schtonn
/
public


			
				
					
						
						
							1234567891011121314151617181920212223242526272829303132333435363738394041424344454647
							<!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="/images/apple-touch-icon-next.png"><link rel="icon" type="image/png" sizes="32x32" href="/images/favicon-32x32-next.png"><link rel="icon" type="image/png" sizes="16x16" href="/images/favicon-16x16-next.png"><link rel="mask-icon" href="/images/logo.svg" color="#222"><link rel="stylesheet" href="/css/main.css"><link rel="stylesheet" href="/lib/font-awesome/css/font-awesome.min.css"><link rel="stylesheet" href="/lib/pace/pace-theme-minimal.min.css"><script src="/lib/pace/pace.min.js"></script><script id="hexo-configurations">var NexT=window.NexT||{},CONFIG={hostname:"schtonn.github.io",root:"/",scheme:"Muse",version:"7.8.0",exturl:!1,sidebar:{position:"left",display:"post",padding:18,offset:12,onmobile:!1},copycode:{enable:!0,show_result:!0,style:"flat"},back2top:{enable:!0,sidebar:!1,scrollpercent:!0},bookmark:{enable:!1,color:"#222",save:"auto"},fancybox:!1,mediumzoom:!1,lazyload:!0,pangu:!1,comments:{style:"tabs",active:"valine",storage:!0,lazyload:!1,nav:null,activeClass:"valine"},algolia:{hits:{per_page:10},labels:{input_placeholder:"Search for Posts",hits_empty:"We didn't find any results for the search: ${query}",hits_stats:"${hits} results found in ${time} ms"}},localsearch:{enable:!1,trigger:"auto",top_n_per_article:1,unescape:!1,preload:!1},motion:{enable:!0,async:!1,transition:{post_block:"fadeIn",post_header:"slideDownIn",post_body:"slideDownIn",coll_header:"slideLeftIn",sidebar:"slideUpIn"}}}</script><meta property="og:type" content="website"><meta property="og:title" content="Alex&#39;s Blog"><meta property="og:url" content="https://schtonn.github.io/index.html"><meta property="og:site_name" content="Alex&#39;s Blog"><meta property="og:locale" content="en_US"><meta property="article:author" content="Alex"><meta name="twitter:card" content="summary"><link rel="canonical" href="https://schtonn.github.io/"><script id="page-configurations">CONFIG.page={sidebar:"",isHome:!0,isPost:!1,lang:"en"}</script><title>Alex's Blog</title><noscript><style>.sidebar-inner,.use-motion .brand,.use-motion .collection-header,.use-motion .comments,.use-motion .menu-item,.use-motion .pagination,.use-motion .post-block,.use-motion .post-body,.use-motion .post-header{opacity:initial}.use-motion .site-subtitle,.use-motion .site-title{opacity:initial;top:initial}.use-motion .logo-line-before i{left:initial}.use-motion .logo-line-after i{right:initial}</style></noscript><link rel="alternate" href="/atom.xml" title="Alex's Blog" type="application/atom+xml"></head><body itemscope itemtype="http://schema.org/WebPage"><div class="container use-motion"><div class="headband"></div><header class="header" itemscope itemtype="http://schema.org/WPHeader"><div class="header-inner"><div class="site-brand-container"><div class="site-nav-toggle"><div class="toggle" aria-label="Toggle navigation bar"><span class="toggle-line toggle-line-first"></span><span class="toggle-line toggle-line-middle"></span><span class="toggle-line toggle-line-last"></span></div></div><div class="site-meta"><a href="/" class="brand" rel="start"><span class="logo-line-before"><i></i></span><h1 class="site-title">Alex's Blog</h1><span class="logo-line-after"><i></i></span></a><p class="site-subtitle" itemprop="description">schtonn</p></div><div class="site-nav-right"><div class="toggle popup-trigger"></div></div></div><nav class="site-nav"><ul id="menu" class="menu"><li class="menu-item menu-item-home"><a href="/" rel="section"><i class="fa fa-fw fa-home"></i> Home</a></li><li class="menu-item menu-item-tags"><a href="/tags/" rel="section"><i class="fa fa-fw fa-tags"></i> Tags</a></li><li class="menu-item menu-item-archives"><a href="/archives/" rel="section"><i class="fa fa-fw fa-archive"></i> Archives</a></li><li class="menu-item menu-item-games"><a href="/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><div class="reading-progress-bar"></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/posts/plan/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content=""></span><script></script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="Alex's Blog"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/posts/plan/" class="post-title-link" itemprop="url">plan</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-01 22:36:07" itemprop="dateCreated datePublished" datetime="2020-03-01T22:36:07+08:00">2020-Mar-01</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: 2020-Apr-07 18:53:18" itemprop="dateModified" datetime="2020-04-07T18:53:18+08:00">2020-Apr-07</time></span></div></header><div class="post-body" itemprop="articleBody"><p>This page is locked.</p><div class="post-button"> <a class="btn" href="/posts/plan/#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/posts/matrix-pow/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content=""></span><script></script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="Alex's Blog"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/posts/matrix-pow/" class="post-title-link" itemprop="url">矩阵快速幂运用</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: 2020-Mar-29 15:59:04" itemprop="dateModified" datetime="2020-03-29T15:59:04+08:00">2020-Mar-29</time></span></div></header><div class="post-body" itemprop="articleBody"><h3 id="引入"><a class="markdownIt-Anchor" href="#引入"></a> 引入</h3><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：</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>M</mi><mo>=</mo><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>2</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>3</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>4</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>5</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>6</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>7</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>8</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>9</mn></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow></mrow><annotation encoding="application/x-tex">M=\left[ \begin{matrix} 1&amp;2&amp;3\\ 4&amp;5&amp;6\\ 7&amp;8&amp;9\end{matrix} \right]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.68333em;vertical-align:0"></span><span class="mord mathdefault" style="margin-right:.10903em">M</span><span class="mspace" style="margin-right:.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:3.60004em;vertical-align:-1.55002em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.05002em"><span style="top:-2.2500000000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-4.05002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.55002em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.05em"><span style="top:-4.21em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">1</span></span></span><span style="top:-3.0099999999999993em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">4</span></span></span><span style="top:-1.8099999999999994em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">7</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.5500000000000007em"><span></span></span></span></span></span><span class="arraycolsep" style="width:.5em"></span><span class="arraycolsep" style="width:.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.05em"><span style="top:-4.21em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">2</span></span></span><span style="top:-3.0099999999999993em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">5</span></span></span><span style="top:-1.8099999999999994em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">8</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.5500000000000007em"><span></span></span></span></span></span><span class="arraycolsep" style="width:.5em"></span><span class="arraycolsep" style="width:.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.05em"><span style="top:-4.21em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">3</span></span></span><span style="top:-3.0099999999999993em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">6</span></span></span><span style="top:-1.8099999999999994em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">9</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.5500000000000007em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.05002em"><span style="top:-2.2500000000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-4.05002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.55002em"><span></span></span></span></span></span></span></span></span></span></span></span></p><p>用<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>M</mi><mrow><mi>i</mi><mo separator="true">,</mo><mi>j</mi></mrow></msub></mrow><annotation encoding="application/x-tex">M_{i,j}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.969438em;vertical-align:-.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:.10903em">M</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.311664em"><span style="top:-2.5500000000000003em;margin-left:-.10903em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mpunct mtight">,</span><span class="mord mathdefault mtight" style="margin-right:.05724em">j</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:.286108em"><span></span></span></span></span></span></span></span></span></span> 表示矩阵第<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.65952em;vertical-align:0"></span><span class="mord mathdefault">i</span></span></span></span> 行第<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>j</mi></mrow><annotation encoding="application/x-tex">j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.85396em;vertical-align:-.19444em"></span><span class="mord mathdefault" style="margin-right:.05724em">j</span></span></span></span> 列的数据，如<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>M</mi><mrow><mn>2</mn><mo separator="true">,</mo><mn>3</mn></mrow></msub><mo>=</mo><mn>6</mn></mrow><annotation encoding="application/x-tex">M_{2,3}=6</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.969438em;vertical-align:-.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:.10903em">M</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.301108em"><span style="top:-2.5500000000000003em;margin-left:-.10903em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span><span class="mpunct mtight">,</span><span class="mord mtight">3</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:.64444em;vertical-align:0"></span><span class="mord">6</span></span></span></span>。</p><div class="post-button"> <a class="btn" href="/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/posts/computer/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content=""></span><script></script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="Alex's Blog"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/posts/computer/" class="post-title-link" itemprop="url">How do computers work?</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-04 12:53:05" itemprop="dateCreated datePublished" datetime="2020-03-04T12:53:05+08:00">2020-Mar-04</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: 2020-Apr-10 20:28:47" itemprop="dateModified" datetime="2020-04-10T20:28:47+08:00">2020-Apr-10</time></span></div></header><div class="post-body" itemprop="articleBody"><p>This page is locked</p><div class="post-button"> <a class="btn" href="/posts/computer/#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/posts/segment-tree/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content=""></span><script></script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="Alex's Blog"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/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: 2020-Mar-29 15:59:45" itemprop="dateModified" datetime="2020-03-29T15:59:45+08:00">2020-Mar-29</time></span></div></header><div class="post-body" itemprop="articleBody"><h3 id="前置知识"><a class="markdownIt-Anchor" href="#前置知识"></a> 前置知识</h3><p>数组，结构体，二叉树</p><h3 id="引入"><a class="markdownIt-Anchor" href="#引入"></a> 引入</h3><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="katex"><span class="katex-mathml"><math><semantics><mrow><mn>1</mn><msup><mn>0</mn><mn>5</mn></msup></mrow><annotation encoding="application/x-tex">10^5</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.8141079999999999em;vertical-align:0"></span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:.8141079999999999em"><span style="top:-3.063em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">5</span></span></span></span></span></span></span></span></span></span></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="katex"><span class="katex-mathml"><math><semantics><mrow><mn>1</mn><msup><mn>0</mn><mn>5</mn></msup></mrow><annotation encoding="application/x-tex">10^5</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.8141079999999999em;vertical-align:0"></span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:.8141079999999999em"><span style="top:-3.063em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">5</span></span></span></span></span></span></span></span></span></span></span> 次操作。<br> 暴力是肯定不行的，数据范围太大，操作太多，会超时。<br> 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="/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/posts/fibonacci/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content=""></span><script></script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="Alex's Blog"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/posts/fibonacci/" class="post-title-link" itemprop="url">斐波那契数列-O(1)</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: 2020-Mar-29 22:23:24" itemprop="dateModified" datetime="2020-03-29T22:23:24+08:00">2020-Mar-29</time></span></div></header><div class="post-body" itemprop="articleBody"><p>引自：《信息学奥赛之-数学一本通》<br> 揍是这样：</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">F</mi><mo>⁡</mo><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><msqrt><mn>5</mn></msqrt><mn>5</mn></mfrac><mo>⋅</mo><mrow><mo fence="true">[</mo><msup><mrow><mo fence="true">(</mo><mn>1</mn><mo>+</mo><msqrt><mn>5</mn></msqrt><mo fence="true">)</mo></mrow><mi>n</mi></msup><mo>−</mo><msup><mrow><mo fence="true">(</mo><mn>1</mn><mo>−</mo><msqrt><mn>5</mn></msqrt><mo fence="true">)</mo></mrow><mi>n</mi></msup><mo fence="true">]</mo></mrow></mrow><annotation encoding="application/x-tex">\operatorname{F}(n)=\dfrac{\sqrt{5}}{5}\cdot\left[\left(1+\sqrt{5}\right)^n-\left(1-\sqrt{5}\right)^n\right]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-.25em"></span><span class="mop"><span class="mord mathrm">F</span></span><span class="mopen">(</span><span class="mord mathdefault">n</span><span class="mclose">)</span><span class="mspace" style="margin-right:.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.27022em;vertical-align:-.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5842200000000002em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">5</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.90722em"><span class="svg-align" style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord" style="padding-left:.833em"><span class="mord">5</span></span></span><span style="top:-2.86722em"><span class="pstrut" style="height:3em"></span><span class="hide-tail" style="min-width:.853em;height:1.08em"><svg width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95 702c-2.7 0-7.17-2.7-13.5-8-5.8-5.3-9.5-10-9.5-14 0-2 .3-3.3 1-4 1.3-2.7 23.83-20.7 67.5-54 44.2-33.3 65.8-50.3 66.5-51 1.3-1.3 3-2 5-2 4.7 0 8.7 3.3 12 10s173 378 173 378c.7 0 35.3-71 104-213 68.7-142 137.5-285 206.5-429 69-144 104.5-217.7 106.5-221 5.3-9.3 12-14 20-14H400000v40H845.2724s-225.272 467-225.272 467-235 486-235 486c-2.7 4.7-9 7-19 7-6 0-10-1-12-3s-194-422-194-422-65 47-65 47zM834 80H400000v40H845z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:.13278em"><span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:.2222222222222222em"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.854312em;vertical-align:-.65002em"></span><span class="minner"><span class="mopen delimcenter" style="top:0"><span class="delimsizing size2">[</span></span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0"><span class="delimsizing size2">(</span></span><span class="mord">1</span><span class="mspace" style="margin-right:.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:.2222222222222222em"></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.956095em"><span class="svg-align" style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord" style="padding-left:.833em"><span class="mord">5</span></span></span><span style="top:-2.916095em"><span class="pstrut" style="height:3em"></span><span class="hide-tail" style="min-width:.853em;height:1.08em"><svg width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95 702c-2.7 0-7.17-2.7-13.5-8-5.8-5.3-9.5-10-9.5-14 0-2 .3-3.3 1-4 1.3-2.7 23.83-20.7 67.5-54 44.2-33.3 65.8-50.3 66.5-51 1.3-1.3 3-2 5-2 4.7 0 8.7 3.3 12 10s173 378 173 378c.7 0 35.3-71 104-213 68.7-142 137.5-285 206.5-429 69-144 104.5-217.7 106.5-221 5.3-9.3 12-14 20-14H400000v40H845.2724s-225.272 467-225.272 467-235 486-235 486c-2.7 4.7-9 7-19 7-6 0-10-1-12-3s-194-422-194-422-65 47-65 47zM834 80H400000v40H845z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:.08390500000000001em"><span></span></span></span></span></span><span class="mclose delimcenter" style="top:0"><span class="delimsizing size2">)</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.204292em"><span style="top:-3.6029em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:.2222222222222222em"></span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0"><span class="delimsizing size2">(</span></span><span class="mord">1</span><span class="mspace" style="margin-right:.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:.2222222222222222em"></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.956095em"><span class="svg-align" style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord" style="padding-left:.833em"><span class="mord">5</span></span></span><span style="top:-2.916095em"><span class="pstrut" style="height:3em"></span><span class="hide-tail" style="min-width:.853em;height:1.08em"><svg width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95 702c-2.7 0-7.17-2.7-13.5-8-5.8-5.3-9.5-10-9.5-14 0-2 .3-3.3 1-4 1.3-2.7 23.83-20.7 67.5-54 44.2-33.3 65.8-50.3 66.5-51 1.3-1.3 3-2 5-2 4.7 0 8.7 3.3 12 10s173 378 173 378c.7 0 35.3-71 104-213 68.7-142 137.5-285 206.5-429 69-144 104.5-217.7 106.5-221 5.3-9.3 12-14 20-14H400000v40H845.2724s-225.272 467-225.272 467-235 486-235 486c-2.7 4.7-9 7-19 7-6 0-10-1-12-3s-194-422-194-422-65 47-65 47zM834 80H400000v40H845z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:.08390500000000001em"><span></span></span></span></span></span><span class="mclose delimcenter" style="top:0"><span class="delimsizing size2">)</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.204292em"><span style="top:-3.6029em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0"><span class="delimsizing size2">]</span></span></span></span></span></span></span></p><p>代码揍这么简单：</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>要是再加个快速幂就更棒了（够快了，懒得写）</p></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/posts/dinic/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content=""></span><script></script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="Alex's Blog"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/posts/dinic/" class="post-title-link" itemprop="url">网络最大流-Dinic</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 11:31:22" itemprop="dateCreated datePublished" datetime="2020-03-02T11:31:22+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: 2020-Mar-29 15:59:26" itemprop="dateModified" datetime="2020-03-29T15:59:26+08:00">2020-Mar-29</time></span></div></header><div class="post-body" itemprop="articleBody"><h3 id="前置知识"><a class="markdownIt-Anchor" href="#前置知识"></a> 前置知识</h3><p>存图方式（<a href="http://baidu.physton.com/?q=%E9%82%BB%E6%8E%A5%E8%A1%A8" target="_blank" rel="noopener" title="简单">邻接表</a>，<a href="http://baidu.physton.com/?q=%E9%82%BB%E6%8E%A5%E7%9F%A9%E9%98%B5" target="_blank" rel="noopener" title="都太简单了">邻接矩阵</a>）,图的遍历（<a href="http://baidu.physton.com/?q=dfs" target="_blank" rel="noopener" title="简单">dfs</a>，<a href="http://baidu.physton.com/?q=bfs" target="_blank" rel="noopener" title="简单">bfs</a>）</p><h3 id="引入"><a class="markdownIt-Anchor" href="#引入"></a> 引入</h3><p>我们举个例子吧：<br> 有一个毒瘤水管工，他会造水管，有一天他造了一个水管网络，就像一个图。其中有一个点只有出边，就是起点，还有一个点只有入边，是终点。<br> 点之间有一些管子，这些管子都有单位时间内的容量，现在毒瘤水管工想知道，他的管子在<strong>单位时间内</strong>在起点终点之间最多能流多少水。</p><div class="post-button"> <a class="btn" href="/posts/dinic/#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/posts/min-span-tree/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content=""></span><script></script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="Alex's Blog"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/posts/min-span-tree/" class="post-title-link" itemprop="url">最小生成树</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-01 22:45:44" itemprop="dateCreated datePublished" datetime="2020-03-01T22:45:44+08:00">2020-Mar-01</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: 2020-Mar-29 15:59:39" itemprop="dateModified" datetime="2020-03-29T15:59:39+08:00">2020-Mar-29</time></span></div></header><div class="post-body" itemprop="articleBody"><h3 id="前置知识"><a class="markdownIt-Anchor" href="#前置知识"></a> 前置知识</h3><p>存图方式（<a href="http://baidu.physton.com/?q=%E9%82%BB%E6%8E%A5%E8%A1%A8" target="_blank" rel="noopener" title="简单">邻接表</a>，<a href="http://baidu.physton.com/?q=%E9%82%BB%E6%8E%A5%E7%9F%A9%E9%98%B5" target="_blank" rel="noopener" title="都太简单了，没有一个打得过的">邻接矩阵</a>），<a href="https://schtonn.github.io/2020/03/01/union-find">并查集</a>。<br> 不会的快进入链接学习吧！</p><h3 id="引入"><a class="markdownIt-Anchor" href="#引入"></a> 引入</h3><p>生成树，就是从一个图中选中<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">n-1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.66666em;vertical-align:-.08333em"></span><span class="mord mathdefault">n</span><span class="mspace" style="margin-right:.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:.64444em;vertical-align:0"></span><span class="mord">1</span></span></span></span>条边，使得这些边构成一棵树，并包含图中的所有节点。<br> 最小生成树，就是找到一种生成树，使得这个生成树的边权和最小。</p><div class="post-button"> <a class="btn" href="/posts/min-span-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/posts/union-find/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content=""></span><script></script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="Alex's Blog"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/posts/union-find/" class="post-title-link" itemprop="url">并查集</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-01 22:44:33" itemprop="dateCreated datePublished" datetime="2020-03-01T22:44:33+08:00">2020-Mar-01</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: 2020-Mar-29 15:59:58" itemprop="dateModified" datetime="2020-03-29T15:59:58+08:00">2020-Mar-29</time></span></div></header><div class="post-body" itemprop="articleBody"><h3 id="前置知识"><a class="markdownIt-Anchor" href="#前置知识"></a> 前置知识</h3><p>哈哈，简单到爆，没有。</p><h3 id="引入"><a class="markdownIt-Anchor" href="#引入"></a> 引入</h3><p>并查集是一种快到爆炸的集合算法，可以进行两项基本操作：合并两个集合（并）、查询两个参数是否在一个集合内（查）。这也是它名字的由来。</p><div class="post-button"> <a class="btn" href="/posts/union-find/#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/posts/tree-link/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content=""></span><script></script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="Alex's Blog"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/posts/tree-link/" class="post-title-link" itemprop="url">树链剖分</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-01 22:41:02" itemprop="dateCreated datePublished" datetime="2020-03-01T22:41:02+08:00">2020-Mar-01</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: 2020-Mar-29 15:59:54" itemprop="dateModified" datetime="2020-03-29T15:59:54+08:00">2020-Mar-29</time></span></div></header><div class="post-body" itemprop="articleBody"><h3 id="前置知识"><a class="markdownIt-Anchor" href="#前置知识"></a> 前置知识</h3><p>必备：存图方式（<a href="http://baidu.physton.com/?q=%E9%82%BB%E6%8E%A5%E8%A1%A8" target="_blank" rel="noopener" title="简单">邻接表</a>，<a href="http://baidu.physton.com/?q=%E9%82%BB%E6%8E%A5%E7%9F%A9%E9%98%B5" target="_blank" rel="noopener" title="都太简单了，没有一个打得过的">邻接矩阵</a>），<a href="http://baidu.physton.com/?q=dfs%E5%BA%8F" target="_blank" rel="noopener">dfs序</a>。<br> 维护：<a href="http://baidu.physton.com/?q=%E7%BA%BF%E6%AE%B5%E6%A0%91" target="_blank" rel="noopener">线段树</a>、<a href="http://baidu.physton.com/?q=%E6%A0%91%E7%8A%B6%E6%95%B0%E7%BB%84" target="_blank" rel="noopener">树状数组</a>、<a href="http://baidu.physton.com/?q=BST" target="_blank" rel="noopener">BST</a>。<br> 不会的快进入链接学习吧！</p><h3 id="引入"><a class="markdownIt-Anchor" href="#引入"></a> 引入</h3><p>树链剖分，简单来说就是把树分割成链，然后维护每一条链。一般的维护算法有线段树，树状数组和BST。复杂度为<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><mi>l</mi><mi>o</mi><mi>g</mi><mi>n</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(log n)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-.25em"></span><span class="mord mathdefault" style="margin-right:.02778em">O</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:.01968em">l</span><span class="mord mathdefault">o</span><span class="mord mathdefault" style="margin-right:.03588em">g</span><span class="mord mathdefault">n</span><span class="mclose">)</span></span></span></span>。</p><div class="post-button"> <a class="btn" href="/posts/tree-link/#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/posts/test/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content=""></span><script></script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="Alex's Blog"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/posts/test/" class="post-title-link" itemprop="url">test</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-01 11:06:43" itemprop="dateCreated datePublished" datetime="2020-03-01T11:06:43+08:00">2020-Mar-01</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: 2020-Mar-29 15:59:49" itemprop="dateModified" datetime="2020-03-29T15:59:49+08:00">2020-Mar-29</time></span></div></header><div class="post-body" itemprop="articleBody"><p><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext mathvariant="monospace">Is</mtext><mtext> </mtext><mtext mathvariant="monospace">KaTeX</mtext><mtext> </mtext><mtext mathvariant="monospace">working?-IT</mtext><mtext> </mtext><mtext mathvariant="monospace">WORKED!NICE!</mtext></mrow><annotation encoding="application/x-tex">\texttt{Is KaTeX working?-IT WORKED!NICE!}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.83333em;vertical-align:-.22222em"></span><span class="mord text"><span class="mord texttt">Is KaTeX working?-IT WORKED!NICE!</span></span></span></span></span></p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msup><mi>a</mi><mi>b</mi></msup></mrow><annotation encoding="application/x-tex">a^b</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.8991079999999999em;vertical-align:0"></span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:.8991079999999999em"><span style="top:-3.113em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span></span></span></span></span></span></span></span></span></p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo fence="true">(</mo><mfrac><mi>a</mi><mi>b</mi></mfrac><mo fence="true">)</mo></mrow><annotation encoding="application/x-tex">\left(\dfrac{a}{b}\right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.8359999999999999em;vertical-align:-.686em"></span><span class="minner"><span class="mopen delimcenter" style="top:0"><span class="delimsizing size2">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.10756em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">b</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">a</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0"><span class="delimsizing size2">)</span></span></span></span></span></span></span></p></div><footer class="post-footer"><div class="post-eof"></div></footer></article></div><script>
  window.addEventListener('tabs:register', () => {
    let { activeClass } = CONFIG.comments;
    if (CONFIG.comments.storage) {
      activeClass = localStorage.getItem('comments_active') || activeClass;
    }
    if (activeClass) {
      let activeTab = document.querySelector(`a[href="#comment-${activeClass}"]`);
      if (activeTab) {
        activeTab.click();
      }
    }
  });
  if (CONFIG.comments.storage) {
    window.addEventListener('tabs:click', event => {
      if (!event.target.matches('.tabs-comment .tab-content .tab-pane')) return;
      let commentClass = event.target.classList[1];
      localStorage.setItem('comments_active', commentClass);
    });
  }
</script></div><div class="toggle sidebar-toggle"><span class="toggle-line toggle-line-first"></span><span class="toggle-line toggle-line-middle"></span><span class="toggle-line toggle-line-last"></span></div><aside class="sidebar"><div class="sidebar-inner"><ul class="sidebar-nav motion-element"><li class="sidebar-nav-toc"> Table of Contents</li><li class="sidebar-nav-overview"> Overview</li></ul><div class="post-toc-wrap sidebar-panel"></div><div class="site-overview-wrap sidebar-panel"><div class="site-author motion-element" itemprop="author" itemscope itemtype="http://schema.org/Person"><p class="site-author-name" itemprop="name">Alex</p><div class="site-description" itemprop="description"></div></div><div class="site-state-wrap motion-element"><nav class="site-state"><div class="site-state-item site-state-posts"> <a href="/archives"><span class="site-state-item-count">10</span> <span class="site-state-item-name">posts</span></a></div><div class="site-state-item site-state-tags"> <a href="/tags/"><span class="site-state-item-count">4</span> <span class="site-state-item-name">tags</span></a></div></nav></div><div class="links-of-author motion-element"><span class="links-of-author-item"><a href="https://github.com/schtonn" title="GitHub → https:&#x2F;&#x2F;github.com&#x2F;schtonn" rel="noopener" target="_blank"><i class="fa fa-fw fa-github"></i> GitHub</a></span><span class="links-of-author-item"><a href="mailto:m18519511495@163.com" title="E-Mail → mailto:m18519511495@163.com" rel="noopener" target="_blank"><i class="fa fa-fw fa-envelope"></i> E-Mail</a></span></div><div class="links-of-blogroll motion-element"><div class="links-of-blogroll-title"><i class="fa fa-fw fa-link"></i> Links</div><ul class="links-of-blogroll-list"><li class="links-of-blogroll-item"> <a href="https://yonghong.github.io/" title="https:&#x2F;&#x2F;yonghong.github.io" rel="noopener" target="_blank">Yonghong</a></li><li class="links-of-blogroll-item"> <a href="https://source.unsplash.com/random/1600x900" title="https:&#x2F;&#x2F;source.unsplash.com&#x2F;random&#x2F;1600x900" rel="noopener" target="_blank">Background</a></li></ul></div></div><div id="treefrog" style="text-align:center;margin-top:18px"><object type="application/x-shockwave-flash" style="outline:0" data="/flash/treefrog.swf?up_bodyColor=444444&up_pattern=0&up_flyColor=777777&up_tongueColor=555555&up_patternColor=000000&up_releaseFly=0&up_frogName=Froggie&up_backgroundImage=http://&up_bellySize=.5&up_footColor=444444&up_eyeColor=444444&up_backgroundColor=222222&" width="300" height="600"><param name="movie" value="http://cdn.abowman.com/widgets/treefrog/treefrog.swf?up_bodyColor=444444&up_pattern=0&up_flyColor=777777&up_tongueColor=555555&up_patternColor=000000&up_releaseFly=0&up_frogName=Froggie&up_backgroundImage=http://&up_bellySize=.5&up_footColor=444444&up_eyeColor=444444&up_backgroundColor=222222&"><param name="AllowScriptAccess" value="always"><param name="wmode" value="opaque"><param name="scale" value="noscale"><param name="salign" value="tl"></object></div></div></aside><div id="sidebar-dimmer"></div></div></main><footer class="footer"><div class="footer-inner"><div class="copyright"> &copy; 2019 – <span itemprop="copyrightYear">2020</span><span class="with-love"><i class="fa fa-user"></i></span> <span class="author" itemprop="copyrightHolder">Alex Xiang</span></div></div></footer></div><script src="/lib/anime.min.js"></script><script src="//cdn.jsdelivr.net/npm/lozad@1/dist/lozad.min.js"></script><script src="/lib/velocity/velocity.min.js"></script><script src="/lib/velocity/velocity.ui.min.js"></script><script src="/js/utils.js"></script><script src="/js/motion.js"></script><script src="/js/schemes/muse.js"></script><script src="/js/next-boot.js"></script><link rel="stylesheet" href="//cdn.jsdelivr.net/npm/katex@0/dist/katex.min.css"><script>
NexT.utils.loadComments(document.querySelector('#valine-comments'), () => {
  NexT.utils.getScript('https://cdn.jsdelivr.net/npm/valine@1/dist/Valine.min.js', () => {
    var GUEST = ['nick', 'mail', 'link'];
    var guest = 'nick,mail,link';
    guest = guest.split(',').filter(item => {
      return GUEST.includes(item);
    });
    new Valine({
      el         : '#valine-comments',
      verify     : true,
      notify     : true,
      appId      : 'BmologYYnRqCv0SLHDeDdA17-gzGzoHsz',
      appKey     : 'w9mVebFMdCmY6Nh9vfcBGaGt',
      placeholder: "Say something.",
      avatar     : 'mm',
      meta       : guest,
      pageSize   : '10' || 10,
      visitor    : false,
      lang       : 'en' || 'zh-cn',
      path       : location.pathname,
      recordIP   : true,
      serverURLs : ''
    });
  }, window.Valine);
});
</script></body></html>