This commit is contained in:
krahets 2023-05-31 01:03:26 +08:00
parent b48cdb9c10
commit fd30aa05a3
85 changed files with 1818 additions and 1432 deletions

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<link rel="icon" href="/assets/images/favicon.png">
<meta name="generator" content="mkdocs-1.4.2, mkdocs-material-9.1.6">
<meta name="generator" content="mkdocs-1.4.2, mkdocs-material-9.1.11">
@ -23,10 +23,10 @@
<link rel="stylesheet" href="/assets/stylesheets/main.ded33207.min.css">
<link rel="stylesheet" href="/assets/stylesheets/main.85bb2934.min.css">
<link rel="stylesheet" href="/assets/stylesheets/palette.a0c5b2b5.min.css">
<link rel="stylesheet" href="/assets/stylesheets/palette.a6bdf11c.min.css">
@ -61,7 +61,7 @@
<body dir="ltr" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="">
<body dir="ltr" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="indigo">
@ -109,25 +109,31 @@
</div>
</div>
<form class="md-header__option" data-md-component="palette">
<form class="md-header__option" data-md-component="palette">
<input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="" aria-label="Switch to dark mode" type="radio" name="__palette" id="__palette_1">
<input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="indigo" aria-label="Switch to dark mode" type="radio" name="__palette" id="__palette_1">
<label class="md-header__button md-icon" title="Switch to dark mode" for="__palette_2" hidden>
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</label>
<label class="md-header__button md-icon" title="Switch to dark mode" for="__palette_2" hidden>
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</label>
<input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="indigo" data-md-color-accent="indigo" aria-label="Switch to light mode" type="radio" name="__palette" id="__palette_2">
<label class="md-header__button md-icon" title="Switch to light mode" for="__palette_1" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m17.75 4.09-2.53 1.94.91 3.06-2.63-1.81-2.63 1.81.91-3.06-2.53-1.94L12.44 4l1.06-3 1.06 3 3.19.09m3.5 6.91-1.64 1.25.59 1.98-1.7-1.17-1.7 1.17.59-1.98L15.75 11l2.06-.05L18.5 9l.69 1.95 2.06.05m-2.28 4.95c.83-.08 1.72 1.1 1.19 1.85-.32.45-.66.87-1.08 1.27C15.17 23 8.84 23 4.94 19.07c-3.91-3.9-3.91-10.24 0-14.14.4-.4.82-.76 1.27-1.08.75-.53 1.93.36 1.85 1.19-.27 2.86.69 5.83 2.89 8.02a9.96 9.96 0 0 0 8.02 2.89m-1.64 2.02a12.08 12.08 0 0 1-7.8-3.47c-2.17-2.19-3.33-5-3.49-7.82-2.81 3.14-2.7 7.96.31 10.98 3.02 3.01 7.84 3.12 10.98.31Z"/></svg>
</label>
<input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="" data-md-color-accent="" aria-label="Switch to light mode" type="radio" name="__palette" id="__palette_2">
<label class="md-header__button md-icon" title="Switch to light mode" for="__palette_1" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m17.75 4.09-2.53 1.94.91 3.06-2.63-1.81-2.63 1.81.91-3.06-2.53-1.94L12.44 4l1.06-3 1.06 3 3.19.09m3.5 6.91-1.64 1.25.59 1.98-1.7-1.17-1.7 1.17.59-1.98L15.75 11l2.06-.05L18.5 9l.69 1.95 2.06.05m-2.28 4.95c.83-.08 1.72 1.1 1.19 1.85-.32.45-.66.87-1.08 1.27C15.17 23 8.84 23 4.94 19.07c-3.91-3.9-3.91-10.24 0-14.14.4-.4.82-.76 1.27-1.08.75-.53 1.93.36 1.85 1.19-.27 2.86.69 5.83 2.89 8.02a9.96 9.96 0 0 0 8.02 2.89m-1.64 2.02a12.08 12.08 0 0 1-7.8-3.47c-2.17-2.19-3.33-5-3.49-7.82-2.81 3.14-2.7 7.96.31 10.98 3.02 3.01 7.84 3.12 10.98.31Z"/></svg>
</label>
</form>
</form>
@ -1891,7 +1897,7 @@
<script id="__config" type="application/json">{"base": "/", "features": ["content.action.edit", "content.code.annotate", "content.code.copy", "content.tabs.link", "content.tooltips", "navigation.indexes", "navigation.sections", "navigation.top", "navigation.footer", "navigation.tracking", "search.highlight", "search.share", "search.suggest", "toc.follow"], "search": "/assets/javascripts/workers/search.208ed371.min.js", "translations": {"clipboard.copied": "\u5df2\u590d\u5236", "clipboard.copy": "\u590d\u5236", "search.result.more.one": "\u5728\u8be5\u9875\u4e0a\u8fd8\u6709 1 \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c", "search.result.more.other": "\u5728\u8be5\u9875\u4e0a\u8fd8\u6709 # \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c", "search.result.none": "\u6ca1\u6709\u627e\u5230\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c", "search.result.one": "\u627e\u5230 1 \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c", "search.result.other": "# \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c", "search.result.placeholder": "\u952e\u5165\u4ee5\u5f00\u59cb\u641c\u7d22", "search.result.term.missing": "\u7f3a\u5c11", "select.version": "\u9009\u62e9\u5f53\u524d\u7248\u672c"}}</script>
<script src="/assets/javascripts/bundle.51198bba.min.js"></script>
<script src="/assets/javascripts/bundle.fac441b0.min.js"></script>
<script src="/javascripts/mathjax.js"></script>

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!function(e,r){"function"==typeof define&&define.amd?define(r):"object"==typeof exports?module.exports=r():r()(e.lunr)}(this,function(){return function(e){if(void 0===e)throw new Error("Lunr is not present. Please include / require Lunr before this script.");if(void 0===e.stemmerSupport)throw new Error("Lunr stemmer support is not present. Please include / require Lunr stemmer support before this script.");e.hy=function(){this.pipeline.reset(),this.pipeline.add(e.hy.trimmer,e.hy.stopWordFilter)},e.hy.wordCharacters="[A-Za-z԰-֏ff-ﭏ]",e.hy.trimmer=e.trimmerSupport.generateTrimmer(e.hy.wordCharacters),e.Pipeline.registerFunction(e.hy.trimmer,"trimmer-hy"),e.hy.stopWordFilter=e.generateStopWordFilter("դու և եք էիր էիք հետո նաև նրանք որը վրա է որ պիտի են այս մեջ ն իր ու ի այդ որոնք այն կամ էր մի ես համար այլ իսկ էին ենք հետ ին թ էինք մենք նրա նա դուք եմ էի ըստ որպես ում".split(" ")),e.Pipeline.registerFunction(e.hy.stopWordFilter,"stopWordFilter-hy"),e.hy.stemmer=function(){return function(e){return"function"==typeof e.update?e.update(function(e){return e}):e}}(),e.Pipeline.registerFunction(e.hy.stemmer,"stemmer-hy")}});

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!function(e,r){"function"==typeof define&&define.amd?define(r):"object"==typeof exports?module.exports=r():r()(e.lunr)}(this,function(){return function(e){if(void 0===e)throw new Error("Lunr is not present. Please include / require Lunr before this script.");if(void 0===e.stemmerSupport)throw new Error("Lunr stemmer support is not present. Please include / require Lunr stemmer support before this script.");e.kn=function(){this.pipeline.reset(),this.pipeline.add(e.kn.trimmer,e.kn.stopWordFilter,e.kn.stemmer),this.searchPipeline&&(this.searchPipeline.reset(),this.searchPipeline.add(e.kn.stemmer))},e.kn.wordCharacters="ಀ-಄ಅ-ಔಕ-ಹಾ-ೌ಼-ಽೕ-ೖೝ-ೞೠ-ೡೢ-ೣ೤೥೦-೯ೱ-ೳ",e.kn.trimmer=e.trimmerSupport.generateTrimmer(e.kn.wordCharacters),e.Pipeline.registerFunction(e.kn.trimmer,"trimmer-kn"),e.kn.stopWordFilter=e.generateStopWordFilter("ಮತ್ತು ಈ ಒಂದು ರಲ್ಲಿ ಹಾಗೂ ಎಂದು ಅಥವಾ ಇದು ರ ಅವರು ಎಂಬ ಮೇಲೆ ಅವರ ತನ್ನ ಆದರೆ ತಮ್ಮ ನಂತರ ಮೂಲಕ ಹೆಚ್ಚು ನ ಆ ಕೆಲವು ಅನೇಕ ಎರಡು ಹಾಗು ಪ್ರಮುಖ ಇದನ್ನು ಇದರ ಸುಮಾರು ಅದರ ಅದು ಮೊದಲ ಬಗ್ಗೆ ನಲ್ಲಿ ರಂದು ಇತರ ಅತ್ಯಂತ ಹೆಚ್ಚಿನ ಸಹ ಸಾಮಾನ್ಯವಾಗಿ ನೇ ಹಲವಾರು ಹೊಸ ದಿ ಕಡಿಮೆ ಯಾವುದೇ ಹೊಂದಿದೆ ದೊಡ್ಡ ಅನ್ನು ಇವರು ಪ್ರಕಾರ ಇದೆ ಮಾತ್ರ ಕೂಡ ಇಲ್ಲಿ ಎಲ್ಲಾ ವಿವಿಧ ಅದನ್ನು ಹಲವು ರಿಂದ ಕೇವಲ ದ ದಕ್ಷಿಣ ಗೆ ಅವನ ಅತಿ ನೆಯ ಬಹಳ ಕೆಲಸ ಎಲ್ಲ ಪ್ರತಿ ಇತ್ಯಾದಿ ಇವು ಬೇರೆ ಹೀಗೆ ನಡುವೆ ಇದಕ್ಕೆ ಎಸ್ ಇವರ ಮೊದಲು ಶ್ರೀ ಮಾಡುವ ಇದರಲ್ಲಿ ರೀತಿಯ ಮಾಡಿದ ಕಾಲ ಅಲ್ಲಿ ಮಾಡಲು ಅದೇ ಈಗ ಅವು ಗಳು ಎ ಎಂಬುದು ಅವನು ಅಂದರೆ ಅವರಿಗೆ ಇರುವ ವಿಶೇಷ ಮುಂದೆ ಅವುಗಳ ಮುಂತಾದ ಮೂಲ ಬಿ ಮೀ ಒಂದೇ ಇನ್ನೂ ಹೆಚ್ಚಾಗಿ ಮಾಡಿ ಅವರನ್ನು ಇದೇ ಯ ರೀತಿಯಲ್ಲಿ ಜೊತೆ ಅದರಲ್ಲಿ ಮಾಡಿದರು ನಡೆದ ಆಗ ಮತ್ತೆ ಪೂರ್ವ ಆತ ಬಂದ ಯಾವ ಒಟ್ಟು ಇತರೆ ಹಿಂದೆ ಪ್ರಮಾಣದ ಗಳನ್ನು ಕುರಿತು ಯು ಆದ್ದರಿಂದ ಅಲ್ಲದೆ ನಗರದ ಮೇಲಿನ ಏಕೆಂದರೆ ರಷ್ಟು ಎಂಬುದನ್ನು ಬಾರಿ ಎಂದರೆ ಹಿಂದಿನ ಆದರೂ ಆದ ಸಂಬಂಧಿಸಿದ ಮತ್ತೊಂದು ಸಿ ಆತನ ".split(" ")),e.kn.stemmer=function(){return function(e){return"function"==typeof e.update?e.update(function(e){return e}):e}}();var r=e.wordcut;r.init(),e.kn.tokenizer=function(t){if(!arguments.length||null==t||void 0==t)return[];if(Array.isArray(t))return t.map(function(r){return isLunr2?new e.Token(r.toLowerCase()):r.toLowerCase()});var n=t.toString().toLowerCase().replace(/^\s+/,"");return r.cut(n).split("|")},e.Pipeline.registerFunction(e.kn.stemmer,"stemmer-kn"),e.Pipeline.registerFunction(e.kn.stopWordFilter,"stopWordFilter-kn")}});

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!function(e,r){"function"==typeof define&&define.amd?define(r):"object"==typeof exports?module.exports=r():r()(e.lunr)}(this,function(){return function(e){if(void 0===e)throw new Error("Lunr is not present. Please include / require Lunr before this script.");if(void 0===e.stemmerSupport)throw new Error("Lunr stemmer support is not present. Please include / require Lunr stemmer support before this script.");e.sa=function(){this.pipeline.reset(),this.pipeline.add(e.sa.trimmer,e.sa.stopWordFilter,e.sa.stemmer),this.searchPipeline&&(this.searchPipeline.reset(),this.searchPipeline.add(e.sa.stemmer))},e.sa.wordCharacters="ऀ-ःऄ-एऐ-टठ-यर-िी-ॏॐ-य़ॠ-९॰-ॿ꣠-꣱ꣲ-ꣷ꣸-ꣻ꣼-ꣽꣾ-ꣿᆰ0-ᆰ9",e.sa.trimmer=e.trimmerSupport.generateTrimmer(e.sa.wordCharacters),e.Pipeline.registerFunction(e.sa.trimmer,"trimmer-sa"),e.sa.stopWordFilter=e.generateStopWordFilter('तथा अयम्‌ एकम्‌ इत्यस्मिन्‌ तथा तत्‌ वा अयम्‌ इत्यस्य ते आहूत उपरि तेषाम्‌ किन्तु तेषाम्‌ तदा इत्यनेन अधिकः इत्यस्य तत्‌ केचन बहवः द्वि तथा महत्वपूर्णः अयम्‌ अस्य विषये अयं अस्ति तत्‌ प्रथमः विषये इत्युपरि इत्युपरि इतर अधिकतमः अधिकः अपि सामान्यतया ठ इतरेतर नूतनम्‌ द न्यूनम्‌ कश्चित्‌ वा विशालः द सः अस्ति तदनुसारम् तत्र अस्ति केवलम्‌ अपि अत्र सर्वे विविधाः तत्‌ बहवः यतः इदानीम्‌ द दक्षिण इत्यस्मै तस्य उपरि नथ अतीव कार्यम्‌ सर्वे एकैकम्‌ इत्यादि। एते सन्ति उत इत्थम्‌ मध्ये एतदर्थं . स कस्य प्रथमः श्री. करोति अस्मिन् प्रकारः निर्मिता कालः तत्र कर्तुं समान अधुना ते सन्ति स एकः अस्ति सः अर्थात् तेषां कृते . स्थितम् विशेषः अग्रिम तेषाम्‌ समान स्रोतः ख म समान इदानीमपि अधिकतया करोतु ते समान इत्यस्य वीथी सह यस्मिन् कृतवान्‌ धृतः तदा पुनः पूर्वं सः आगतः किम्‌ कुल इतर पुरा मात्रा स विषये उ अतएव अपि नगरस्य उपरि यतः प्रतिशतं कतरः कालः साधनानि भूत तथापि जात सम्बन्धि अन्यत्‌ ग अतः अस्माकं स्वकीयाः अस्माकं इदानीं अन्तः इत्यादयः भवन्तः इत्यादयः एते एताः तस्य अस्य इदम् एते तेषां तेषां तेषां तान् तेषां तेषां तेषां समानः सः एकः च तादृशाः बहवः अन्ये च वदन्ति यत् कियत् कस्मै कस्मै यस्मै यस्मै यस्मै यस्मै न अतिनीचः किन्तु प्रथमं सम्पूर्णतया ततः चिरकालानन्तरं पुस्तकं सम्पूर्णतया अन्तः किन्तु अत्र वा इह इव श्रद्धाय अवशिष्यते परन्तु अन्ये वर्गाः सन्ति ते सन्ति शक्नुवन्ति सर्वे मिलित्वा सर्वे एकत्र"'.split(" ")),e.sa.stemmer=function(){return function(e){return"function"==typeof e.update?e.update(function(e){return e}):e}}();var r=e.wordcut;r.init(),e.sa.tokenizer=function(t){if(!arguments.length||null==t||void 0==t)return[];if(Array.isArray(t))return t.map(function(r){return isLunr2?new e.Token(r.toLowerCase()):r.toLowerCase()});var i=t.toString().toLowerCase().replace(/^\s+/,"");return r.cut(i).split("|")},e.Pipeline.registerFunction(e.sa.stemmer,"stemmer-sa"),e.Pipeline.registerFunction(e.sa.stopWordFilter,"stopWordFilter-sa")}});

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<link rel="next" href="../../chapter_reference/">
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@ -67,7 +67,7 @@
<body dir="ltr" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="">
<body dir="ltr" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="indigo">
@ -120,25 +120,31 @@
</div>
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<form class="md-header__option" data-md-component="palette">
<form class="md-header__option" data-md-component="palette">
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@ -1989,6 +1995,7 @@
<div class="admonition question">
<p class="admonition-title">删除节点后,是否需要把 <code>P.next</code> 设为 <span class="arithmatex">\(\text{None}\)</span> 呢?</p>
<p>不修改 <code>P.next</code> 也可以。从该链表的角度看,从头结点遍历到尾结点已经遇不到 <code>P</code> 了。这意味着结点 <code>P</code> 已经从链表中删除了,此时结点 <code>P</code> 指向哪里都不会对这条链表产生影响了。</p>
<p>从垃圾回收的角度看,对于 Java, Python, Go 等拥有自动垃圾回收的语言来说,节点 <code>P</code> 是否被回收取决于是否有仍存在指向它的引用,而不是 <code>P.next</code> 的值。在 C, C++ 等语言中,我们需要手动释放节点内存。</p>
</div>
<div class="admonition question">
<p class="admonition-title">在链表中插入和删除操作的时间复杂度是 <span class="arithmatex">\(O(1)\)</span> 。但是增删之前都需要 <span class="arithmatex">\(O(n)\)</span> 查找元素,那为什么时间复杂度不是 <span class="arithmatex">\(O(n)\)</span> 呢?</p>
@ -2180,7 +2187,7 @@
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@ -3655,7 +3661,7 @@ O(1) &lt; O(\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \newline
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@ -4788,7 +4794,7 @@ n! = n \times (n - 1) \times (n - 2) \times \cdots \times 2 \times 1
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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>
</label>
<input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="" data-md-color-accent="" aria-label="Switch to light mode" type="radio" name="__palette" id="__palette_2">
<label class="md-header__button md-icon" title="Switch to light mode" for="__palette_1" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m17.75 4.09-2.53 1.94.91 3.06-2.63-1.81-2.63 1.81.91-3.06-2.53-1.94L12.44 4l1.06-3 1.06 3 3.19.09m3.5 6.91-1.64 1.25.59 1.98-1.7-1.17-1.7 1.17.59-1.98L15.75 11l2.06-.05L18.5 9l.69 1.95 2.06.05m-2.28 4.95c.83-.08 1.72 1.1 1.19 1.85-.32.45-.66.87-1.08 1.27C15.17 23 8.84 23 4.94 19.07c-3.91-3.9-3.91-10.24 0-14.14.4-.4.82-.76 1.27-1.08.75-.53 1.93.36 1.85 1.19-.27 2.86.69 5.83 2.89 8.02a9.96 9.96 0 0 0 8.02 2.89m-1.64 2.02a12.08 12.08 0 0 1-7.8-3.47c-2.17-2.19-3.33-5-3.49-7.82-2.81 3.14-2.7 7.96.31 10.98 3.02 3.01 7.84 3.12 10.98.31Z"/></svg>
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</form>
</form>
@ -2240,7 +2246,7 @@ G &amp; = \{ V, E \} \newline
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@ -21,7 +21,7 @@
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<meta name="generator" content="mkdocs-1.4.2, mkdocs-material-9.1.6">
<meta name="generator" content="mkdocs-1.4.2, mkdocs-material-9.1.11">
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<link rel="stylesheet" href="../../assets/stylesheets/main.ded33207.min.css">
<link rel="stylesheet" href="../../assets/stylesheets/main.85bb2934.min.css">
<link rel="stylesheet" href="../../assets/stylesheets/palette.a0c5b2b5.min.css">
<link rel="stylesheet" href="../../assets/stylesheets/palette.a6bdf11c.min.css">
@ -67,7 +67,7 @@
<body dir="ltr" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="">
<body dir="ltr" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="indigo">
@ -120,25 +120,31 @@
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</div>
<form class="md-header__option" data-md-component="palette">
<form class="md-header__option" data-md-component="palette">
<input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="" aria-label="Switch to dark mode" type="radio" name="__palette" id="__palette_1">
<input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="indigo" aria-label="Switch to dark mode" type="radio" name="__palette" id="__palette_1">
<label class="md-header__button md-icon" title="Switch to dark mode" for="__palette_2" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="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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<label class="md-header__button md-icon" title="Switch to dark mode" for="__palette_2" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 7a5 5 0 0 1 5 5 5 5 0 0 1-5 5 5 5 0 0 1-5-5 5 5 0 0 1 5-5m0 2a3 3 0 0 0-3 3 3 3 0 0 0 3 3 3 3 0 0 0 3-3 3 3 0 0 0-3-3m0-7 2.39 3.42C13.65 5.15 12.84 5 12 5c-.84 0-1.65.15-2.39.42L12 2M3.34 7l4.16-.35A7.2 7.2 0 0 0 5.94 8.5c-.44.74-.69 1.5-.83 2.29L3.34 7m.02 10 1.76-3.77a7.131 7.131 0 0 0 2.38 4.14L3.36 17M20.65 7l-1.77 3.79a7.023 7.023 0 0 0-2.38-4.15l4.15.36m-.01 10-4.14.36c.59-.51 1.12-1.14 1.54-1.86.42-.73.69-1.5.83-2.29L20.64 17M12 22l-2.41-3.44c.74.27 1.55.44 2.41.44.82 0 1.63-.17 2.37-.44L12 22Z"/></svg>
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<input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="indigo" data-md-color-accent="indigo" aria-label="Switch to light mode" type="radio" name="__palette" id="__palette_2">
<label class="md-header__button md-icon" title="Switch to light mode" for="__palette_1" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="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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<label class="md-header__button md-icon" title="Switch to light mode" for="__palette_1" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m17.75 4.09-2.53 1.94.91 3.06-2.63-1.81-2.63 1.81.91-3.06-2.53-1.94L12.44 4l1.06-3 1.06 3 3.19.09m3.5 6.91-1.64 1.25.59 1.98-1.7-1.17-1.7 1.17.59-1.98L15.75 11l2.06-.05L18.5 9l.69 1.95 2.06.05m-2.28 4.95c.83-.08 1.72 1.1 1.19 1.85-.32.45-.66.87-1.08 1.27C15.17 23 8.84 23 4.94 19.07c-3.91-3.9-3.91-10.24 0-14.14.4-.4.82-.76 1.27-1.08.75-.53 1.93.36 1.85 1.19-.27 2.86.69 5.83 2.89 8.02a9.96 9.96 0 0 0 8.02 2.89m-1.64 2.02a12.08 12.08 0 0 1-7.8-3.47c-2.17-2.19-3.33-5-3.49-7.82-2.81 3.14-2.7 7.96.31 10.98 3.02 3.01 7.84 3.12 10.98.31Z"/></svg>
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@ -3563,7 +3569,7 @@
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@ -21,7 +21,7 @@
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<meta name="generator" content="mkdocs-1.4.2, mkdocs-material-9.1.11">
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<link rel="stylesheet" href="../../assets/stylesheets/main.85bb2934.min.css">
<link rel="stylesheet" href="../../assets/stylesheets/palette.a0c5b2b5.min.css">
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<body dir="ltr" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="">
<body dir="ltr" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="indigo">
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</div>
<form class="md-header__option" data-md-component="palette">
<form class="md-header__option" data-md-component="palette">
<input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="" aria-label="Switch to dark mode" type="radio" name="__palette" id="__palette_1">
<input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="indigo" aria-label="Switch to dark mode" type="radio" name="__palette" id="__palette_1">
<label class="md-header__button md-icon" title="Switch to dark mode" for="__palette_2" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="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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<label class="md-header__button md-icon" title="Switch to dark mode" for="__palette_2" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 7a5 5 0 0 1 5 5 5 5 0 0 1-5 5 5 5 0 0 1-5-5 5 5 0 0 1 5-5m0 2a3 3 0 0 0-3 3 3 3 0 0 0 3 3 3 3 0 0 0 3-3 3 3 0 0 0-3-3m0-7 2.39 3.42C13.65 5.15 12.84 5 12 5c-.84 0-1.65.15-2.39.42L12 2M3.34 7l4.16-.35A7.2 7.2 0 0 0 5.94 8.5c-.44.74-.69 1.5-.83 2.29L3.34 7m.02 10 1.76-3.77a7.131 7.131 0 0 0 2.38 4.14L3.36 17M20.65 7l-1.77 3.79a7.023 7.023 0 0 0-2.38-4.15l4.15.36m-.01 10-4.14.36c.59-.51 1.12-1.14 1.54-1.86.42-.73.69-1.5.83-2.29L20.64 17M12 22l-2.41-3.44c.74.27 1.55.44 2.41.44.82 0 1.63-.17 2.37-.44L12 22Z"/></svg>
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<label class="md-header__button md-icon" title="Switch to light mode" for="__palette_1" hidden>
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<label class="md-header__button md-icon" title="Switch to light mode" for="__palette_1" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m17.75 4.09-2.53 1.94.91 3.06-2.63-1.81-2.63 1.81.91-3.06-2.53-1.94L12.44 4l1.06-3 1.06 3 3.19.09m3.5 6.91-1.64 1.25.59 1.98-1.7-1.17-1.7 1.17.59-1.98L15.75 11l2.06-.05L18.5 9l.69 1.95 2.06.05m-2.28 4.95c.83-.08 1.72 1.1 1.19 1.85-.32.45-.66.87-1.08 1.27C15.17 23 8.84 23 4.94 19.07c-3.91-3.9-3.91-10.24 0-14.14.4-.4.82-.76 1.27-1.08.75-.53 1.93.36 1.85 1.19-.27 2.86.69 5.83 2.89 8.02a9.96 9.96 0 0 0 8.02 2.89m-1.64 2.02a12.08 12.08 0 0 1-7.8-3.47c-2.17-2.19-3.33-5-3.49-7.82-2.81 3.14-2.7 7.96.31 10.98 3.02 3.01 7.84 3.12 10.98.31Z"/></svg>
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@ -2189,7 +2195,7 @@
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@ -67,7 +67,7 @@
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@ -120,25 +120,31 @@
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</form>
@ -3323,7 +3329,7 @@ f(12836) = f(20336) = 36
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@ -21,7 +21,7 @@
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@ -120,25 +120,31 @@
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@ -2028,7 +2034,7 @@
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@ -21,7 +21,7 @@
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@ -67,7 +67,7 @@
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<body dir="ltr" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="indigo">
@ -120,25 +120,31 @@
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<form class="md-header__option" data-md-component="palette">
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@ -2262,7 +2268,7 @@ T(h) &amp; = 2 \frac{1 - 2^h}{1 - 2} - h \newline
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<p>在正式探讨算法之前,有一个有趣的事实值得分享:<strong>实际上,你已经学会了许多算法,并习惯将他们应用到日常生活中了</strong>。下面,我将举两个具体例子来证实这一点。</p>
<p><strong>例一:组装积木</strong>。一套积木,除了包含许多零件之外,还附有详细的组装说明书。我们按照说明书一步步操作,就能组装出精美的积木模型。</p>
<p>从数据结构与算法的角度来看,积木的各种形状和连接方式代表数据结构,而组装说明书上的一系列步骤则是算法。</p>
<p><img alt="拼装积木" src="../algorithms_are_everywhere.assets/assembling_blocks.jpg" /></p>
<p align="center"> Fig. 拼装积木 </p>
<p><strong>例二:查阅字典</strong>。在字典里,每个汉字都对应一个拼音,而字典是按照拼音的英文字母顺序排列的。假设我们需要查找一个拼音首字母为 <span class="arithmatex">\(r\)</span> 的字,通常会这样操作:</p>
<ol>
<li>翻开字典约一半的页数,查看该页首字母是什么(假设为 <span class="arithmatex">\(m\)</span> </li>
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<h1 id="117">11.7. &nbsp; 堆排序<a class="headerlink" href="#117" title="Permanent link">&para;</a></h1>
<div class="admonition tip">
<p class="admonition-title">Tip</p>
<p>阅读本节前,请确保已完成堆章节的学习</p>
<p>阅读本节前,请确保已学完「堆」章节</p>
</div>
<p>「堆排序 Heap Sort」是一种基于堆数据结构实现的高效排序算法。我们可以利用已经学过的“建堆操作”和“元素出堆操作”实现堆排序</p>
<ol>
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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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@ -2643,7 +2649,7 @@ x_k = \lfloor\frac{x}{d^{k-1}}\rfloor \bmod d
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