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  1. <!DOCTYPE html><html lang="en"><head><meta charset="UTF-8"><meta name="viewport" content="width=device-width,initial-scale=1,maximum-scale=2"><meta name="theme-color" content="#222"><meta name="generator" content="Hexo 4.2.0"><link rel="apple-touch-icon" sizes="180x180" href="/blog/blog/images/apple-touch-icon-next.png"><link rel="icon" type="image/png" sizes="32x32" href="/blog/blog/images/favicon-frog.png"><link rel="icon" type="image/png" sizes="16x16" href="/blog/blog/images/favicon-frog.png"><link rel="mask-icon" href="/blog/blog/images/logo.svg" color="#222"><link rel="stylesheet" href="/blog/css/main.css"><link rel="stylesheet" href="//fonts.googleapis.com/css?family=Comic Sans MS:300,300italic,400,400italic,700,700italic|Consolas:300,300italic,400,400italic,700,700italic&display=swap&subset=latin,latin-ext"><link rel="stylesheet" href="/blog/lib/font-awesome/css/font-awesome.min.css"><link rel="stylesheet" href="/blog/lib/pace/pace-theme-minimal.min.css"><script 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class="menu-item menu-item-home"><a href="/blog/" rel="section"><i class="fa fa-fw fa-home"></i> Home</a></li><li class="menu-item menu-item-tags"><a href="/blog/tags/" rel="section"><i class="fa fa-fw fa-tags"></i> Tags</a></li><li class="menu-item menu-item-archives"><a href="/blog/archives/" rel="section"><i class="fa fa-fw fa-archive"></i> Archives</a></li><li class="menu-item menu-item-games"><a href="/blog/games/" rel="section"><i class="fa fa-fw fa-gamepad"></i> Games</a></li></ul></nav></div></header><div class="back-to-top"><i class="fa fa-arrow-up"></i> <span>0%</span></div><main class="main"><div class="main-inner"><div class="content-wrap"><div class="content index posts-expand"><article itemscope itemtype="http://schema.org/Article" class="post-block" lang="en"><link itemprop="mainEntityOfPage" href="https://schtonn.github.io/blog/posts/ex-KMP/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/blog/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content="blog"></span><script type="text/javascript" src="/blog/js/md5.js"></script><script></script><script>document.oncopy=function(e){window.event&&(e=window.event);try{var t=e.srcElement;return"INPUT"==t.tagName&&"text"==t.type.toLowerCase()||"TEXTAREA"==t.tagName}catch(e){return!1}}</script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="schtonn"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/blog/posts/ex-KMP/" class="post-title-link" itemprop="url">拓展 KMP</a></h2><div class="post-meta"><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-o"></i></span> <span class="post-meta-item-text">Posted on</span> <time title="Created: 2020-Dec-16 22:40:10" itemprop="dateCreated datePublished" datetime="2020-12-16T22:40:10+08:00">2020-Dec-16</time></span><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-check-o"></i></span> <span class="post-meta-item-text">Edited on</span> <time title="Modified: 2021-Apr-17 11:45:55" itemprop="dateModified" datetime="2021-04-17T11:45:55+08:00">2021-Apr-17</time></span></div></header><div class="post-body" itemprop="articleBody"><h2 id="前置知识">前置知识</h2><p>字符串基础操作;强烈建议先学习 <a href="/blog/posts/KMP">KMP</a> 和 <a href="/blog/posts/manacher">manacher</a>,对理解有很大帮助。</p><h2 id="引入">引入</h2><p>假设模式串是 <code>pat</code>,文本串是 <code>txt</code>。</p><p>拓展 KMP,有时也叫 Z 函数,是求 <code>pat</code> 和 <code>txt</code> 的(所有)后缀的最大公共前缀长度,用 <code>z[i]</code> 表示。</p><div class="post-button"> <a class="btn" href="/blog/posts/ex-KMP/#more" rel="contents">Read more &raquo;</a></div></div><footer class="post-footer"><div class="post-eof"></div></footer></article><article itemscope itemtype="http://schema.org/Article" class="post-block" lang="en"><link itemprop="mainEntityOfPage" href="https://schtonn.github.io/blog/posts/KMP/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/blog/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content="blog"></span><script type="text/javascript" src="/blog/js/md5.js"></script><script></script><script>document.oncopy=function(e){window.event&&(e=window.event);try{var t=e.srcElement;return"INPUT"==t.tagName&&"text"==t.type.toLowerCase()||"TEXTAREA"==t.tagName}catch(e){return!1}}</script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="schtonn"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/blog/posts/KMP/" class="post-title-link" itemprop="url">KMP</a></h2><div class="post-meta"><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-o"></i></span> <span class="post-meta-item-text">Posted on</span> <time title="Created: 2020-Dec-16 18:42:34" itemprop="dateCreated datePublished" datetime="2020-12-16T18:42:34+08:00">2020-Dec-16</time></span><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-check-o"></i></span> <span class="post-meta-item-text">Edited on</span> <time title="Modified: 2022-Oct-19 23:02:06" itemprop="dateModified" datetime="2022-10-19T23:02:06+08:00">2022-Oct-19</time></span></div></header><div class="post-body" itemprop="articleBody"><h2 id="前置知识">前置知识</h2><p>字符串基础操作。</p><h2 id="引入">引入</h2><p>KMP 是一种字符串匹配算法,意思就是说给出模式串 <code>pat</code> 和文本串 <code>txt</code>(长度各为 <code>m</code> 和 <code>n</code>),找出模式串在文本串中出现的所有位置。</p><p>考虑用暴力来解决这一问题,那么:</p><p>对于文本串的每一位置,循序匹配模式串,遇到不匹配就退出。此算法时间复杂度 <span class="math inline">\(O(mn)\)</span>。</p><p>KMP算法则用了一 <span class="math inline">\(O(m)\)</span> 的预处理将时间复杂度缩减到了 <span class="math inline">\(O(n)\)</span>。</p><div class="post-button"> <a class="btn" href="/blog/posts/KMP/#more" rel="contents">Read more &raquo;</a></div></div><footer class="post-footer"><div class="post-eof"></div></footer></article><article itemscope itemtype="http://schema.org/Article" class="post-block" lang="en"><link itemprop="mainEntityOfPage" href="https://schtonn.github.io/blog/posts/quick-pow/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/blog/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content="blog"></span><script type="text/javascript" src="/blog/js/md5.js"></script><script></script><script>document.oncopy=function(e){window.event&&(e=window.event);try{var t=e.srcElement;return"INPUT"==t.tagName&&"text"==t.type.toLowerCase()||"TEXTAREA"==t.tagName}catch(e){return!1}}</script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="schtonn"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/blog/posts/quick-pow/" class="post-title-link" itemprop="url">快速幂</a></h2><div class="post-meta"><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-o"></i></span> <span class="post-meta-item-text">Posted on</span> <time title="Created: 2020-Nov-17 21:33:40" itemprop="dateCreated datePublished" datetime="2020-11-17T21:33:40+08:00">2020-Nov-17</time></span><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-check-o"></i></span> <span class="post-meta-item-text">Edited on</span> <time title="Modified: 2022-Oct-19 23:02:06" itemprop="dateModified" datetime="2022-10-19T23:02:06+08:00">2022-Oct-19</time></span></div></header><div class="post-body" itemprop="articleBody"><h2 id="引入">引入</h2><p>快速幂是一种效率极高,以至于题目中不得不取模防止数据越界的求幂算法。计算 <span class="math inline">\(a^n\)</span> 的复杂度为 <span class="math inline">\(O(\log n)\)</span>。</p><div class="post-button"> <a class="btn" href="/blog/posts/quick-pow/#more" rel="contents">Read more &raquo;</a></div></div><footer class="post-footer"><div class="post-eof"></div></footer></article><article itemscope itemtype="http://schema.org/Article" class="post-block" lang="en"><link itemprop="mainEntityOfPage" href="https://schtonn.github.io/blog/posts/num-convert/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/blog/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content="blog"></span><script type="text/javascript" src="/blog/js/md5.js"></script><script></script><script>document.oncopy=function(e){window.event&&(e=window.event);try{var t=e.srcElement;return"INPUT"==t.tagName&&"text"==t.type.toLowerCase()||"TEXTAREA"==t.tagName}catch(e){return!1}}</script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="schtonn"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/blog/posts/num-convert/" class="post-title-link" itemprop="url">进制转换</a></h2><div class="post-meta"><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-o"></i></span> <span class="post-meta-item-text">Posted on</span> <time title="Created: 2020-Jul-28 20:44:27" itemprop="dateCreated datePublished" datetime="2020-07-28T20:44:27+08:00">2020-Jul-28</time></span><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-check-o"></i></span> <span class="post-meta-item-text">Edited on</span> <time title="Modified: 2022-Oct-19 23:02:06" itemprop="dateModified" datetime="2022-10-19T23:02:06+08:00">2022-Oct-19</time></span></div></header><div class="post-body" itemprop="articleBody"><h2 id="引入">引入</h2><p>说起进制,大家应该都不陌生。今天来讲一讲进制转换。</p><div class="post-button"> <a class="btn" href="/blog/posts/num-convert/#more" rel="contents">Read more &raquo;</a></div></div><footer class="post-footer"><div class="post-eof"></div></footer></article><article itemscope itemtype="http://schema.org/Article" class="post-block" lang="en"><link itemprop="mainEntityOfPage" href="https://schtonn.github.io/blog/posts/domino/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/blog/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content="blog"></span><script type="text/javascript" src="/blog/js/md5.js"></script><script></script><script>document.oncopy=function(e){window.event&&(e=window.event);try{var t=e.srcElement;return"INPUT"==t.tagName&&"text"==t.type.toLowerCase()||"TEXTAREA"==t.tagName}catch(e){return!1}}</script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="schtonn"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/blog/posts/domino/" class="post-title-link" itemprop="url">各种奇奇怪怪的多米诺骨牌</a></h2><div class="post-meta"><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-o"></i></span> <span class="post-meta-item-text">Posted on</span> <time title="Created: 2020-Jun-21 12:22:19" itemprop="dateCreated datePublished" datetime="2020-06-21T12:22:19+08:00">2020-Jun-21</time></span><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-check-o"></i></span> <span class="post-meta-item-text">Edited on</span> <time title="Modified: 2022-Oct-19 23:02:06" itemprop="dateModified" datetime="2022-10-19T23:02:06+08:00">2022-Oct-19</time></span></div></header><div class="post-body" itemprop="articleBody"><h2 id="前置知识">前置知识</h2><p>动态规划,二进制基础知识。</p><h2 id="引入">引入</h2><p>假设我们有一个矩形的棋盘,里面有 <span class="math inline">\(n\)</span> 行 <span class="math inline">\(m\)</span> 列的 <span class="math inline">\(1\times1\)</span> 的方格,现在我们要往里面放 <span class="math inline">\(1\times2\)</span> 的多米诺骨牌。要求骨牌不能重叠,正好填满棋盘的所有方格。求所有方案数。</p><p>这时我们可以利用状态压缩,对每一层进行动态规划。</p><div class="post-button"> <a class="btn" href="/blog/posts/domino/#more" rel="contents">Read more &raquo;</a></div></div><footer class="post-footer"><div class="post-eof"></div></footer></article><article itemscope itemtype="http://schema.org/Article" class="post-block" lang="en"><link itemprop="mainEntityOfPage" href="https://schtonn.github.io/blog/posts/manacher/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/blog/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content="blog"></span><script type="text/javascript" src="/blog/js/md5.js"></script><script></script><script>document.oncopy=function(e){window.event&&(e=window.event);try{var t=e.srcElement;return"INPUT"==t.tagName&&"text"==t.type.toLowerCase()||"TEXTAREA"==t.tagName}catch(e){return!1}}</script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="schtonn"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/blog/posts/manacher/" class="post-title-link" itemprop="url">Manacher</a></h2><div class="post-meta"><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-o"></i></span> <span class="post-meta-item-text">Posted on</span> <time title="Created: 2020-Jun-14 22:47:39" itemprop="dateCreated datePublished" datetime="2020-06-14T22:47:39+08:00">2020-Jun-14</time></span><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-check-o"></i></span> <span class="post-meta-item-text">Edited on</span> <time title="Modified: 2022-Oct-19 23:02:06" itemprop="dateModified" datetime="2022-10-19T23:02:06+08:00">2022-Oct-19</time></span></div></header><div class="post-body" itemprop="articleBody"><h2 id="前置知识">前置知识</h2><p>字符串基础操作。</p><h2 id="引入">引入</h2><p>回文串,即 <span class="math inline">\(s=s_{rev}\)</span>,也就是本身与反转相等。</p><p>想要找到字符串 <span class="math inline">\(s\)</span> 中最大的回文子串,很容易想到的是一种复杂度为 <span class="math inline">\(O(n^2)\)</span> 的朴素算法,也就是对于每一个点都向外扩展。</p><p>这里介绍一种复杂度为 <span class="math inline">\(O(n)\)</span> 的最大回文子串算法,叫做 Manacher。</p><div class="post-button"> <a class="btn" href="/blog/posts/manacher/#more" rel="contents">Read more &raquo;</a></div></div><footer class="post-footer"><div class="post-eof"></div></footer></article><article itemscope itemtype="http://schema.org/Article" class="post-block" lang="en"><link itemprop="mainEntityOfPage" href="https://schtonn.github.io/blog/posts/hamilton/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/blog/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content="blog"></span><script type="text/javascript" src="/blog/js/md5.js"></script><script></script><script>document.oncopy=function(e){window.event&&(e=window.event);try{var t=e.srcElement;return"INPUT"==t.tagName&&"text"==t.type.toLowerCase()||"TEXTAREA"==t.tagName}catch(e){return!1}}</script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="schtonn"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/blog/posts/hamilton/" class="post-title-link" itemprop="url">哈密尔顿回路</a></h2><div class="post-meta"><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-o"></i></span> <span class="post-meta-item-text">Posted on</span> <time title="Created: 2020-Jun-14 22:03:13" itemprop="dateCreated datePublished" datetime="2020-06-14T22:03:13+08:00">2020-Jun-14</time></span><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-check-o"></i></span> <span class="post-meta-item-text">Edited on</span> <time title="Modified: 2022-Oct-19 23:02:06" itemprop="dateModified" datetime="2022-10-19T23:02:06+08:00">2022-Oct-19</time></span></div></header><div class="post-body" itemprop="articleBody"><h2 id="前置知识">前置知识</h2><p>图论,动态规划,二进制基础知识。</p><h2 id="引入">引入</h2><p>我们都知道欧拉回路,也就是经过每条边正好一遍的路径。</p><p>哈密尔顿回路和欧拉回路很像,但是需要经过每个点正好一遍。</p><p>欧拉回路有稳定的解法,然而哈密尔顿回路是 <code>NPC</code> 的,没有多项式时间解法。</p><p>我们使用动态规划来解决哈密尔顿回路问题。</p><div class="post-button"> <a class="btn" href="/blog/posts/hamilton/#more" rel="contents">Read more &raquo;</a></div></div><footer class="post-footer"><div class="post-eof"></div></footer></article><article itemscope itemtype="http://schema.org/Article" class="post-block" lang="en"><link itemprop="mainEntityOfPage" href="https://schtonn.github.io/blog/posts/matrix-pow/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/blog/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content="blog"></span><script type="text/javascript" src="/blog/js/md5.js"></script><script></script><script>document.oncopy=function(e){window.event&&(e=window.event);try{var t=e.srcElement;return"INPUT"==t.tagName&&"text"==t.type.toLowerCase()||"TEXTAREA"==t.tagName}catch(e){return!1}}</script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="schtonn"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/blog/posts/matrix-pow/" class="post-title-link" itemprop="url">矩阵快速幂简述</a></h2><div class="post-meta"><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-o"></i></span> <span class="post-meta-item-text">Posted on</span> <time title="Created: 2020-Mar-21 19:20:08" itemprop="dateCreated datePublished" datetime="2020-03-21T19:20:08+08:00">2020-Mar-21</time></span><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-check-o"></i></span> <span class="post-meta-item-text">Edited on</span> <time title="Modified: 2022-Oct-19 23:02:06" itemprop="dateModified" datetime="2022-10-19T23:02:06+08:00">2022-Oct-19</time></span></div></header><div class="post-body" itemprop="articleBody"><h2 id="引入">引入</h2><p>想要了解矩阵快速幂,就不得不提到矩阵的概念。矩阵就像一个二维数组,存储了一组数据,如: <span class="math display">\[M=\left[ \begin{matrix} 1&amp;2&amp;3\\ 4&amp;5&amp;6\\ 7&amp;8&amp;9\end{matrix} \right]\]</span> 用 <span class="math inline">\(M_{i,j}\)</span> 表示矩阵第 <span class="math inline">\(i\)</span> 行第 <span class="math inline">\(j\)</span> 列的数据,如 <span class="math inline">\(M_{2,3}=6\)</span>。</p><div class="post-button"> <a class="btn" href="/blog/posts/matrix-pow/#more" rel="contents">Read more &raquo;</a></div></div><footer class="post-footer"><div class="post-eof"></div></footer></article><article itemscope itemtype="http://schema.org/Article" class="post-block" lang="en"><link itemprop="mainEntityOfPage" href="https://schtonn.github.io/blog/posts/segment-tree/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/blog/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content="blog"></span><script type="text/javascript" src="/blog/js/md5.js"></script><script></script><script>document.oncopy=function(e){window.event&&(e=window.event);try{var t=e.srcElement;return"INPUT"==t.tagName&&"text"==t.type.toLowerCase()||"TEXTAREA"==t.tagName}catch(e){return!1}}</script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="schtonn"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/blog/posts/segment-tree/" class="post-title-link" itemprop="url">线段树</a></h2><div class="post-meta"><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-o"></i></span> <span class="post-meta-item-text">Posted on</span> <time title="Created: 2020-Mar-02 11:37:36" itemprop="dateCreated datePublished" datetime="2020-03-02T11:37:36+08:00">2020-Mar-02</time></span><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-check-o"></i></span> <span class="post-meta-item-text">Edited on</span> <time title="Modified: 2022-Oct-19 23:02:06" itemprop="dateModified" datetime="2022-10-19T23:02:06+08:00">2022-Oct-19</time></span></div></header><div class="post-body" itemprop="articleBody"><h2 id="前置知识">前置知识</h2><p>数组,结构体,二叉树</p><h2 id="引入">引入</h2><p>有时候我们会遇到一些大规模的区间查找和区间修改问题,比如让你维护一个 <span class="math inline">\(10^5\)</span> 长度的数列,要求操作有区间求和、区间加(区间每个数加上一个值),让你在一秒内完成 <span class="math inline">\(10^5\)</span> 次操作。</p><p>暴力是肯定不行的,数据范围太大,操作太多,会超时。</p><p>所以我们就有一种专门解决大范围区间修改查询的数据结构:线段树。</p><div class="post-button"> <a class="btn" href="/blog/posts/segment-tree/#more" rel="contents">Read more &raquo;</a></div></div><footer class="post-footer"><div class="post-eof"></div></footer></article><article itemscope itemtype="http://schema.org/Article" class="post-block" lang="en"><link itemprop="mainEntityOfPage" href="https://schtonn.github.io/blog/posts/fibonacci/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/blog/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content="blog"></span><script type="text/javascript" src="/blog/js/md5.js"></script><script></script><script>document.oncopy=function(e){window.event&&(e=window.event);try{var t=e.srcElement;return"INPUT"==t.tagName&&"text"==t.type.toLowerCase()||"TEXTAREA"==t.tagName}catch(e){return!1}}</script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="schtonn"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/blog/posts/fibonacci/" class="post-title-link" itemprop="url">斐波那契数列</a></h2><div class="post-meta"><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-o"></i></span> <span class="post-meta-item-text">Posted on</span> <time title="Created: 2020-Mar-02 11:35:44" itemprop="dateCreated datePublished" datetime="2020-03-02T11:35:44+08:00">2020-Mar-02</time></span><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-check-o"></i></span> <span class="post-meta-item-text">Edited on</span> <time title="Modified: 2021-Apr-17 11:14:20" itemprop="dateModified" datetime="2021-04-17T11:14:20+08:00">2021-Apr-17</time></span></div></header><div class="post-body" itemprop="articleBody"><p>引自:《信息学奥赛之-数学一本通》</p><p>就是这样: <span class="math display">\[\operatorname{F}(n)=\dfrac{\sqrt{5}}{5}\left[\left(\frac{1+\sqrt5}{2}\right)^n-\left(\frac{1-\sqrt5}{2}\right)^n\right]\]</span> 代码就这么简单:</p><figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="keyword">int</span> <span class="title">fibo</span><span class="params">(<span class="keyword">int</span> n)</span></span>&#123;</span><br><span class="line"> <span class="keyword">return</span> (<span class="built_in">sqrt</span>(<span class="number">5</span>)/<span class="number">5</span>)*(<span class="built_in">pow</span>((<span class="number">1</span>+<span class="built_in">sqrt</span>(<span class="number">5</span>))/<span class="number">2</span>,n)-<span class="built_in">pow</span>((<span class="number">1</span>-<span class="built_in">sqrt</span>(<span class="number">5</span>))/<span class="number">2</span>,n));</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure><p></p></div><footer class="post-footer"><div 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