） - Hello 算法</title>
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<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>
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<body dir="ltr" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="">
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<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>
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跳转至
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<header class="md-header" data-md-component="header">
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<nav class="md-header__inner md-grid" aria-label="页眉">
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<a href="../.." title="Hello 算法" class="md-header__button md-logo" aria-label="Hello 算法" data-md-component="logo">
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</a>
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<label class="md-header__button md-icon" for="__drawer">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 6h18v2H3V6m0 5h18v2H3v-2m0 5h18v2H3v-2Z"/></svg>
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<div class="md-header__title" data-md-component="header-title">
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<span class="md-ellipsis">
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Hello 算法
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</span>
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</div>
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<div class="md-header__topic" data-md-component="header-topic">
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<span class="md-ellipsis">
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哈希表（HashMap）
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</span>
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</div>
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<form class="md-header__option" data-md-component="palette">
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<input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="" aria-label="Switch to dark mode" type="radio" name="__palette" id="__palette_1">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 7a5 5 0 0 1 5 5 5 5 0 0 1-5 5 5 5 0 0 1-5-5 5 5 0 0 1 5-5m0 2a3 3 0 0 0-3 3 3 3 0 0 0 3 3 3 3 0 0 0 3-3 3 3 0 0 0-3-3m0-7 2.39 3.42C13.65 5.15 12.84 5 12 5c-.84 0-1.65.15-2.39.42L12 2M3.34 7l4.16-.35A7.2 7.2 0 0 0 5.94 8.5c-.44.74-.69 1.5-.83 2.29L3.34 7m.02 10 1.76-3.77a7.131 7.131 0 0 0 2.38 4.14L3.36 17M20.65 7l-1.77 3.79a7.023 7.023 0 0 0-2.38-4.15l4.15.36m-.01 10-4.14.36c.59-.51 1.12-1.14 1.54-1.86.42-.73.69-1.5.83-2.29L20.64 17M12 22l-2.41-3.44c.74.27 1.55.44 2.41.44.82 0 1.63-.17 2.37-.44L12 22Z"/></svg>
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<input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="" data-md-color-accent="" aria-label="Switch to light mode" type="radio" name="__palette" id="__palette_2">
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<label class="md-header__button md-icon" title="Switch to light mode" for="__palette_1" hidden>
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m17.75 4.09-2.53 1.94.91 3.06-2.63-1.81-2.63 1.81.91-3.06-2.53-1.94L12.44 4l1.06-3 1.06 3 3.19.09m3.5 6.91-1.64 1.25.59 1.98-1.7-1.17-1.7 1.17.59-1.98L15.75 11l2.06-.05L18.5 9l.69 1.95 2.06.05m-2.28 4.95c.83-.08 1.72 1.1 1.19 1.85-.32.45-.66.87-1.08 1.27C15.17 23 8.84 23 4.94 19.07c-3.91-3.9-3.91-10.24 0-14.14.4-.4.82-.76 1.27-1.08.75-.53 1.93.36 1.85 1.19-.27 2.86.69 5.83 2.89 8.02a9.96 9.96 0 0 0 8.02 2.89m-1.64 2.02a12.08 12.08 0 0 1-7.8-3.47c-2.17-2.19-3.33-5-3.49-7.82-2.81 3.14-2.7 7.96.31 10.98 3.02 3.01 7.84 3.12 10.98.31Z"/></svg>
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</form>
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<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>
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<form class="md-search__form" name="search">
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<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>
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<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>
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<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>
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<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>
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<div class="md-search-result__meta">
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正在初始化搜索引擎
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</div>
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<ol class="md-search-result__list"></ol>
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<div class="md-header__source">
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<a href="https://github.com/krahets/hello-algo" title="前往仓库" class="md-source" data-md-component="source">
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<div class="md-source__icon md-icon">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 496 512"><!--! Font Awesome Free 6.2.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2022 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>
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<div class="md-source__repository">
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krahets/hello-algo
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</div>
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</nav>
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<a href="../.." title="Hello 算法" class="md-nav__button md-logo" aria-label="Hello 算法" data-md-component="logo">
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<img src="../../assets/images/logo.png" alt="logo">
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</a>
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Hello 算法
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</label>
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<div class="md-nav__source">
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<a href="https://github.com/krahets/hello-algo" title="前往仓库" class="md-source" data-md-component="source">
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<label class="md-nav__link" for="__nav_5">
|
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数组与链表
|
|||
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<span class="md-nav__icon md-icon"></span>
|
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|
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</label>
|
|||
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|
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<nav class="md-nav" aria-label="数组与链表" data-md-level="1">
|
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<label class="md-nav__title" for="__nav_5">
|
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<span class="md-nav__icon md-icon"></span>
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数组与链表
|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
|
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数组（Array）
|
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|
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</a>
|
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<li class="md-nav__item">
|
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<a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
|
|||
|
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链表（LinkedList）
|
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|
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</a>
|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
|
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|
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列表（List）
|
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|
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</a>
|
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<li class="md-nav__item">
|
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|
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<a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
|
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|
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小结
|
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|
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</a>
|
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|
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</li>
|
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|
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|
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|
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<input class="md-nav__toggle md-toggle" data-md-toggle="__nav_6" type="checkbox" id="__nav_6" >
|
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|
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<label class="md-nav__link" for="__nav_6">
|
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|
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栈与队列
|
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|
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<span class="md-nav__icon md-icon"></span>
|
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</label>
|
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|
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<nav class="md-nav" aria-label="栈与队列" data-md-level="1">
|
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<label class="md-nav__title" for="__nav_6">
|
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|
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<span class="md-nav__icon md-icon"></span>
|
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|
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栈与队列
|
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|
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</label>
|
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<ul class="md-nav__list" data-md-scrollfix>
|
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|
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|
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|
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|
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<li class="md-nav__item">
|
|||
|
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<a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
|
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|
|
栈（Stack）
|
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|
|
</a>
|
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|
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</li>
|
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|
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|
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|
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<li class="md-nav__item">
|
|||
|
|
<a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
|
|||
|
|
队列（Queue）
|
|||
|
|
</a>
|
|||
|
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</li>
|
|||
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|
|||
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|
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|
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|
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<li class="md-nav__item">
|
|||
|
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<a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
|
|||
|
|
双向队列（Deque）
|
|||
|
|
</a>
|
|||
|
|
</li>
|
|||
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|
|
|||
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|
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|
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|
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|
|||
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|
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|
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<li class="md-nav__item">
|
|||
|
|
<a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
|
|||
|
|
小结
|
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|
|
</a>
|
|||
|
|
</li>
|
|||
|
|
|
|||
|
|
|
|||
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|
|||
|
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|
|||
|
|
</ul>
|
|||
|
|
</nav>
|
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|
|||
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|
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|
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|
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<li class="md-nav__item md-nav__item--active md-nav__item--section md-nav__item--nested">
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<input class="md-nav__toggle md-toggle" data-md-toggle="__nav_7" type="checkbox" id="__nav_7" checked>
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|
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|
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|
|||
|
|
|
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|
|
<label class="md-nav__link" for="__nav_7">
|
|||
|
|
散列表
|
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|
|
<span class="md-nav__icon md-icon"></span>
|
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|
|
</label>
|
|||
|
|
|
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|
|
<nav class="md-nav" aria-label="散列表" data-md-level="1">
|
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|
|
<label class="md-nav__title" for="__nav_7">
|
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|
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<span class="md-nav__icon md-icon"></span>
|
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散列表
|
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|
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</label>
|
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|
|
<ul class="md-nav__list" data-md-scrollfix>
|
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<li class="md-nav__item md-nav__item--active">
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<input class="md-nav__toggle md-toggle" data-md-toggle="toc" type="checkbox" id="__toc">
|
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|
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|
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|
|||
|
|
<label class="md-nav__link md-nav__link--active" for="__toc">
|
|||
|
|
哈希表（HashMap）
|
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|
|
<span class="md-nav__icon md-icon"></span>
|
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|
|
</label>
|
|||
|
|
|
|||
|
|
<a href="./" class="md-nav__link md-nav__link--active">
|
|||
|
|
哈希表（HashMap）
|
|||
|
|
</a>
|
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|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
<nav class="md-nav md-nav--secondary" aria-label="目录">
|
|||
|
|
|
|||
|
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|
|||
|
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|
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|
|||
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|
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|
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|
|
<label class="md-nav__title" for="__toc">
|
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|
|
<span class="md-nav__icon md-icon"></span>
|
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|
|
目录
|
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|
|
</label>
|
|||
|
|
<ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
|
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|
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|
|||
|
|
<li class="md-nav__item">
|
|||
|
|
<a href="#_2" class="md-nav__link">
|
|||
|
|
哈希表优势
|
|||
|
|
</a>
|
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|
|
|
|||
|
|
</li>
|
|||
|
|
|
|||
|
|
<li class="md-nav__item">
|
|||
|
|
<a href="#_3" class="md-nav__link">
|
|||
|
|
哈希表常用操作
|
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|
|
</a>
|
|||
|
|
|
|||
|
|
</li>
|
|||
|
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|
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|
|
<li class="md-nav__item">
|
|||
|
|
<a href="#_4" class="md-nav__link">
|
|||
|
|
哈希函数
|
|||
|
|
</a>
|
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|
|
|
|||
|
|
</li>
|
|||
|
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|
|||
|
|
<li class="md-nav__item">
|
|||
|
|
<a href="#_5" class="md-nav__link">
|
|||
|
|
哈希冲突
|
|||
|
|
</a>
|
|||
|
|
|
|||
|
|
</li>
|
|||
|
|
|
|||
|
|
</ul>
|
|||
|
|
|
|||
|
|
</nav>
|
|||
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|
|
|||
|
|
</li>
|
|||
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|
|||
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|
|||
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|
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|
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|
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|
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|
|||
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|
|||
|
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|
|||
|
|
<li class="md-nav__item">
|
|||
|
|
<a href="../hash_collision/" class="md-nav__link">
|
|||
|
|
哈希冲突处理
|
|||
|
|
</a>
|
|||
|
|
</li>
|
|||
|
|
|
|||
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|
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|
|||
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|
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|
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|
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|
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|
|||
|
|
<li class="md-nav__item">
|
|||
|
|
<a href="../summary/" class="md-nav__link">
|
|||
|
|
小结
|
|||
|
|
</a>
|
|||
|
|
</li>
|
|||
|
|
|
|||
|
|
|
|||
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|
|||
|
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|
|||
|
|
</ul>
|
|||
|
|
</nav>
|
|||
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</li>
|
|||
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|
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|
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|
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<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
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|
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|
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|
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|
|
<input class="md-nav__toggle md-toggle" data-md-toggle="__nav_8" type="checkbox" id="__nav_8" >
|
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|
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|
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|
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|
|||
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|
|||
|
|
<label class="md-nav__link" for="__nav_8">
|
|||
|
|
二叉树
|
|||
|
|
<span class="md-nav__icon md-icon"></span>
|
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|
|
</label>
|
|||
|
|
|
|||
|
|
<nav class="md-nav" aria-label="二叉树" data-md-level="1">
|
|||
|
|
<label class="md-nav__title" for="__nav_8">
|
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|
|
<span class="md-nav__icon md-icon"></span>
|
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|
|
二叉树
|
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|
|
</label>
|
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|
|
<ul class="md-nav__list" data-md-scrollfix>
|
|||
|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
|
|||
|
|
<a href="../../chapter_tree/binary_tree/" class="md-nav__link">
|
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|
|
二叉树（Binary Tree）
|
|||
|
|
</a>
|
|||
|
|
</li>
|
|||
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|
|||
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|
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|
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|
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|
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<li class="md-nav__item">
|
|||
|
|
<a href="../../chapter_tree/binary_tree_types/" class="md-nav__link">
|
|||
|
|
二叉树常见类型
|
|||
|
|
</a>
|
|||
|
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</li>
|
|||
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|
|||
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|
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|
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|
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<li class="md-nav__item">
|
|||
|
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<a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
|
|||
|
|
二叉搜索树
|
|||
|
|
</a>
|
|||
|
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</li>
|
|||
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|
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|
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|
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|
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<li class="md-nav__item">
|
|||
|
|
<a href="../../chapter_tree/avl_tree/" class="md-nav__link">
|
|||
|
|
AVL 树 *
|
|||
|
|
</a>
|
|||
|
|
</li>
|
|||
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|
|||
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|
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|
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|
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|
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<li class="md-nav__item">
|
|||
|
|
<a href="../../chapter_tree/summary/" class="md-nav__link">
|
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|
|
小结
|
|||
|
|
</a>
|
|||
|
|
</li>
|
|||
|
|
|
|||
|
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|
|||
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|
|||
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|
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|
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</ul>
|
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|
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</nav>
|
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</li>
|
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|
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|
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|
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<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
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<input class="md-nav__toggle md-toggle" data-md-toggle="__nav_9" type="checkbox" id="__nav_9" >
|
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<label class="md-nav__link" for="__nav_9">
|
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查找算法
|
|||
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<span class="md-nav__icon md-icon"></span>
|
|||
|
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</label>
|
|||
|
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|
|||
|
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<nav class="md-nav" aria-label="查找算法" data-md-level="1">
|
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<label class="md-nav__title" for="__nav_9">
|
|||
|
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<span class="md-nav__icon md-icon"></span>
|
|||
|
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查找算法
|
|||
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</label>
|
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<ul class="md-nav__list" data-md-scrollfix>
|
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<li class="md-nav__item">
|
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<a href="../../chapter_searching/linear_search/" class="md-nav__link">
|
|||
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线性查找
|
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|
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</a>
|
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</li>
|
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<li class="md-nav__item">
|
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<a href="../../chapter_searching/binary_search/" class="md-nav__link">
|
|||
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二分查找
|
|||
|
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</a>
|
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|
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<li class="md-nav__item">
|
|||
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<a href="../../chapter_searching/hashing_search/" class="md-nav__link">
|
|||
|
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哈希查找
|
|||
|
|
</a>
|
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|
|||
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<li class="md-nav__item">
|
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<a href="../../chapter_searching/summary/" class="md-nav__link">
|
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|
小结
|
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</a>
|
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|
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|
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|
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<label class="md-nav__link" for="__nav_10">
|
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排序算法
|
|||
|
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<span class="md-nav__icon md-icon"></span>
|
|||
|
|
</label>
|
|||
|
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|
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|
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<nav class="md-nav" aria-label="排序算法" data-md-level="1">
|
|||
|
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<label class="md-nav__title" for="__nav_10">
|
|||
|
|
<span class="md-nav__icon md-icon"></span>
|
|||
|
|
排序算法
|
|||
|
|
</label>
|
|||
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<ul class="md-nav__list" data-md-scrollfix>
|
|||
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<li class="md-nav__item">
|
|||
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<a href="../../chapter_sorting/intro_to_sort/" class="md-nav__link">
|
|||
|
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排序简介
|
|||
|
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</a>
|
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|
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<li class="md-nav__item">
|
|||
|
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<a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
|
|||
|
|
冒泡排序
|
|||
|
|
</a>
|
|||
|
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</li>
|
|||
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|
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<li class="md-nav__item">
|
|||
|
|
<a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
|
|||
|
|
插入排序
|
|||
|
|
</a>
|
|||
|
|
</li>
|
|||
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|
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|
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|
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<li class="md-nav__item">
|
|||
|
|
<a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
|
|||
|
|
快速排序
|
|||
|
|
</a>
|
|||
|
|
</li>
|
|||
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|
|||
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|
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|
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<li class="md-nav__item">
|
|||
|
|
<a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
|
|||
|
|
归并排序
|
|||
|
|
</a>
|
|||
|
|
</li>
|
|||
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|
|||
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|
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|
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<li class="md-nav__item">
|
|||
|
|
<a href="../../chapter_sorting/summary/" class="md-nav__link">
|
|||
|
|
小结
|
|||
|
|
</a>
|
|||
|
|
</li>
|
|||
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|
|||
|
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|
|||
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|
|||
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|
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</ul>
|
|||
|
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</nav>
|
|||
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|
|||
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|
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<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
|||
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|
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|
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|
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|
|
<input class="md-nav__toggle md-toggle" data-md-toggle="__nav_11" type="checkbox" id="__nav_11" >
|
|||
|
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|
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|
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|
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<div class="md-nav__link md-nav__link--index ">
|
|||
|
|
<a href="../../chapter_reference/">参考文献</a>
|
|||
|
|
|
|||
|
|
</div>
|
|||
|
|
|
|||
|
|
<nav class="md-nav" aria-label="参考文献" data-md-level="1">
|
|||
|
|
<label class="md-nav__title" for="__nav_11">
|
|||
|
|
<span class="md-nav__icon md-icon"></span>
|
|||
|
|
参考文献
|
|||
|
|
</label>
|
|||
|
|
<ul class="md-nav__list" data-md-scrollfix>
|
|||
|
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|
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|
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|
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|
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|
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</ul>
|
|||
|
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</nav>
|
|||
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</li>
|
|||
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|
|||
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|
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|
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|
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</ul>
|
|||
|
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</nav>
|
|||
|
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</div>
|
|||
|
|
</div>
|
|||
|
|
</div>
|
|||
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|
|||
|
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|
|||
|
|
|
|||
|
|
<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">
|
|||
|
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|
|||
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|
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|
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<nav class="md-nav md-nav--secondary" aria-label="目录">
|
|||
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|
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|
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<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>
|
|||
|
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|
|||
|
|
<li class="md-nav__item">
|
|||
|
|
<a href="#_2" class="md-nav__link">
|
|||
|
|
哈希表优势
|
|||
|
|
</a>
|
|||
|
|
|
|||
|
|
</li>
|
|||
|
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|
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|
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<li class="md-nav__item">
|
|||
|
|
<a href="#_3" class="md-nav__link">
|
|||
|
|
哈希表常用操作
|
|||
|
|
</a>
|
|||
|
|
|
|||
|
|
</li>
|
|||
|
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|
|||
|
|
<li class="md-nav__item">
|
|||
|
|
<a href="#_4" class="md-nav__link">
|
|||
|
|
哈希函数
|
|||
|
|
</a>
|
|||
|
|
|
|||
|
|
</li>
|
|||
|
|
|
|||
|
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<li class="md-nav__item">
|
|||
|
|
<a href="#_5" class="md-nav__link">
|
|||
|
|
哈希冲突
|
|||
|
|
</a>
|
|||
|
|
|
|||
|
|
</li>
|
|||
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|
|||
|
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</ul>
|
|||
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|
|||
|
|
</nav>
|
|||
|
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</div>
|
|||
|
|
</div>
|
|||
|
|
</div>
|
|||
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|
|||
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|
|
|||
|
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|
|||
|
|
<div class="md-content" data-md-component="content">
|
|||
|
|
<article class="md-content__inner md-typeset">
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
<a href="https://github.com/krahets/hello-algo/tree/master/docs/chapter_hashing/hash_map.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="M20.71 7.04c.39-.39.39-1.04 0-1.41l-2.34-2.34c-.37-.39-1.02-.39-1.41 0l-1.84 1.83 3.75 3.75M3 17.25V21h3.75L17.81 9.93l-3.75-3.75L3 17.25Z"/></svg>
|
|||
|
|
</a>
|
|||
|
|
|
|||
|
|
|
|||
|
|
<h1 id="_1">哈希表<a class="headerlink" href="#_1" title="Permanent link">¶</a></h1>
|
|||
|
|
<p>哈希表通过建立「键 key」和「值 value」之间的映射，实现高效的元素查找。具体地，输入一个 key ，在哈希表中查询并获取 value ，时间复杂度为 <span class="arithmatex">\(O(1)\)</span> 。</p>
|
|||
|
|
<p>例如，给定一个包含 <span class="arithmatex">\(n\)</span> 个学生的数据库，每个学生有 "姓名 <code>name</code> ” 和 “学号 <code>id</code> ” 两项数据，希望实现一个查询功能：<strong>输入一个学号，返回对应的姓名</strong>，则可以使用哈希表实现。</p>
|
|||
|
|
<p><img alt="hash_map" src="../hash_map.assets/hash_map.png" /></p>
|
|||
|
|
<p align="center"> Fig. 哈希表抽象表示 </p>
|
|||
|
|
|
|||
|
|
<h2 id="_2">哈希表优势<a class="headerlink" href="#_2" title="Permanent link">¶</a></h2>
|
|||
|
|
<p>除了哈希表之外，还可以使用以下数据结构来实现上述查询功能：</p>
|
|||
|
|
<ul>
|
|||
|
|
<li><strong>无序数组：</strong> 每个元素为 <code>[学号, 姓名]</code> ；</li>
|
|||
|
|
<li><strong>有序数组：</strong> 将 <code>1.</code> 中的数组按照学号从小到大排序；</li>
|
|||
|
|
<li><strong>链表：</strong> 每个结点的值为 <code>[学号, 姓名]</code> ；</li>
|
|||
|
|
<li><strong>二叉搜索树：</strong> 每个结点的值为 <code>[学号, 姓名]</code> ，根据学号大小来构建树；</li>
|
|||
|
|
</ul>
|
|||
|
|
<p>使用上述方法，各项操作的时间复杂度如下表所示（在此不做赘述，详解可见 <a href="https://www.hello-algo.com/chapter_tree/binary_search_tree/#_6">二叉搜索树章节</a>）。无论是查找元素、还是增删元素，哈希表的时间复杂度都是 <span class="arithmatex">\(O(1)\)</span> ，全面胜出！</p>
|
|||
|
|
<div class="center-table">
|
|||
|
|
<table>
|
|||
|
|
<thead>
|
|||
|
|
<tr>
|
|||
|
|
<th></th>
|
|||
|
|
<th>无序数组</th>
|
|||
|
|
<th>有序数组</th>
|
|||
|
|
<th>链表</th>
|
|||
|
|
<th>二叉搜索树</th>
|
|||
|
|
<th>哈希表</th>
|
|||
|
|
</tr>
|
|||
|
|
</thead>
|
|||
|
|
<tbody>
|
|||
|
|
<tr>
|
|||
|
|
<td>查找元素</td>
|
|||
|
|
<td><span class="arithmatex">\(O(n)\)</span></td>
|
|||
|
|
<td><span class="arithmatex">\(O(\log n)\)</span></td>
|
|||
|
|
<td><span class="arithmatex">\(O(n)\)</span></td>
|
|||
|
|
<td><span class="arithmatex">\(O(\log n)\)</span></td>
|
|||
|
|
<td><span class="arithmatex">\(O(1)\)</span></td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td>插入元素</td>
|
|||
|
|
<td><span class="arithmatex">\(O(1)\)</span></td>
|
|||
|
|
<td><span class="arithmatex">\(O(n)\)</span></td>
|
|||
|
|
<td><span class="arithmatex">\(O(1)\)</span></td>
|
|||
|
|
<td><span class="arithmatex">\(O(\log n)\)</span></td>
|
|||
|
|
<td><span class="arithmatex">\(O(1)\)</span></td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td>删除元素</td>
|
|||
|
|
<td><span class="arithmatex">\(O(n)\)</span></td>
|
|||
|
|
<td><span class="arithmatex">\(O(n)\)</span></td>
|
|||
|
|
<td><span class="arithmatex">\(O(n)\)</span></td>
|
|||
|
|
<td><span class="arithmatex">\(O(\log n)\)</span></td>
|
|||
|
|
<td><span class="arithmatex">\(O(1)\)</span></td>
|
|||
|
|
</tr>
|
|||
|
|
</tbody>
|
|||
|
|
</table>
|
|||
|
|
</div>
|
|||
|
|
<h2 id="_3">哈希表常用操作<a class="headerlink" href="#_3" title="Permanent link">¶</a></h2>
|
|||
|
|
<p>哈希表的基本操作包括 <strong>初始化、查询操作、添加与删除键值对</strong>。</p>
|
|||
|
|
<div class="tabbed-set tabbed-alternate" data-tabs="1:8"><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" /><div class="tabbed-labels"><label for="__tabbed_1_1">Java</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Python</label><label for="__tabbed_1_4">Go</label><label for="__tabbed_1_5">JavaScript</label><label for="__tabbed_1_6">TypeScript</label><label for="__tabbed_1_7">C</label><label for="__tabbed_1_8">C#</label></div>
|
|||
|
|
<div class="tabbed-content">
|
|||
|
|
<div class="tabbed-block">
|
|||
|
|
<div class="highlight"><span class="filename">hash_map.java</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="cm">/* 初始化哈希表 */</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="n">Map</span><span class="o"><</span><span class="n">Integer</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="o">></span><span class="w"> </span><span class="n">map</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">HashMap</span><span class="o"><></span><span class="p">();</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>
|
|||
|
|
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="cm">/* 添加操作 */</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="c1">// 在哈希表中添加键值对 (key, value)</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="n">map</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="mi">12836</span><span class="p">,</span><span class="w"> </span><span class="s">"小哈"</span><span class="p">);</span><span class="w"> </span>
|
|||
|
|
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="n">map</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="mi">15937</span><span class="p">,</span><span class="w"> </span><span class="s">"小啰"</span><span class="p">);</span><span class="w"> </span>
|
|||
|
|
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="n">map</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="mi">16750</span><span class="p">,</span><span class="w"> </span><span class="s">"小算"</span><span class="p">);</span><span class="w"> </span>
|
|||
|
|
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="n">map</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="mi">13276</span><span class="p">,</span><span class="w"> </span><span class="s">"小法"</span><span class="p">);</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="n">map</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="mi">10583</span><span class="p">,</span><span class="w"> </span><span class="s">"小鸭"</span><span class="p">);</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>
|
|||
|
|
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="cm">/* 查询操作 */</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a><span class="c1">// 向哈希表输入键 key ，得到值 value</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a><span class="n">String</span><span class="w"> </span><span class="n">name</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="mi">15937</span><span class="p">);</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>
|
|||
|
|
<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a><span class="cm">/* 删除操作 */</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a><span class="c1">// 在哈希表中删除键值对 (key, value)</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a><span class="n">map</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="mi">10583</span><span class="p">);</span><span class="w"></span>
|
|||
|
|
</code></pre></div>
|
|||
|
|
</div>
|
|||
|
|
<div class="tabbed-block">
|
|||
|
|
<div class="highlight"><span class="filename">hash_map.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a>
|
|||
|
|
</code></pre></div>
|
|||
|
|
</div>
|
|||
|
|
<div class="tabbed-block">
|
|||
|
|
<div class="highlight"><span class="filename">hash_map.py</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a>
|
|||
|
|
</code></pre></div>
|
|||
|
|
</div>
|
|||
|
|
<div class="tabbed-block">
|
|||
|
|
<div class="highlight"><span class="filename">hash_map.go</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a>
|
|||
|
|
</code></pre></div>
|
|||
|
|
</div>
|
|||
|
|
<div class="tabbed-block">
|
|||
|
|
<div class="highlight"><span class="filename">hash_map.js</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a>
|
|||
|
|
</code></pre></div>
|
|||
|
|
</div>
|
|||
|
|
<div class="tabbed-block">
|
|||
|
|
<div class="highlight"><span class="filename">hash_map.ts</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a>
|
|||
|
|
</code></pre></div>
|
|||
|
|
</div>
|
|||
|
|
<div class="tabbed-block">
|
|||
|
|
<div class="highlight"><span class="filename">hash_map.c</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a>
|
|||
|
|
</code></pre></div>
|
|||
|
|
</div>
|
|||
|
|
<div class="tabbed-block">
|
|||
|
|
<div class="highlight"><span class="filename">hash_map.cs</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a>
|
|||
|
|
</code></pre></div>
|
|||
|
|
</div>
|
|||
|
|
</div>
|
|||
|
|
</div>
|
|||
|
|
<p>遍历哈希表有三种方式，即 <strong>遍历键值对、遍历键、遍历值</strong>。</p>
|
|||
|
|
<div class="tabbed-set tabbed-alternate" data-tabs="2:8"><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" /><div class="tabbed-labels"><label for="__tabbed_2_1">Java</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Python</label><label for="__tabbed_2_4">Go</label><label for="__tabbed_2_5">JavaScript</label><label for="__tabbed_2_6">TypeScript</label><label for="__tabbed_2_7">C</label><label for="__tabbed_2_8">C#</label></div>
|
|||
|
|
<div class="tabbed-content">
|
|||
|
|
<div class="tabbed-block">
|
|||
|
|
<div class="highlight"><span class="filename">hash_map.java</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 遍历哈希表 */</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="c1">// 遍历键值对 key->value</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Map</span><span class="p">.</span><span class="na">Entry</span><span class="w"> </span><span class="o"><</span><span class="n">Integer</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="o">></span><span class="w"> </span><span class="n">kv</span><span class="p">:</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="na">entrySet</span><span class="p">())</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w"> </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="n">kv</span><span class="p">.</span><span class="na">getKey</span><span class="p">()</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">" -> "</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">kv</span><span class="p">.</span><span class="na">getValue</span><span class="p">());</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="p">}</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="c1">// 单独遍历键 key</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><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">key</span><span class="p">:</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="na">keySet</span><span class="p">())</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w"> </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="n">key</span><span class="p">);</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="p">}</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="c1">// 单独遍历值 value</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">String</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="na">values</span><span class="p">())</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w"> </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="n">val</span><span class="p">);</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="p">}</span><span class="w"></span>
|
|||
|
|
</code></pre></div>
|
|||
|
|
</div>
|
|||
|
|
<div class="tabbed-block">
|
|||
|
|
<div class="highlight"><span class="filename">hash_map.cpp</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a>
|
|||
|
|
</code></pre></div>
|
|||
|
|
</div>
|
|||
|
|
<div class="tabbed-block">
|
|||
|
|
<div class="highlight"><span class="filename">hash_map.py</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a>
|
|||
|
|
</code></pre></div>
|
|||
|
|
</div>
|
|||
|
|
<div class="tabbed-block">
|
|||
|
|
<div class="highlight"><span class="filename">hash_map.go</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a>
|
|||
|
|
</code></pre></div>
|
|||
|
|
</div>
|
|||
|
|
<div class="tabbed-block">
|
|||
|
|
<div class="highlight"><span class="filename">hash_map.js</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a>
|
|||
|
|
</code></pre></div>
|
|||
|
|
</div>
|
|||
|
|
<div class="tabbed-block">
|
|||
|
|
<div class="highlight"><span class="filename">hash_map.ts</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a>
|
|||
|
|
</code></pre></div>
|
|||
|
|
</div>
|
|||
|
|
<div class="tabbed-block">
|
|||
|
|
<div class="highlight"><span class="filename">hash_map.c</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a>
|
|||
|
|
</code></pre></div>
|
|||
|
|
</div>
|
|||
|
|
<div class="tabbed-block">
|
|||
|
|
<div class="highlight"><span class="filename">hash_map.cs</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a>
|
|||
|
|
</code></pre></div>
|
|||
|
|
</div>
|
|||
|
|
</div>
|
|||
|
|
</div>
|
|||
|
|
<h2 id="_4">哈希函数<a class="headerlink" href="#_4" title="Permanent link">¶</a></h2>
|
|||
|
|
<p>哈希表中存储元素的数据结构被称为「桶 Bucket」，底层实现可能是数组、链表、二叉树（红黑树），或是它们的组合。</p>
|
|||
|
|
<p>最简单地，<strong>我们可以仅用一个「数组」来实现哈希表</strong>。首先，将所有 value 放入数组中，那么每个 value 在数组中都有唯一的「索引」。显然，访问 value 需要给定索引，而为了 <strong>建立 key 和索引之间的映射关系</strong>，我们需要使用「哈希函数 Hash Function」。</p>
|
|||
|
|
<p>设数组为 <code>bucket</code> ，哈希函数为 <code>f(x)</code> ，输入键为 <code>key</code> 。那么获取 value 的步骤为：</p>
|
|||
|
|
<ol>
|
|||
|
|
<li>通过哈希函数计算出索引，即 <code>index = f(key)</code> ；</li>
|
|||
|
|
<li>通过索引在数组中获取值，即 <code>value = bucket[index]</code> ；</li>
|
|||
|
|
</ol>
|
|||
|
|
<p>以上述学生数据 <code>key 学号 -> value 姓名</code> 为例，我们可以将「哈希函数」设计为</p>
|
|||
|
|
<div class="arithmatex">\[
|
|||
|
|
f(x) = x \% 100
|
|||
|
|
\]</div>
|
|||
|
|
<p><img alt="hash_function" src="../hash_map.assets/hash_function.png" /></p>
|
|||
|
|
<p align="center"> Fig. 哈希函数 </p>
|
|||
|
|
|
|||
|
|
<div class="tabbed-set tabbed-alternate" data-tabs="3:8"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Java</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Python</label><label for="__tabbed_3_4">Go</label><label for="__tabbed_3_5">JavaScript</label><label for="__tabbed_3_6">TypeScript</label><label for="__tabbed_3_7">C</label><label for="__tabbed_3_8">C#</label></div>
|
|||
|
|
<div class="tabbed-content">
|
|||
|
|
<div class="tabbed-block">
|
|||
|
|
<div class="highlight"><span class="filename">array_hash_map.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 键值对 int->String */</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kd">class</span> <span class="nc">Entry</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">;</span><span class="w"> </span><span class="c1">// 键</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// 值</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="nf">Entry</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="na">key</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>
|
|||
|
|
<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w"> </span><span class="p">}</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="p">}</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a>
|
|||
|
|
<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="cm">/* 基于数组简易实现的哈希表 */</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="kd">class</span> <span class="nc">ArrayHashMap</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w"> </span><span class="kd">private</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Entry</span><span class="o">></span><span class="w"> </span><span class="n">bucket</span><span class="p">;</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="nf">ArrayHashMap</span><span class="p">()</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w"> </span><span class="c1">// 初始化一个长度为 100 的桶（数组）</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="w"> </span><span class="n">bucket</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">ArrayList</span><span class="o"><></span><span class="p">();</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></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"><</span><span class="w"> </span><span class="mi">100</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><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w"> </span><span class="n">bucket</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="kc">null</span><span class="p">);</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="w"> </span><span class="p">}</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a><span class="w"> </span><span class="p">}</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a>
|
|||
|
|
<a id="__codelineno-16-22" name="__codelineno-16-22" href="#__codelineno-16-22"></a><span class="w"> </span><span class="cm">/* 哈希函数 */</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-23" name="__codelineno-16-23" href="#__codelineno-16-23"></a><span class="w"> </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">hashFunc</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-24" name="__codelineno-16-24" href="#__codelineno-16-24"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">100</span><span class="p">;</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-25" name="__codelineno-16-25" href="#__codelineno-16-25"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-26" name="__codelineno-16-26" href="#__codelineno-16-26"></a><span class="w"> </span><span class="p">}</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-27" name="__codelineno-16-27" href="#__codelineno-16-27"></a>
|
|||
|
|
<a id="__codelineno-16-28" name="__codelineno-16-28" href="#__codelineno-16-28"></a><span class="w"> </span><span class="cm">/* 查询操作 */</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-29" name="__codelineno-16-29" href="#__codelineno-16-29"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-30" name="__codelineno-16-30" href="#__codelineno-16-30"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-31" name="__codelineno-16-31" href="#__codelineno-16-31"></a><span class="w"> </span><span class="n">Entry</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">bucket</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">index</span><span class="p">);</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-32" name="__codelineno-16-32" href="#__codelineno-16-32"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-33" name="__codelineno-16-33" href="#__codelineno-16-33"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="na">val</span><span class="p">;</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-34" name="__codelineno-16-34" href="#__codelineno-16-34"></a><span class="w"> </span><span class="p">}</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-35" name="__codelineno-16-35" href="#__codelineno-16-35"></a>
|
|||
|
|
<a id="__codelineno-16-36" name="__codelineno-16-36" href="#__codelineno-16-36"></a><span class="w"> </span><span class="cm">/* 添加操作 */</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-37" name="__codelineno-16-37" href="#__codelineno-16-37"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-38" name="__codelineno-16-38" href="#__codelineno-16-38"></a><span class="w"> </span><span class="n">Entry</span><span class="w"> </span><span class="n">pair</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">Entry</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-39" name="__codelineno-16-39" href="#__codelineno-16-39"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-40" name="__codelineno-16-40" href="#__codelineno-16-40"></a><span class="w"> </span><span class="n">bucket</span><span class="p">.</span><span class="na">set</span><span class="p">(</span><span class="n">index</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="p">);</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-41" name="__codelineno-16-41" href="#__codelineno-16-41"></a><span class="w"> </span><span class="p">}</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-42" name="__codelineno-16-42" href="#__codelineno-16-42"></a>
|
|||
|
|
<a id="__codelineno-16-43" name="__codelineno-16-43" href="#__codelineno-16-43"></a><span class="w"> </span><span class="cm">/* 删除操作 */</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-44" name="__codelineno-16-44" href="#__codelineno-16-44"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-45" name="__codelineno-16-45" href="#__codelineno-16-45"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-46" name="__codelineno-16-46" href="#__codelineno-16-46"></a><span class="w"> </span><span class="c1">// 置为空字符，代表删除</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-47" name="__codelineno-16-47" href="#__codelineno-16-47"></a><span class="w"> </span><span class="n">bucket</span><span class="p">.</span><span class="na">set</span><span class="p">(</span><span class="n">index</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">);</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-48" name="__codelineno-16-48" href="#__codelineno-16-48"></a><span class="w"> </span><span class="p">}</span><span class="w"></span>
|
|||
|
|
<a id="__codelineno-16-49" name="__codelineno-16-49" href="#__codelineno-16-49"></a><span class="p">}</span><span class="w"></span>
|
|||
|
|
</code></pre></div>
|
|||
|
|
</div>
|
|||
|
|
<div class="tabbed-block">
|
|||
|
|
<div class="highlight"><span class="filename">array_hash_map.cpp</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a>
|
|||
|
|
</code></pre></div>
|
|||
|
|
</div>
|
|||
|
|
<div class="tabbed-block">
|
|||
|
|
<div class="highlight"><span class="filename">array_hash_map.py</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a>
|
|||
|
|
</code></pre></div>
|
|||
|
|
</div>
|
|||
|
|
<div class="tabbed-block">
|
|||
|
|
<div class="highlight"><span class="filename">array_hash_map.go</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a>
|
|||
|
|
</code></pre></div>
|
|||
|
|
</div>
|
|||
|
|
<div class="tabbed-block">
|
|||
|
|
<div class="highlight"><span class="filename">array_hash_map.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a>
|
|||
|
|
</code></pre></div>
|
|||
|
|
</div>
|
|||
|
|
<div class="tabbed-block">
|
|||
|
|
<div class="highlight"><span class="filename">array_hash_map.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a>
|
|||
|
|
</code></pre></div>
|
|||
|
|
</div>
|
|||
|
|
<div class="tabbed-block">
|
|||
|
|
<div class="highlight"><span class="filename">array_hash_map.c</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a>
|
|||
|
|
</code></pre></div>
|
|||
|
|
</div>
|
|||
|
|
<div class="tabbed-block">
|
|||
|
|
<div class="highlight"><span class="filename">array_hash_map.cs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a>
|
|||
|
|
</code></pre></div>
|
|||
|
|
</div>
|
|||
|
|
</div>
|
|||
|
|
</div>
|
|||
|
|
<h2 id="_5">哈希冲突<a class="headerlink" href="#_5" title="Permanent link">¶</a></h2>
|
|||
|
|
<p>细心的同学可能会发现，<strong>哈希函数 <span class="arithmatex">\(f(x) = x \% 100\)</span> 会在某些情况下失效</strong>。具体地，当输入的 key 后两位相同时，哈希函数的计算结果也相同，指向同一个 value 。例如，分别查询两个学号 12836 和 20336 ，则有</p>
|
|||
|
|
<div class="arithmatex">\[
|
|||
|
|
f(12836) = f(20336) = 36
|
|||
|
|
\]</div>
|
|||
|
|
<p>两个学号指向了同一个姓名，这明显是不对的，我们将这种现象称为「哈希冲突 Hash Collision」，其会严重影响查询的正确性。如何避免哈希冲突的问题将被留在下章讨论。</p>
|
|||
|
|
<p><img alt="hash_collision" src="../hash_map.assets/hash_collision.png" /></p>
|
|||
|
|
<p align="center"> Fig. 哈希冲突 </p>
|
|||
|
|
|
|||
|
|
<p>综上所述，一个优秀的「哈希函数」应该具备以下特性：</p>
|
|||
|
|
<ul>
|
|||
|
|
<li>尽量少地发生哈希冲突；</li>
|
|||
|
|
<li>时间复杂度 <span class="arithmatex">\(O(1)\)</span> ，计算尽可能高效；</li>
|
|||
|
|
<li>空间使用率高，即 “键值对占用空间 / 哈希表总占用空间” 尽可能大；</li>
|
|||
|
|
</ul>
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
<h2 id="__comments">评论</h2>
|
|||
|
|
<!-- Insert generated snippet here -->
|
|||
|
|
<script
|
|||
|
|
src="https://giscus.app/client.js"
|
|||
|
|
data-repo="krahets/hello-algo"
|
|||
|
|
data-repo-id="R_kgDOIXtSqw"
|
|||
|
|
data-category="Announcements"
|
|||
|
|
data-category-id="DIC_kwDOIXtSq84CSZk_"
|
|||
|
|
data-mapping="pathname"
|
|||
|
|
data-strict="0"
|
|||
|
|
data-reactions-enabled="1"
|
|||
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|
data-emit-metadata="0"
|
|||
|
|
data-input-position="bottom"
|
|||
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data-theme="preferred_color_scheme"
|
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data-lang="zh-CN"
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crossorigin="anonymous"
|
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async
|
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>
|
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</script>
|
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<!-- Synchronize Giscus theme with palette -->
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<script>
|
|||
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var giscus = document.querySelector("script[src*=giscus]")
|
|||
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|
|||
|
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/* Set palette on initial load */
|
|||
|
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var palette = __md_get("__palette")
|
|||
|
|
if (palette && typeof palette.color === "object") {
|
|||
|
|
var theme = palette.color.scheme === "slate" ? "dark" : "light"
|
|||
|
|
giscus.setAttribute("data-theme", theme)
|
|||
|
|
}
|
|||
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|
|||
|
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/* Register event handlers after documented loaded */
|
|||
|
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document.addEventListener("DOMContentLoaded", function() {
|
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|
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var ref = document.querySelector("[data-md-component=palette]")
|
|||
|
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ref.addEventListener("change", function() {
|
|||
|
|
var palette = __md_get("__palette")
|
|||
|
|
if (palette && typeof palette.color === "object") {
|
|||
|
|
var theme = palette.color.scheme === "slate" ? "dark" : "light"
|
|||
|
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|
|||
|
|
/* Instruct Giscus to change theme */
|
|||
|
|
var frame = document.querySelector(".giscus-frame")
|
|||
|
|
frame.contentWindow.postMessage(
|
|||
|
|
{ giscus: { setConfig: { theme } } },
|
|||
|
|
"https://giscus.app"
|
|||
|
|
)
|
|||
|
|
}
|
|||
|
|
})
|
|||
|
|
})
|
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|
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</script>
|
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</article>
|
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|
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<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>
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</main>
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<footer class="md-footer">
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<div class="md-footer-meta md-typeset">
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<div class="md-footer-meta__inner md-grid">
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<div class="md-copyright">
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Copyright © 2020 - 2022 Krahets
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</div>
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<div class="md-social">
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<a href="https://github.com/krahets" target="_blank" rel="noopener" title="github.com" class="md-social__link">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 496 512"><!--! Font Awesome Free 6.2.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2022 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>
|
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|
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<a href="https://twitter.com/krahets" target="_blank" rel="noopener" title="twitter.com" class="md-social__link">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.2.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2022 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>
|
|||
|
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</a>
|
|||
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|
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|
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|
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|
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|
|
<a href="https://leetcode.cn/u/jyd/" target="_blank" rel="noopener" title="leetcode.cn" class="md-social__link">
|
|||
|
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 640 512"><!--! Font Awesome Free 6.2.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2022 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>
|
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</a>
|
|||
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</div>
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</div>
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</footer>
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<div class="md-dialog__inner md-typeset"></div>
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<script id="__config" type="application/json">{"base": "../..", "features": ["announce.dismiss", "content.code.annotate", "content.code.copy", "content.tabs.link", "content.tooltips", "navigation.indexes", "navigation.sections", "navigation.tracking", "search.highlight", "search.share", "search.suggest", "toc.follow"], "search": "../../assets/javascripts/workers/search.208e55ea.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>
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<script src="../../assets/javascripts/bundle.f1ef77e2.min.js"></script>
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</html>
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