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krahets
2026-03-29 05:07:03 +08:00
parent 9e8c0cb36c
commit 9466700256
841 changed files with 38622 additions and 119252 deletions
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en/chapter_sorting/bucket_sort/index.html
+52 -130
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@@ -35,7 +35,7 @@
<link rel="icon" href="../../assets/images/favicon.png">
<meta name="generator" content="mkdocs-1.6.1, mkdocs-material-9.7.1">
<meta name="generator" content="zensical-0.0.29">
@@ -43,10 +43,15 @@
<link rel="stylesheet" href="../../assets/stylesheets/main.484c7ddc.min.css">
<link rel="stylesheet" href="../../assets/stylesheets/palette.ab4e12ef.min.css">
<link rel="stylesheet" href="../../assets/stylesheets/modern/main.6f2fbb28.min.css">
<link rel="stylesheet" href="../../assets/stylesheets/modern/palette.dfe2e883.min.css">
@@ -60,29 +65,20 @@
<link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Lato:300,300i,400,400i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Lato:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
<style>:root{--md-text-font:"Lato";--md-code-font:"JetBrains Mono"}</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>
<script>__md_scope=new URL("../..",location),__md_hash=e=>[...e].reduce(((e,t)=>(e<<5)-e+t.charCodeAt(0)),0),__md_get=(e,t=localStorage,a=__md_scope)=>JSON.parse(t.getItem(("__palette"===e?"/":a.pathname)+"."+e)),__md_set=(e,t,a=localStorage,_=__md_scope)=>{try{a.setItem(("__palette"===e?"/":_.pathname)+"."+e,JSON.stringify(t))}catch(e){}},document.documentElement.setAttribute("data-platform",navigator.platform)</script>
<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>
</head>
@@ -97,7 +93,7 @@
<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>
<label class="md-overlay" for="__drawer" aria-label="Navigation"></label>
<div data-md-component="skip">
@@ -139,12 +135,12 @@
<nav class="md-header__inner md-grid" aria-label="Header">
<a href="../.." title="Hello Algo" class="md-header__button md-logo" aria-label="Hello Algo" data-md-component="logo">
<img src="../../assets/images/logo.svg" alt="logo">
<img src="../../assets/images/logo.svg" alt="Hello Algo">
</a>
<label class="md-header__button md-icon" for="__drawer">
<label class="md-header__button md-icon" for="__drawer" aria-label="Navigation">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 6h18v2H3zm0 5h18v2H3zm0 5h18v2H3z"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-menu" viewBox="0 0 24 24"><path d="M4 5h16M4 12h16M4 19h16"/></svg>
</label>
<div class="md-header__title" data-md-component="header-title">
<div class="md-header__ellipsis">
@@ -156,7 +152,7 @@
<div class="md-header__topic" data-md-component="header-topic">
<span class="md-ellipsis">
11.8 Bucket Sort
11.8 &nbsp; Bucket Sort
</span>
</div>
@@ -169,7 +165,7 @@
<input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="teal" aria-label="Dark mode" type="radio" name="__palette" id="__palette_0">
<input class="md-option" data-md-color-media="none" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="teal" aria-label="Dark mode" type="radio" name="__palette" id="__palette_0">
<label class="md-header__button md-icon" title="Dark 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 19.07zm-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13zm-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87zM19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35zm4.33-2.7 1.15-2.77 2.2 2.54zm1.15-4.96-1.14-2.78 3.34.24zM9.63 18.93l2.77 1.15-2.53 2.19z"/></svg>
@@ -179,7 +175,7 @@
<input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="black" data-md-color-accent="teal" aria-label="Light mode" type="radio" name="__palette" id="__palette_1">
<input class="md-option" data-md-color-media="none" data-md-color-scheme="slate" data-md-color-primary="black" data-md-color-accent="teal" aria-label="Light mode" type="radio" name="__palette" id="__palette_1">
<label class="md-header__button md-icon" title="Light mode" for="__palette_0" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07zm-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13zm-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87zM19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35zm4.33-2.7 1.15-2.77 2.2 2.54zm1.15-4.96-1.14-2.78 3.34.24zM9.63 18.93l2.77 1.15-2.53 2.19z"/></svg>
@@ -197,7 +193,7 @@
<div class="md-select">
<button class="md-header__button md-icon" aria-label="Select language">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12.87 15.07-2.54-2.51.03-.03A17.5 17.5 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 3.11zM18.5 10h-2L12 22h2l1.12-3h4.75L21 22h2zm-2.62 7 1.62-4.33L19.12 17z"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-languages" viewBox="0 0 24 24"><path d="m5 8 6 6M4 14l6-6 2-3M2 5h12M7 2h1M22 22l-5-10-5 10M14 18h6"/></svg>
</button>
<div class="md-select__inner">
<ul class="md-select__list">
@@ -240,64 +236,30 @@
<label class="md-header__button md-icon" for="__search">
<label class="md-header__button md-icon" for="__search" aria-label="Search">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.52 6.52 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 5"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-search" viewBox="0 0 24 24"><path d="m21 21-4.34-4.34"/><circle cx="11" cy="11" r="8"/></svg>
</label>
<div class="md-search" data-md-component="search" role="dialog">
<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="Search" placeholder="Search" autocapitalize="off" autocorrect="off" autocomplete="off" spellcheck="false" data-md-component="search-query" required>
<label class="md-search__icon md-icon" for="__search">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.52 6.52 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 5"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11z"/></svg>
</label>
<nav class="md-search__options" aria-label="Search">
<a href="javascript:void(0)" class="md-search__icon md-icon" title="Share" aria-label="Share" data-clipboard data-clipboard-text="" data-md-component="search-share" tabindex="-1">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 16.08c-.76 0-1.44.3-1.96.77L8.91 12.7c.05-.23.09-.46.09-.7s-.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 2.91s2.92-1.3 2.92-2.91A2.92 2.92 0 0 0 18 16.08"/></svg>
</a>
<button type="reset" class="md-search__icon md-icon" title="Clear" aria-label="Clear" tabindex="-1">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 6.41 17.59 5 12 10.59 6.41 5 5 6.41 10.59 12 5 17.59 6.41 19 12 13.41 17.59 19 19 17.59 13.41 12z"/></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" tabindex="0" data-md-scrollfix>
<div class="md-search-result" data-md-component="search-result">
<div class="md-search-result__meta">
Initializing search
</div>
<ol class="md-search-result__list" role="presentation"></ol>
</div>
</div>
</div>
</div>
<div class="md-search" data-md-component="search" role="dialog" aria-label="Search">
<button type="button" class="md-search__button">
Search
</button>
</div>
<div class="md-header__source">
<div class="md-header__source">
<a href="https://github.com/krahets/hello-algo" title="Go to repository" class="md-source" data-md-component="source">
<div class="md-source__icon md-icon">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path d="M173.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6m-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3m44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9M252.8 8C114.1 8 8 113.3 8 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C436.2 457.8 504 362.9 504 252 504 113.3 391.5 8 252.8 8M105.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1m-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7m32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1m-11.4-14.7c-1.6 1-1.6 3.6 0 5.9s4.3 3.3 5.6 2.3c1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2"/></svg>
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</div>
<div class="md-source__repository">
krahets/hello-algo
</div>
</a>
</div>
</div>
</nav>
</header>
@@ -325,7 +287,7 @@
<label class="md-nav__title" for="__drawer">
<a href="../.." title="Hello Algo" class="md-nav__button md-logo" aria-label="Hello Algo" data-md-component="logo">
<img src="../../assets/images/logo.svg" alt="logo">
<img src="../../assets/images/logo.svg" alt="Hello Algo">
</a>
Hello Algo
@@ -335,7 +297,7 @@
<a href="https://github.com/krahets/hello-algo" title="Go to repository" class="md-source" data-md-component="source">
<div class="md-source__icon md-icon">
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@@ -4422,7 +4386,7 @@
<li>Sort each bucket separately (here we use the built-in sorting function of the programming language).</li>
<li>Merge the results in order from smallest to largest bucket.</li>
</ol>
<p><a class="glightbox" href="../bucket_sort.assets/bucket_sort_overview.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Bucket sort algorithm flow" class="animation-figure" src="../bucket_sort.assets/bucket_sort_overview.png" /></a></p>
<p><img alt="Bucket sort algorithm flow" class="animation-figure" src="../bucket_sort.assets/bucket_sort_overview.png" /></p>
<p align="center"> Figure 11-13 &nbsp; Bucket sort algorithm flow </p>
<p>The code is as follows:</p>
@@ -4830,12 +4794,12 @@
<p>Theoretically, bucket sort can achieve <span class="arithmatex">\(O(n)\)</span> time complexity. <strong>The key is to evenly distribute elements to each bucket</strong>, because real data is often not evenly distributed. For example, if we want to evenly distribute all products on Taobao into 10 buckets by price range, there may be very many products below 100 yuan and very few above 1000 yuan. If the price intervals are evenly divided into 10, the difference in the number of products in each bucket will be very large.</p>
<p>To achieve even distribution, we can first set an approximate dividing line to roughly divide the data into 3 buckets. <strong>After distribution is complete, continue dividing buckets with more products into 3 buckets until the number of elements in all buckets is roughly equal</strong>.</p>
<p>As shown in Figure 11-14, this method essentially creates a recursion tree, with the goal of making the values of leaf nodes as even as possible. Of course, it is not necessary to divide the data into 3 buckets every round; the specific division method can be flexibly chosen according to data characteristics.</p>
<p><a class="glightbox" href="../bucket_sort.assets/scatter_in_buckets_recursively.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Recursively dividing buckets" class="animation-figure" src="../bucket_sort.assets/scatter_in_buckets_recursively.png" /></a></p>
<p><img alt="Recursively dividing buckets" class="animation-figure" src="../bucket_sort.assets/scatter_in_buckets_recursively.png" /></p>
<p align="center"> Figure 11-14 &nbsp; Recursively dividing buckets </p>
<p>If we know the probability distribution of product prices in advance, <strong>we can set the price dividing line for each bucket based on the data probability distribution</strong>. It is worth noting that the data distribution does not necessarily need to be specifically calculated, but can also be approximated using a certain probability model based on data characteristics.</p>
<p>As shown in Figure 11-15, we assume that product prices follow a normal distribution, which allows us to reasonably set price intervals to evenly distribute products to each bucket.</p>
<p><a class="glightbox" href="../bucket_sort.assets/scatter_in_buckets_distribution.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Dividing buckets based on probability distribution" class="animation-figure" src="../bucket_sort.assets/scatter_in_buckets_distribution.png" /></a></p>
<p><img alt="Dividing buckets based on probability distribution" class="animation-figure" src="../bucket_sort.assets/scatter_in_buckets_distribution.png" /></p>
<p align="center"> Figure 11-15 &nbsp; Dividing buckets based on probability distribution </p>
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