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<html lang="zh"><head><title>算法</title><meta charset="utf-8"/><link rel="preconnect" href="https://fonts.googleapis.com"/><link rel="preconnect" href="https://fonts.gstatic.com"/><link rel="stylesheet" href="https://fonts.googleapis.com/css2?family=IBM Plex Mono&family=Noto Serif Simplified Chinese:wght@400;700&family=Source Sans Pro:ital,wght@0,400;0,600;1,400;1,600&display=swap"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><meta property="og:title" content="算法"/><meta property="og:description" content="算法的定义和设计."/><meta property="og:image" content="https://wiki.7wate.com/static/og-image.png"/><meta property="og:width" content="1200"/><meta property="og:height" content="675"/><link rel="icon" href="../../static/icon.png"/><meta name="description" content="算法的定义和设计."/><meta name="generator" content="Quartz"/><link href="../../index.css" rel="stylesheet" type="text/css" spa-preserve/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.9/katex.min.css" rel="stylesheet" type="text/css" spa-preserve/><script src="../../prescript.js" type="application/javascript" spa-preserve></script><script type="application/javascript" spa-preserve>const fetchData = fetch("../../static/contentIndex.json").then(data => data.json())</script></head><body data-slug="Technology/StructuresAlgorithms/算法"><div id="quartz-root" class="page"><div id="quartz-body"><div class="left sidebar"><h2 class="page-title"><a href="../..">🪴 X·Eden</a></h2><div class="spacer mobile-only"></div><div class="search"><button class="search-button" id="search-button"><p>搜索</p><svg role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 19.9 19.7"><title>Search</title><g class="search-path" fill="none"><path stroke-linecap="square" d="M18.5 18.3l-5.4-5.4"></path><circle cx="8" cy="8" r="7"></circle></g></svg></button><div id="search-container"><div id="search-space"><input autocomplete="off" id="search-bar" name="search" type="text" aria-label="搜索些什么" placeholder="搜索些什么"/><div id="search-layout" data-preview="true"></div></div></div></div><button class="darkmode" id="darkmode"><svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" id="dayIcon" x="0px" y="0px" viewBox="0 0 35 35" style="enable-background:new 0 0 35 35" xml:space="preserve" aria-label="暗色模式"><title>暗色模式</title><path d="M6,17.5C6,16.672,5.328,16,4.5,16h-3C0.672,16,0,16.672,0,17.5 S0.672,19,1.5,19h3C5.328,19,6,18.328,6,17.5z M7.5,26c-0.414,0-0.789,0.168-1.061,0.439l-2,2C4.168,28.711,4,29.086,4,29.5 C4,30.328,4.671,31,5.5,31c0.414,0,0.789-0.168,1.06-0.44l2-2C8.832,28.289,9,27.914,9,27.5C9,26.672,8.329,26,7.5,26z M17.5,6 C18.329,6,19,5.328,19,4.5v-3C19,0.672,18.329,0,17.5,0S16,0.672,16,1.5v3C16,5.328,16.671,6,17.5,6z M27.5,9 c0.414,0,0.789-0.168,1.06-0.439l2-2C30.832,6.289,31,5.914,31,5.5C31,4.672,30.329,4,29.5,4c-0.414,0-0.789,0.168-1.061,0.44 l-2,2C26.168,6.711,26,7.086,26,7.5C26,8.328,26.671,9,27.5,9z M6.439,8.561C6.711,8.832,7.086,9,7.5,9C8.328,9,9,8.328,9,7.5 c0-0.414-0.168-0.789-0.439-1.061l-2-2C6.289,4.168,5.914,4,5.5,4C4.672,4,4,4.672,4,5.5c0,0.414,0.168,0.789,0.439,1.06 L6.439,8.561z M33.5,16h-3c-0.828,0-1.5,0.672-1.5,1.5s0.672,1.5,1.5,1.5h3c0.828,0,1.5-0.672,1.5-1.5S34.328,16,33.5,16z M28.561,26.439C28.289,26.168,27.914,26,27.5,26c-0.828,0-1.5,0.672-1.5,1.5c0,0.414,0.168,0.789,0.439,1.06l2,2 C28.711,30.832,29.086,31,29.5,31c0.828,0,1.5-0.672,1.5-1.5c0-0.414-0.168-0.789-0.439-1.061L28.561,26.439z M17.5,29 c-0.829,0-1.5,0.672-1.5,1.5v3c0,0.828,0.671,1.5,1.5,1.5s1.5-0.672,1.5-1.5v-3C19,29.672,18.329,29,17.5,29z M17.5,7 C11.71,7,7,11.71,7,17.5S11.71,28,17.5,28S28,23.29,28,17.5S23.29,7,17.5,7z M17.5,25c-4.136,0-7.5-3.364-7.5-7.5 c0-4.136,3.364-7.5,7.5-7.5c4.136,0,7.5,3.364,7.5,7.5C25,21.636,21.636,25,17.5,25z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" id="nightIcon" x="0px" y="0px" viewBox="0 0 100 100" style="enable-bac
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<p>算法是解决特定问题求解步骤的描述，在计算机中表现为指令的有限步骤或序列。</p>
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<h2 id="特性">特性<a role="anchor" aria-hidden="true" tabindex="-1" data-no-popover="true" href="#特性" class="internal"><svg width="18" height="18" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"><path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path></svg></a></h2>
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<p>良好的算法须拥有如下五个特定：<strong>输入、输出、有穷性、确定性、可行性。</strong></p>
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<h3 id="输入">输入<a role="anchor" aria-hidden="true" tabindex="-1" data-no-popover="true" href="#输入" class="internal"><svg width="18" height="18" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"><path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path></svg></a></h3>
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<p>算法应具有<strong>零个或多个输入</strong>。</p>
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<h3 id="输出">输出<a role="anchor" aria-hidden="true" tabindex="-1" data-no-popover="true" href="#输出" class="internal"><svg width="18" height="18" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"><path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path></svg></a></h3>
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<p>算法<strong>至少有一个</strong>或多个输出。</p>
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<h3 id="有穷性">有穷性<a role="anchor" aria-hidden="true" tabindex="-1" data-no-popover="true" href="#有穷性" class="internal"><svg width="18" height="18" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"><path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path></svg></a></h3>
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<p>算法在执行有限的步骤后，自动结束而不会出现无限循环，并且每一个步骤都在可接受的时间内完成。</p>
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<h3 id="确定性">确定性<a role="anchor" aria-hidden="true" tabindex="-1" data-no-popover="true" href="#确定性" class="internal"><svg width="18" height="18" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"><path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path></svg></a></h3>
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<p>算法的每一步骤都具有确定性的含义，不会出现二义性。</p>
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<h3 id="可行性">可行性<a role="anchor" aria-hidden="true" tabindex="-1" data-no-popover="true" href="#可行性" class="internal"><svg width="18" height="18" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"><path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path></svg></a></h3>
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<p>算法的每一步都必须是可行的，也就是说，每一步都能够通过执行有限次数完成。</p>
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<h2 id="设计原则">设计原则<a role="anchor" aria-hidden="true" tabindex="-1" data-no-popover="true" href="#设计原则" class="internal"><svg width="18" height="18" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"><path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path></svg></a></h2>
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<h3 id="正确性">正确性<a role="anchor" aria-hidden="true" tabindex="-1" data-no-popover="true" href="#正确性" class="internal"><svg width="18" height="18" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"><path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path></svg></a></h3>
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<p>算法的正确性是指算法至少应该具有输入、输出和加工处理无歧义性、能正确反应问题的需求、能够得到问题的正确答案。</p>
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<ol>
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<li>没有语法错误。</li>
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<li>合法的输入数据能够产生满足要求的输出结构。</li>
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<li>非法的输入数据能够得出满足规格说明的结构。</li>
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<li>刁难的测试数据都有满足要求的输出结果。</li>
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</ol>
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<h3 id="可读性">可读性<a role="anchor" aria-hidden="true" tabindex="-1" data-no-popover="true" href="#可读性" class="internal"><svg width="18" height="18" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"><path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path></svg></a></h3>
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<p>便于阅读、理解和交流。</p>
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<h3 id="健壮性">健壮性<a role="anchor" aria-hidden="true" tabindex="-1" data-no-popover="true" href="#健壮性" class="internal"><svg width="18" height="18" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"><path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path></svg></a></h3>
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<p>当输入数据不合法时，算法也能做出相关处理，而不是产生异常或莫名其妙的结果。</p>
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<h3 id="时间效率和存储量低">时间效率和存储量低<a role="anchor" aria-hidden="true" tabindex="-1" data-no-popover="true" href="#时间效率和存储量低" class="internal"><svg width="18" height="18" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"><path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path></svg></a></h3>
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<p>设计算法应该尽量满足时间效率高和存储量低的需求。</p>
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<h2 id="度量方法">度量方法<a role="anchor" aria-hidden="true" tabindex="-1" data-no-popover="true" href="#度量方法" class="internal"><svg width="18" height="18" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"><path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path></svg></a></h2>
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<p>评价算法的优良必须有相对应的准则，目前从两方面出考量：方法论、复杂度。</p>
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<h3 id="方法论">方法论<a role="anchor" aria-hidden="true" tabindex="-1" data-no-popover="true" href="#方法论" class="internal"><svg width="18" height="18" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"><path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path></svg></a></h3>
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<ul>
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<li>事后统计法</li>
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<li>事前分析估算法</li>
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<li>函数的渐近增长</li>
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</ul>
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<h3 id="复杂度">复杂度<a role="anchor" aria-hidden="true" tabindex="-1" data-no-popover="true" href="#复杂度" class="internal"><svg width="18" height="18" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"><path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path></svg></a></h3>
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<ul>
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<li>时间（Time）复杂度：T(n) = O(f(n))</li>
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<li>空间（Space）复杂度：S(n) = O(f(n))</li>
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<li>最坏情况与平均情况</li>
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</ul></article><hr/><div class="page-footer"></div></div><div class="right sidebar"><div class="graph"><h3>关系图谱</h3><div class="graph-outer"><div id="graph-container" data-cfg="{"drag":true,"zoom":true,"depth":1,"scale":1.1,"repelForce":0.5,"centerForce":0.3,"linkDistance":30,"fontSize":0.6,"opacityScale":1,"showTags":true,"removeTags":[],"focusOnHover":false}"></div><button id="global-graph-icon" aria-label="Global Graph"><svg version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" x="0px" y="0px" viewBox="0 0 55 55" fill="currentColor" xml:space="preserve"><path d="M49,0c-3.309,0-6,2.691-6,6c0,1.035,0.263,2.009,0.726,2.86l-9.829,9.829C32.542,17.634,30.846,17,29,17
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s-2-0.897-2-2s0.897-2,2-2S47,39.897,47,41z M49,10c-2.206,0-4-1.794-4-4s1.794-4,4-4s4,1.794,4,4S51.206,10,49,10z"></path></svg></button></div><div id="global-graph-outer"><div id="global-graph-container" data-cfg="{"drag":true,"zoom":true,"depth":-1,"scale":0.9,"repelForce":0.5,"centerForce":0.3,"linkDistance":30,"fontSize":0.6,"opacityScale":1,"showTags":true,"removeTags":[],"focusOnHover":true}"></div></div></div><div class="toc desktop-only"><button type="button" id="toc" class aria-controls="toc-content" aria-expanded="true"><h3>目录</h3><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="fold"><polyline points="6 9 12 15 18 9"></polyline></svg></button><div id="toc-content" class><ul class="overflow"><li class="depth-0"><a href="#概述" data-for="概述">概述</a></li><li class="depth-0"><a href="#特性" data-for="特性">特性</a></li><li class="depth-1"><a href="#输入" data-for="输入">输入</a></li><li class="depth-1"><a href="#输出" data-for="输出">输出</a></li><li class="depth-1"><a href="#有穷性" data-for="有穷性">有穷性</a></li><li class="depth-1"><a href="#确定性" data-for="确定性">确定性</a></li><li class="depth-1"><a href="#可行性" data-for="可行性">可行性</a></li><li class="depth-0"><a href="#设计原则" data-for="设计原则">设计原则</a></li><li class="depth-1"><a href="#正确性" data-for="正确性">正确性</a></li><li class="depth-1"><a href="#可读性" data-for="可读性">可读性</a></li><li class="depth-1"><a href="#健壮性" data-for="健壮性">健壮性</a></li><li class="depth-1"><a href="#时间效率和存储量低" data-for="时间效率和存储量低">时间效率和存储量低</a></li><li class="depth-0"><a href="#度量方法" data-for="度量方法">度量方法</a></li><li class="depth-1"><a href="#方法论" data-for="方法论">方法论</a></li><li class="depth-1"><a href="#复杂度" data-for="复杂度">复杂度</a></li></ul></div></div><div class="explorer mobile-only"><button type="button" id="explorer" data-behavior="collapse" data-collapsed="collapsed" data-savestate="true" data-tree="[{"path":"Personal","collapsed":true},{"path":"Personal/Blog","collapsed":true},{"path":"Personal/Blog/2018","collapsed":true},{"path":"Personal/Blog/2020","collapsed":true},{"path":"Personal/Blog/2021","collapsed":true},{"path":"Personal/Blog/2022","collapsed":true},{"path":"Personal/Blog/2023","collapsed":true},{"path":"Personal/Blog/2024","collapsed":true},{"path":"Personal/Book","collapsed":true},{"path":"Personal/Book/个人成长","collapsed":true},{"path":"Personal/Book/医学健康","collapsed":true},{"path":"Personal/Book/历史","collapsed":true},{"path":"Personal/Book/哲学宗教","collapsed":true},{"path":"Personal/Book/心理","collapsed":true},{"path":"Personal/Book/政治军事","collapsed":true},{"path":"Personal/Book/教育学习","collapsed":true},{"path":"Personal/Book/文学","collapsed":true},{"path":"Personal/Book/生活百科","collapsed":true},{"path":"Personal/Book/社会文化","collapsed":true},{"path":"Personal/Book/科学技术","collapsed":true},{"path":"Personal/Book/经济理财","collapsed":true},{"path":"
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