index.html 63 KB

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354355356357358359360361362363364365366367368369370371372373374375376377378379380381382383384385386387388389390391392393394395396397398399400401402403404405406407408409410411412413414415416417418419420421422423424425426427428429430431432433434435436437438439440441442443444445446447448449450451452453454455456457458459460461462463464465466467468469470471472473474475476477478479480481482483484485486487488489490491492493494495496497498499500501502503504505506507508509510511512513514515516517518519520521522523524525526527528529530531532533534535536537538539540541542543544545546547548549550551552553554555556557558559560561562563564565566567568569570571572573574575576577578579580581582583584585586587588589590591592593594595596597598599600601602603604605606607608609610611612613614615616617618619620621622623624625626627628629630631632633634635636637638639640641642643644645646647648649650651652653654655656657658659660661662663664665666667668669670671672673674675676677678679680681682683684685686687688689690691692693694695696697698699700701702703704705706707708709710711712713714715716717718719720721722723724725726727728729730731732733734735736737738739740741742743744745746747748749750751752753754755756757758759760761762763764765766767768769770771772773774775776777778779780781782783784785786787788789790791792793794795796797798799800801802803804805806807808809810811812813814815816817818819820821822823824825826827828829830831832833834835836837838839840841842843844845846847848849850851852853854855856857858859860861862863864865866867868869870871872873874875876877878879880881882883884885886887888889890891892893894895896897898899900901902903904905906907908909910911912913914915916917918919920921922923924925926927928929930931932933934935936937938939940941942943944945946947948949950951952953954955956957958959960961962963964965966967968969970971972973974975976977978979980981982983984985986987988989990991992993994995996997998999100010011002100310041005100610071008100910101011101210131014101510161017101810191020102110221023102410251026102710281029103010311032103310341035103610371038103910401041104210431044104510461047104810491050105110521053105410551056105710581059106010611062106310641065106610671068106910701071107210731074107510761077107810791080108110821083108410851086108710881089109010911092109310941095109610971098109911001101110211031104110511061107110811091110111111121113111411151116111711181119112011211122112311241125112611271128112911301131113211331134113511361137113811391140114111421143114411451146114711481149115011511152115311541155115611571158115911601161116211631164116511661167116811691170117111721173117411751176117711781179118011811182118311841185118611871188118911901191119211931194119511961197119811991200120112021203120412051206120712081209121012111212121312141215121612171218121912201221122212231224122512261227122812291230123112321233123412351236123712381239124012411242124312441245124612471248124912501251125212531254125512561257125812591260126112621263126412651266126712681269127012711272127312741275127612771278127912801281128212831284128512861287128812891290129112921293
  1. <!DOCTYPE html>
  2. <html lang="en">
  3. <head>
  4. <meta charset="UTF-8">
  5. <meta name="viewport" content="width=device-width, initial-scale=1, maximum-scale=2">
  6. <meta name="theme-color" content="#222">
  7. <meta name="generator" content="Hexo 4.2.0">
  8. <link rel="apple-touch-icon" sizes="180x180" href="/images/apple-touch-icon-next.png">
  9. <link rel="icon" type="image/png" sizes="32x32" href="/images/favicon-32x32-next.png">
  10. <link rel="icon" type="image/png" sizes="16x16" href="/images/favicon-16x16-next.png">
  11. <link rel="mask-icon" href="/images/logo.svg" color="#222">
  12. <link rel="stylesheet" href="/css/main.css">
  13. <link rel="stylesheet" href="/lib/font-awesome/css/font-awesome.min.css">
  14. <link rel="stylesheet" href="/lib/pace/pace-theme-minimal.min.css">
  15. <script src="/lib/pace/pace.min.js"></script>
  16. <script id="hexo-configurations">
  17. var NexT = window.NexT || {};
  18. var CONFIG = {"hostname":"schtonn.github.io","root":"/","scheme":"Muse","version":"7.7.2","exturl":false,"sidebar":{"position":"left","display":"post","padding":18,"offset":12,"onmobile":false},"copycode":{"enable":true,"show_result":true,"style":"flat"},"back2top":{"enable":true,"sidebar":false,"scrollpercent":true},"bookmark":{"enable":false,"color":"#222","save":"auto"},"fancybox":false,"mediumzoom":false,"lazyload":true,"pangu":false,"comments":{"style":"tabs","active":"valine","storage":true,"lazyload":false,"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":false,"trigger":"auto","top_n_per_article":1,"unescape":false,"preload":false},"motion":{"enable":true,"async":false,"transition":{"post_block":"fadeIn","post_header":"slideDownIn","post_body":"slideDownIn","coll_header":"slideLeftIn","sidebar":"slideLeftIn"}}};
  19. </script>
  20. <meta name="description" content="The blog of a middle school OIer">
  21. <meta property="og:type" content="website">
  22. <meta property="og:title" content="Alex&#39;s Blog">
  23. <meta property="og:url" content="https://schtonn.github.io/index.html">
  24. <meta property="og:site_name" content="Alex&#39;s Blog">
  25. <meta property="og:description" content="The blog of a middle school OIer">
  26. <meta property="og:locale" content="en_US">
  27. <meta property="article:author" content="Alex">
  28. <meta name="twitter:card" content="summary">
  29. <link rel="canonical" href="https://schtonn.github.io/">
  30. <script id="page-configurations">
  31. // https://hexo.io/docs/variables.html
  32. CONFIG.page = {
  33. sidebar: "",
  34. isHome : true,
  35. isPost : false
  36. };
  37. </script>
  38. <title>Alex's Blog</title>
  39. <noscript>
  40. <style>
  41. .use-motion .brand,
  42. .use-motion .menu-item,
  43. .sidebar-inner,
  44. .use-motion .post-block,
  45. .use-motion .pagination,
  46. .use-motion .comments,
  47. .use-motion .post-header,
  48. .use-motion .post-body,
  49. .use-motion .collection-header { opacity: initial; }
  50. .use-motion .site-title,
  51. .use-motion .site-subtitle {
  52. opacity: initial;
  53. top: initial;
  54. }
  55. .use-motion .logo-line-before i { left: initial; }
  56. .use-motion .logo-line-after i { right: initial; }
  57. </style>
  58. </noscript>
  59. </head>
  60. <body itemscope itemtype="http://schema.org/WebPage">
  61. <div class="container use-motion">
  62. <div class="headband"></div>
  63. <header class="header" itemscope itemtype="http://schema.org/WPHeader">
  64. <div class="header-inner"><div class="site-brand-container">
  65. <div class="site-nav-toggle">
  66. <div class="toggle" aria-label="Toggle navigation bar">
  67. <span class="toggle-line toggle-line-first"></span>
  68. <span class="toggle-line toggle-line-middle"></span>
  69. <span class="toggle-line toggle-line-last"></span>
  70. </div>
  71. </div>
  72. <div class="site-meta">
  73. <div>
  74. <a href="/" class="brand" rel="start">
  75. <span class="logo-line-before"><i></i></span>
  76. <span class="site-title">Alex's Blog</span>
  77. <span class="logo-line-after"><i></i></span>
  78. </a>
  79. </div>
  80. <p class="site-subtitle">Middle school OIer</p>
  81. </div>
  82. <div class="site-nav-right">
  83. <div class="toggle popup-trigger">
  84. </div>
  85. </div>
  86. </div>
  87. <nav class="site-nav">
  88. <ul id="menu" class="menu">
  89. <li class="menu-item menu-item-home">
  90. <a href="/" rel="section"><i class="fa fa-fw fa-home"></i>Home</a>
  91. </li>
  92. <li class="menu-item menu-item-tags">
  93. <a href="/tags/" rel="section"><i class="fa fa-fw fa-tags"></i>Tags</a>
  94. </li>
  95. <li class="menu-item menu-item-archives">
  96. <a href="/archives/" rel="section"><i class="fa fa-fw fa-archive"></i>Archives</a>
  97. </li>
  98. <li class="menu-item menu-item-games">
  99. <a href="/games/" rel="section"><i class="fa fa-fw fa-gamepad"></i>games</a>
  100. </li>
  101. <li class="menu-item menu-item-sans">
  102. <a href="/sans/" rel="section"><i class="fa fa-fw fa-heart"></i>sans</a>
  103. </li>
  104. </ul>
  105. </nav>
  106. </div>
  107. </header>
  108. <div class="back-to-top">
  109. <i class="fa fa-arrow-up"></i>
  110. <span>0%</span>
  111. </div>
  112. <div class="reading-progress-bar"></div>
  113. <main class="main">
  114. <div class="main-inner">
  115. <div class="content-wrap">
  116. <div class="content">
  117. <div class="posts-expand">
  118. <article itemscope itemtype="http://schema.org/Article" class="post-block home" lang="en">
  119. <link itemprop="mainEntityOfPage" href="https://schtonn.github.io/posts/2020/plan/">
  120. <script>
  121. (function(){
  122. if(''){
  123. if (prompt('Password?') !== ''){
  124. alert('GOAWAY!');
  125. history.back();
  126. }
  127. }
  128. })();
  129. </script>
  130. <span hidden itemprop="author" itemscope itemtype="http://schema.org/Person">
  131. <meta itemprop="image" content="/images/avatar.gif">
  132. <meta itemprop="name" content="Alex">
  133. <meta itemprop="description" content="The blog of a middle school OIer">
  134. </span>
  135. <span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization">
  136. <meta itemprop="name" content="Alex's Blog">
  137. </span>
  138. <header class="post-header">
  139. <h1 class="post-title" itemprop="name headline">
  140. <a href="/posts/2020/plan/" class="post-title-link" itemprop="url">plan</a>
  141. </h1>
  142. <div class="post-meta">
  143. <i class="fa fa-thumb-tack"></i>
  144. <font color=7D26CD>Pinned</font>
  145. <span class="post-meta-divider">|</span>
  146. <span class="post-meta-item">
  147. <span class="post-meta-item-icon">
  148. <i class="fa fa-calendar-o"></i>
  149. </span>
  150. <span class="post-meta-item-text">Posted on</span>
  151. <time title="Created: 2020-Mar-01 22:36:07" itemprop="dateCreated datePublished" datetime="2020-03-01T22:36:07+08:00">2020-Mar-01</time>
  152. </span>
  153. <span class="post-meta-item">
  154. <span class="post-meta-item-icon">
  155. <i class="fa fa-calendar-check-o"></i>
  156. </span>
  157. <span class="post-meta-item-text">Edited on</span>
  158. <time title="Modified: 2020-Mar-21 22:17:17" itemprop="dateModified" datetime="2020-03-21T22:17:17+08:00">2020-Mar-21</time>
  159. </span>
  160. </div>
  161. </header>
  162. <div class="post-body" itemprop="articleBody">
  163. <p>This page is locked.</p>
  164. <!--noindex-->
  165. <div class="post-button">
  166. <a class="btn" href="/posts/2020/plan/#more" rel="contents">
  167. Read more &raquo;
  168. </a>
  169. </div>
  170. <!--/noindex-->
  171. </div>
  172. <footer class="post-footer">
  173. <div class="post-eof"></div>
  174. </footer>
  175. </article>
  176. <article itemscope itemtype="http://schema.org/Article" class="post-block home" lang="en">
  177. <link itemprop="mainEntityOfPage" href="https://schtonn.github.io/posts/2020/matrix-pow/">
  178. <script>
  179. (function(){
  180. if(''){
  181. if (prompt('Password?') !== ''){
  182. alert('GOAWAY!');
  183. history.back();
  184. }
  185. }
  186. })();
  187. </script>
  188. <span hidden itemprop="author" itemscope itemtype="http://schema.org/Person">
  189. <meta itemprop="image" content="/images/avatar.gif">
  190. <meta itemprop="name" content="Alex">
  191. <meta itemprop="description" content="The blog of a middle school OIer">
  192. </span>
  193. <span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization">
  194. <meta itemprop="name" content="Alex's Blog">
  195. </span>
  196. <header class="post-header">
  197. <h1 class="post-title" itemprop="name headline">
  198. <a href="/posts/2020/matrix-pow/" class="post-title-link" itemprop="url">矩阵快速幂运用</a>
  199. </h1>
  200. <div class="post-meta">
  201. <span class="post-meta-item">
  202. <span class="post-meta-item-icon">
  203. <i class="fa fa-calendar-o"></i>
  204. </span>
  205. <span class="post-meta-item-text">Posted on</span>
  206. <time title="Created: 2020-Mar-21 19:20:08 / Modified: 22:47:29" itemprop="dateCreated datePublished" datetime="2020-03-21T19:20:08+08:00">2020-Mar-21</time>
  207. </span>
  208. </div>
  209. </header>
  210. <div class="post-body" itemprop="articleBody">
  211. <h3 id="引入"><a class="markdownIt-Anchor" href="#引入"></a> 引入</h3>
  212. <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>
  213. <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[
  214. \begin{matrix}
  215. 1&amp;2&amp;3\\
  216. 4&amp;5&amp;6\\
  217. 7&amp;8&amp;9\end{matrix}
  218. \right]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.10903em;">M</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></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:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></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:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></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>
  219. <p>用 <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>M</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub></mrow><annotation encoding="application/x-tex">M_{ij}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10903em;">M</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.10903em;margin-right:0.05em;"><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="mord mathdefault mtight" style="margin-right:0.05724em;">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><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:0.65952em;vertical-align:0em;"></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:0.85396em;vertical-align:-0.19444em;"></span><span class="mord mathdefault" style="margin-right:0.05724em;">j</span></span></span></span> 列的数据,如 <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>M</mi><mn>23</mn></msub><mo>=</mo><mn>6</mn></mrow><annotation encoding="application/x-tex">M_{23}=6</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10903em;">M</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.10903em;margin-right:0.05em;"><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="mord mtight">3</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">6</span></span></span></span>。</p>
  220. <!--noindex-->
  221. <div class="post-button">
  222. <a class="btn" href="/posts/2020/matrix-pow/#more" rel="contents">
  223. Read more &raquo;
  224. </a>
  225. </div>
  226. <!--/noindex-->
  227. </div>
  228. <footer class="post-footer">
  229. <div class="post-eof"></div>
  230. </footer>
  231. </article>
  232. <article itemscope itemtype="http://schema.org/Article" class="post-block home" lang="en">
  233. <link itemprop="mainEntityOfPage" href="https://schtonn.github.io/posts/2020/computer/">
  234. <script>
  235. (function(){
  236. if(''){
  237. if (prompt('Password?') !== ''){
  238. alert('GOAWAY!');
  239. history.back();
  240. }
  241. }
  242. })();
  243. </script>
  244. <span hidden itemprop="author" itemscope itemtype="http://schema.org/Person">
  245. <meta itemprop="image" content="/images/avatar.gif">
  246. <meta itemprop="name" content="Alex">
  247. <meta itemprop="description" content="The blog of a middle school OIer">
  248. </span>
  249. <span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization">
  250. <meta itemprop="name" content="Alex's Blog">
  251. </span>
  252. <header class="post-header">
  253. <h1 class="post-title" itemprop="name headline">
  254. <a href="/posts/2020/computer/" class="post-title-link" itemprop="url">How do computers work?</a>
  255. </h1>
  256. <div class="post-meta">
  257. <span class="post-meta-item">
  258. <span class="post-meta-item-icon">
  259. <i class="fa fa-calendar-o"></i>
  260. </span>
  261. <span class="post-meta-item-text">Posted on</span>
  262. <time title="Created: 2020-Mar-04 12:53:05" itemprop="dateCreated datePublished" datetime="2020-03-04T12:53:05+08:00">2020-Mar-04</time>
  263. </span>
  264. <span class="post-meta-item">
  265. <span class="post-meta-item-icon">
  266. <i class="fa fa-calendar-check-o"></i>
  267. </span>
  268. <span class="post-meta-item-text">Edited on</span>
  269. <time title="Modified: 2020-Mar-25 21:41:26" itemprop="dateModified" datetime="2020-03-25T21:41:26+08:00">2020-Mar-25</time>
  270. </span>
  271. </div>
  272. </header>
  273. <div class="post-body" itemprop="articleBody">
  274. <p>This page is locked</p>
  275. <!--noindex-->
  276. <div class="post-button">
  277. <a class="btn" href="/posts/2020/computer/#more" rel="contents">
  278. Read more &raquo;
  279. </a>
  280. </div>
  281. <!--/noindex-->
  282. </div>
  283. <footer class="post-footer">
  284. <div class="post-eof"></div>
  285. </footer>
  286. </article>
  287. <article itemscope itemtype="http://schema.org/Article" class="post-block home" lang="en">
  288. <link itemprop="mainEntityOfPage" href="https://schtonn.github.io/posts/2020/segment-tree/">
  289. <script>
  290. (function(){
  291. if(''){
  292. if (prompt('Password?') !== ''){
  293. alert('GOAWAY!');
  294. history.back();
  295. }
  296. }
  297. })();
  298. </script>
  299. <span hidden itemprop="author" itemscope itemtype="http://schema.org/Person">
  300. <meta itemprop="image" content="/images/avatar.gif">
  301. <meta itemprop="name" content="Alex">
  302. <meta itemprop="description" content="The blog of a middle school OIer">
  303. </span>
  304. <span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization">
  305. <meta itemprop="name" content="Alex's Blog">
  306. </span>
  307. <header class="post-header">
  308. <h1 class="post-title" itemprop="name headline">
  309. <a href="/posts/2020/segment-tree/" class="post-title-link" itemprop="url">线段树</a>
  310. </h1>
  311. <div class="post-meta">
  312. <span class="post-meta-item">
  313. <span class="post-meta-item-icon">
  314. <i class="fa fa-calendar-o"></i>
  315. </span>
  316. <span class="post-meta-item-text">Posted on</span>
  317. <time title="Created: 2020-Mar-02 11:37:36" itemprop="dateCreated datePublished" datetime="2020-03-02T11:37:36+08:00">2020-Mar-02</time>
  318. </span>
  319. <span class="post-meta-item">
  320. <span class="post-meta-item-icon">
  321. <i class="fa fa-calendar-check-o"></i>
  322. </span>
  323. <span class="post-meta-item-text">Edited on</span>
  324. <time title="Modified: 2020-Mar-06 18:43:32" itemprop="dateModified" datetime="2020-03-06T18:43:32+08:00">2020-Mar-06</time>
  325. </span>
  326. </div>
  327. </header>
  328. <div class="post-body" itemprop="articleBody">
  329. <h3 id="前置知识"><a class="markdownIt-Anchor" href="#前置知识"></a> 前置知识</h3>
  330. <p>数组,结构体,二叉树</p>
  331. <h3 id="引入"><a class="markdownIt-Anchor" href="#引入"></a> 引入</h3>
  332. <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:0.8141079999999999em;vertical-align:0em;"></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:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><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:0.8141079999999999em;vertical-align:0em;"></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:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><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 />
  333. 暴力是肯定不行的,数据范围太大,操作太多,会超时。<br />
  334. 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>
  335. <!--noindex-->
  336. <div class="post-button">
  337. <a class="btn" href="/posts/2020/segment-tree/#more" rel="contents">
  338. Read more &raquo;
  339. </a>
  340. </div>
  341. <!--/noindex-->
  342. </div>
  343. <footer class="post-footer">
  344. <div class="post-eof"></div>
  345. </footer>
  346. </article>
  347. <article itemscope itemtype="http://schema.org/Article" class="post-block home" lang="en">
  348. <link itemprop="mainEntityOfPage" href="https://schtonn.github.io/posts/2020/ferbonacci/">
  349. <script>
  350. (function(){
  351. if(''){
  352. if (prompt('Password?') !== ''){
  353. alert('GOAWAY!');
  354. history.back();
  355. }
  356. }
  357. })();
  358. </script>
  359. <span hidden itemprop="author" itemscope itemtype="http://schema.org/Person">
  360. <meta itemprop="image" content="/images/avatar.gif">
  361. <meta itemprop="name" content="Alex">
  362. <meta itemprop="description" content="The blog of a middle school OIer">
  363. </span>
  364. <span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization">
  365. <meta itemprop="name" content="Alex's Blog">
  366. </span>
  367. <header class="post-header">
  368. <h1 class="post-title" itemprop="name headline">
  369. <a href="/posts/2020/ferbonacci/" class="post-title-link" itemprop="url">斐波那契数列-O(1)</a>
  370. </h1>
  371. <div class="post-meta">
  372. <span class="post-meta-item">
  373. <span class="post-meta-item-icon">
  374. <i class="fa fa-calendar-o"></i>
  375. </span>
  376. <span class="post-meta-item-text">Posted on</span>
  377. <time title="Created: 2020-Mar-02 11:35:44" itemprop="dateCreated datePublished" datetime="2020-03-02T11:35:44+08:00">2020-Mar-02</time>
  378. </span>
  379. <span class="post-meta-item">
  380. <span class="post-meta-item-icon">
  381. <i class="fa fa-calendar-check-o"></i>
  382. </span>
  383. <span class="post-meta-item-text">Edited on</span>
  384. <time title="Modified: 2020-Mar-03 20:40:56" itemprop="dateModified" datetime="2020-03-03T20:40:56+08:00">2020-Mar-03</time>
  385. </span>
  386. </div>
  387. </header>
  388. <div class="post-body" itemprop="articleBody">
  389. <p>引自:《信息学奥赛之-数学一本通》<br />
  390. 揍是这样:</p>
  391. <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]
  392. </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></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:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.27022em;vertical-align:-0.686em;"></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:0.04em;"></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:0.90722em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><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:0.853em;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,-8c-5.8,-5.3,-9.5,
  393. -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,
  394. -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,
  395. 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,
  396. -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467
  397. s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422
  398. s-65,47,-65,47z M834 80H400000v40H845z'/></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.13278em;"><span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.854312em;vertical-align:-0.65002em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size2">[</span></span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size2">(</span></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.956095em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><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:0.853em;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,-8c-5.8,-5.3,-9.5,
  399. -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,
  400. -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,
  401. 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,
  402. -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467
  403. s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422
  404. s-65,47,-65,47z M834 80H400000v40H845z'/></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.08390500000000001em;"><span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;"><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:0.05em;"><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:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size2">(</span></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.956095em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><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:0.853em;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,-8c-5.8,-5.3,-9.5,
  405. -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,
  406. -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,
  407. 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,
  408. -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467
  409. s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422
  410. s-65,47,-65,47z M834 80H400000v40H845z'/></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.08390500000000001em;"><span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;"><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:0.05em;"><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:0em;"><span class="delimsizing size2">]</span></span></span></span></span></span></span></p>
  411. <p>代码揍这么简单:</p>
  412. <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">ferbo</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>
  413. <p>要是再加个快速幂就更棒了(够快了,懒得写)</p>
  414. </div>
  415. <footer class="post-footer">
  416. <div class="post-eof"></div>
  417. </footer>
  418. </article>
  419. <article itemscope itemtype="http://schema.org/Article" class="post-block home" lang="en">
  420. <link itemprop="mainEntityOfPage" href="https://schtonn.github.io/posts/2020/dinic/">
  421. <script>
  422. (function(){
  423. if(''){
  424. if (prompt('Password?') !== ''){
  425. alert('GOAWAY!');
  426. history.back();
  427. }
  428. }
  429. })();
  430. </script>
  431. <span hidden itemprop="author" itemscope itemtype="http://schema.org/Person">
  432. <meta itemprop="image" content="/images/avatar.gif">
  433. <meta itemprop="name" content="Alex">
  434. <meta itemprop="description" content="The blog of a middle school OIer">
  435. </span>
  436. <span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization">
  437. <meta itemprop="name" content="Alex's Blog">
  438. </span>
  439. <header class="post-header">
  440. <h1 class="post-title" itemprop="name headline">
  441. <a href="/posts/2020/dinic/" class="post-title-link" itemprop="url">网络最大流-Dinic</a>
  442. </h1>
  443. <div class="post-meta">
  444. <span class="post-meta-item">
  445. <span class="post-meta-item-icon">
  446. <i class="fa fa-calendar-o"></i>
  447. </span>
  448. <span class="post-meta-item-text">Posted on</span>
  449. <time title="Created: 2020-Mar-02 11:31:22" itemprop="dateCreated datePublished" datetime="2020-03-02T11:31:22+08:00">2020-Mar-02</time>
  450. </span>
  451. <span class="post-meta-item">
  452. <span class="post-meta-item-icon">
  453. <i class="fa fa-calendar-check-o"></i>
  454. </span>
  455. <span class="post-meta-item-text">Edited on</span>
  456. <time title="Modified: 2020-Mar-03 20:41:19" itemprop="dateModified" datetime="2020-03-03T20:41:19+08:00">2020-Mar-03</time>
  457. </span>
  458. </div>
  459. </header>
  460. <div class="post-body" itemprop="articleBody">
  461. <h3 id="前置知识"><a class="markdownIt-Anchor" href="#前置知识"></a> 前置知识</h3>
  462. <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>
  463. <h3 id="引入"><a class="markdownIt-Anchor" href="#引入"></a> 引入</h3>
  464. <p>我们举个例子吧:<br />
  465. 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 />
  466. 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>
  467. <!--noindex-->
  468. <div class="post-button">
  469. <a class="btn" href="/posts/2020/dinic/#more" rel="contents">
  470. Read more &raquo;
  471. </a>
  472. </div>
  473. <!--/noindex-->
  474. </div>
  475. <footer class="post-footer">
  476. <div class="post-eof"></div>
  477. </footer>
  478. </article>
  479. <article itemscope itemtype="http://schema.org/Article" class="post-block home" lang="en">
  480. <link itemprop="mainEntityOfPage" href="https://schtonn.github.io/posts/2020/min-span-tree/">
  481. <script>
  482. (function(){
  483. if(''){
  484. if (prompt('Password?') !== ''){
  485. alert('GOAWAY!');
  486. history.back();
  487. }
  488. }
  489. })();
  490. </script>
  491. <span hidden itemprop="author" itemscope itemtype="http://schema.org/Person">
  492. <meta itemprop="image" content="/images/avatar.gif">
  493. <meta itemprop="name" content="Alex">
  494. <meta itemprop="description" content="The blog of a middle school OIer">
  495. </span>
  496. <span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization">
  497. <meta itemprop="name" content="Alex's Blog">
  498. </span>
  499. <header class="post-header">
  500. <h1 class="post-title" itemprop="name headline">
  501. <a href="/posts/2020/min-span-tree/" class="post-title-link" itemprop="url">最小生成树</a>
  502. </h1>
  503. <div class="post-meta">
  504. <span class="post-meta-item">
  505. <span class="post-meta-item-icon">
  506. <i class="fa fa-calendar-o"></i>
  507. </span>
  508. <span class="post-meta-item-text">Posted on</span>
  509. <time title="Created: 2020-Mar-01 22:45:44" itemprop="dateCreated datePublished" datetime="2020-03-01T22:45:44+08:00">2020-Mar-01</time>
  510. </span>
  511. <span class="post-meta-item">
  512. <span class="post-meta-item-icon">
  513. <i class="fa fa-calendar-check-o"></i>
  514. </span>
  515. <span class="post-meta-item-text">Edited on</span>
  516. <time title="Modified: 2020-Mar-05 21:16:57" itemprop="dateModified" datetime="2020-03-05T21:16:57+08:00">2020-Mar-05</time>
  517. </span>
  518. </div>
  519. </header>
  520. <div class="post-body" itemprop="articleBody">
  521. <h3 id="前置知识"><a class="markdownIt-Anchor" href="#前置知识"></a> 前置知识</h3>
  522. <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 />
  523. 不会的快进入链接学习吧!</p>
  524. <h3 id="引入"><a class="markdownIt-Anchor" href="#引入"></a> 引入</h3>
  525. <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:0.66666em;vertical-align:-0.08333em;"></span><span class="mord mathdefault">n</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></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 />
  526. 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>
  527. <!--noindex-->
  528. <div class="post-button">
  529. <a class="btn" href="/posts/2020/min-span-tree/#more" rel="contents">
  530. Read more &raquo;
  531. </a>
  532. </div>
  533. <!--/noindex-->
  534. </div>
  535. <footer class="post-footer">
  536. <div class="post-eof"></div>
  537. </footer>
  538. </article>
  539. <article itemscope itemtype="http://schema.org/Article" class="post-block home" lang="en">
  540. <link itemprop="mainEntityOfPage" href="https://schtonn.github.io/posts/2020/union-find/">
  541. <script>
  542. (function(){
  543. if(''){
  544. if (prompt('Password?') !== ''){
  545. alert('GOAWAY!');
  546. history.back();
  547. }
  548. }
  549. })();
  550. </script>
  551. <span hidden itemprop="author" itemscope itemtype="http://schema.org/Person">
  552. <meta itemprop="image" content="/images/avatar.gif">
  553. <meta itemprop="name" content="Alex">
  554. <meta itemprop="description" content="The blog of a middle school OIer">
  555. </span>
  556. <span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization">
  557. <meta itemprop="name" content="Alex's Blog">
  558. </span>
  559. <header class="post-header">
  560. <h1 class="post-title" itemprop="name headline">
  561. <a href="/posts/2020/union-find/" class="post-title-link" itemprop="url">并查集</a>
  562. </h1>
  563. <div class="post-meta">
  564. <span class="post-meta-item">
  565. <span class="post-meta-item-icon">
  566. <i class="fa fa-calendar-o"></i>
  567. </span>
  568. <span class="post-meta-item-text">Posted on</span>
  569. <time title="Created: 2020-Mar-01 22:44:33" itemprop="dateCreated datePublished" datetime="2020-03-01T22:44:33+08:00">2020-Mar-01</time>
  570. </span>
  571. <span class="post-meta-item">
  572. <span class="post-meta-item-icon">
  573. <i class="fa fa-calendar-check-o"></i>
  574. </span>
  575. <span class="post-meta-item-text">Edited on</span>
  576. <time title="Modified: 2020-Mar-03 20:39:35" itemprop="dateModified" datetime="2020-03-03T20:39:35+08:00">2020-Mar-03</time>
  577. </span>
  578. </div>
  579. </header>
  580. <div class="post-body" itemprop="articleBody">
  581. <h3 id="前置知识"><a class="markdownIt-Anchor" href="#前置知识"></a> 前置知识</h3>
  582. <p>哈哈,简单到爆,没有。</p>
  583. <h3 id="引入"><a class="markdownIt-Anchor" href="#引入"></a> 引入</h3>
  584. <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>
  585. <!--noindex-->
  586. <div class="post-button">
  587. <a class="btn" href="/posts/2020/union-find/#more" rel="contents">
  588. Read more &raquo;
  589. </a>
  590. </div>
  591. <!--/noindex-->
  592. </div>
  593. <footer class="post-footer">
  594. <div class="post-eof"></div>
  595. </footer>
  596. </article>
  597. <article itemscope itemtype="http://schema.org/Article" class="post-block home" lang="en">
  598. <link itemprop="mainEntityOfPage" href="https://schtonn.github.io/posts/2020/tree-link/">
  599. <script>
  600. (function(){
  601. if(''){
  602. if (prompt('Password?') !== ''){
  603. alert('GOAWAY!');
  604. history.back();
  605. }
  606. }
  607. })();
  608. </script>
  609. <span hidden itemprop="author" itemscope itemtype="http://schema.org/Person">
  610. <meta itemprop="image" content="/images/avatar.gif">
  611. <meta itemprop="name" content="Alex">
  612. <meta itemprop="description" content="The blog of a middle school OIer">
  613. </span>
  614. <span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization">
  615. <meta itemprop="name" content="Alex's Blog">
  616. </span>
  617. <header class="post-header">
  618. <h1 class="post-title" itemprop="name headline">
  619. <a href="/posts/2020/tree-link/" class="post-title-link" itemprop="url">树链剖分</a>
  620. </h1>
  621. <div class="post-meta">
  622. <span class="post-meta-item">
  623. <span class="post-meta-item-icon">
  624. <i class="fa fa-calendar-o"></i>
  625. </span>
  626. <span class="post-meta-item-text">Posted on</span>
  627. <time title="Created: 2020-Mar-01 22:41:02" itemprop="dateCreated datePublished" datetime="2020-03-01T22:41:02+08:00">2020-Mar-01</time>
  628. </span>
  629. <span class="post-meta-item">
  630. <span class="post-meta-item-icon">
  631. <i class="fa fa-calendar-check-o"></i>
  632. </span>
  633. <span class="post-meta-item-text">Edited on</span>
  634. <time title="Modified: 2020-Mar-03 20:39:51" itemprop="dateModified" datetime="2020-03-03T20:39:51+08:00">2020-Mar-03</time>
  635. </span>
  636. </div>
  637. </header>
  638. <div class="post-body" itemprop="articleBody">
  639. <h3 id="前置知识"><a class="markdownIt-Anchor" href="#前置知识"></a> 前置知识</h3>
  640. <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 />
  641. 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 />
  642. 不会的快进入链接学习吧!</p>
  643. <h3 id="引入"><a class="markdownIt-Anchor" href="#引入"></a> 引入</h3>
  644. <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:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.01968em;">l</span><span class="mord mathdefault">o</span><span class="mord mathdefault" style="margin-right:0.03588em;">g</span><span class="mord mathdefault">n</span><span class="mclose">)</span></span></span></span>。</p>
  645. <!--noindex-->
  646. <div class="post-button">
  647. <a class="btn" href="/posts/2020/tree-link/#more" rel="contents">
  648. Read more &raquo;
  649. </a>
  650. </div>
  651. <!--/noindex-->
  652. </div>
  653. <footer class="post-footer">
  654. <div class="post-eof"></div>
  655. </footer>
  656. </article>
  657. <article itemscope itemtype="http://schema.org/Article" class="post-block home" lang="en">
  658. <link itemprop="mainEntityOfPage" href="https://schtonn.github.io/posts/2020/test/">
  659. <script>
  660. (function(){
  661. if(''){
  662. if (prompt('Password?') !== ''){
  663. alert('GOAWAY!');
  664. history.back();
  665. }
  666. }
  667. })();
  668. </script>
  669. <span hidden itemprop="author" itemscope itemtype="http://schema.org/Person">
  670. <meta itemprop="image" content="/images/avatar.gif">
  671. <meta itemprop="name" content="Alex">
  672. <meta itemprop="description" content="The blog of a middle school OIer">
  673. </span>
  674. <span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization">
  675. <meta itemprop="name" content="Alex's Blog">
  676. </span>
  677. <header class="post-header">
  678. <h1 class="post-title" itemprop="name headline">
  679. <a href="/posts/2020/test/" class="post-title-link" itemprop="url">test</a>
  680. </h1>
  681. <div class="post-meta">
  682. <span class="post-meta-item">
  683. <span class="post-meta-item-icon">
  684. <i class="fa fa-calendar-o"></i>
  685. </span>
  686. <span class="post-meta-item-text">Posted on</span>
  687. <time title="Created: 2020-Mar-01 11:06:43" itemprop="dateCreated datePublished" datetime="2020-03-01T11:06:43+08:00">2020-Mar-01</time>
  688. </span>
  689. <span class="post-meta-item">
  690. <span class="post-meta-item-icon">
  691. <i class="fa fa-calendar-check-o"></i>
  692. </span>
  693. <span class="post-meta-item-text">Edited on</span>
  694. <time title="Modified: 2020-Mar-05 21:01:44" itemprop="dateModified" datetime="2020-03-05T21:01:44+08:00">2020-Mar-05</time>
  695. </span>
  696. </div>
  697. </header>
  698. <div class="post-body" itemprop="articleBody">
  699. <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:0.83333em;vertical-align:-0.22222em;"></span><span class="mord text"><span class="mord texttt">Is KaTeX working?-IT WORKED!NICE!</span></span></span></span></span></p>
  700. <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
  701. </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8991079999999999em;vertical-align:0em;"></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:0.8991079999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><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>
  702. <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)
  703. </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.8359999999999999em;vertical-align:-0.686em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><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:0.04em;"></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:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size2">)</span></span></span></span></span></span></span></p>
  704. </div>
  705. <footer class="post-footer">
  706. <div class="post-eof"></div>
  707. </footer>
  708. </article>
  709. </div>
  710. </div>
  711. <script>
  712. window.addEventListener('tabs:register', () => {
  713. let activeClass = CONFIG.comments.activeClass;
  714. if (CONFIG.comments.storage) {
  715. activeClass = localStorage.getItem('comments_active') || activeClass;
  716. }
  717. if (activeClass) {
  718. let activeTab = document.querySelector(`a[href="#comment-${activeClass}"]`);
  719. if (activeTab) {
  720. activeTab.click();
  721. }
  722. }
  723. });
  724. if (CONFIG.comments.storage) {
  725. window.addEventListener('tabs:click', event => {
  726. if (!event.target.matches('.tabs-comment .tab-content .tab-pane')) return;
  727. let commentClass = event.target.classList[1];
  728. localStorage.setItem('comments_active', commentClass);
  729. });
  730. }
  731. </script>
  732. </div>
  733. <div class="toggle sidebar-toggle">
  734. <span class="toggle-line toggle-line-first"></span>
  735. <span class="toggle-line toggle-line-middle"></span>
  736. <span class="toggle-line toggle-line-last"></span>
  737. </div>
  738. <aside class="sidebar">
  739. <div class="sidebar-inner">
  740. <ul class="sidebar-nav motion-element">
  741. <li class="sidebar-nav-toc">
  742. Table of Contents
  743. </li>
  744. <li class="sidebar-nav-overview">
  745. Overview
  746. </li>
  747. </ul>
  748. <!--noindex-->
  749. <div class="post-toc-wrap sidebar-panel">
  750. </div>
  751. <!--/noindex-->
  752. <div class="site-overview-wrap sidebar-panel">
  753. <div class="site-author motion-element" itemprop="author" itemscope itemtype="http://schema.org/Person">
  754. <p class="site-author-name" itemprop="name">Alex</p>
  755. <div class="site-description" itemprop="description">The blog of a middle school OIer</div>
  756. </div>
  757. <div class="site-state-wrap motion-element">
  758. <nav class="site-state">
  759. <div class="site-state-item site-state-posts">
  760. <a href="/archives/">
  761. <span class="site-state-item-count">10</span>
  762. <span class="site-state-item-name">posts</span>
  763. </a>
  764. </div>
  765. <div class="site-state-item site-state-tags">
  766. <a href="/tags/">
  767. <span class="site-state-item-count">4</span>
  768. <span class="site-state-item-name">tags</span></a>
  769. </div>
  770. </nav>
  771. </div>
  772. <div class="links-of-author motion-element">
  773. <span class="links-of-author-item">
  774. <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>
  775. </span>
  776. <span class="links-of-author-item">
  777. <a href="skype:alex?call|chat" title="Skype → skype:alex?call|chat" rel="noopener" target="_blank"><i class="fa fa-fw fa-skype"></i>Skype</a>
  778. </span>
  779. </div>
  780. <div class="links-of-blogroll motion-element">
  781. <div class="links-of-blogroll-title">
  782. <i class="fa fa-fw fa-link"></i>
  783. Links
  784. </div>
  785. <ul class="links-of-blogroll-list">
  786. <li class="links-of-blogroll-item">
  787. <a href="https://yonghong.github.io/" title="https:&#x2F;&#x2F;yonghong.github.io" rel="noopener" target="_blank">Yonghong</a>
  788. </li>
  789. <li class="links-of-blogroll-item">
  790. <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>
  791. </li>
  792. </ul>
  793. </div>
  794. </div>
  795. <div id="treefrog" style="text-align: center;margin-top: 18px;">
  796. <object type="application/x-shockwave-flash" style="outline:none;" data="/js/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><param name="AllowScriptAccess" value="always"></param><param name="wmode" value="opaque"></param><param name="scale" value="noscale"/><param name="salign" value="tl"/></object>
  797. </div>
  798. </div>
  799. </aside>
  800. <div id="sidebar-dimmer"></div>
  801. </div>
  802. </main>
  803. <footer class="footer">
  804. <div class="footer-inner">
  805. <div class="copyright">
  806. &copy;
  807. <span itemprop="copyrightYear">2020</span>
  808. <span class="with-love">
  809. <i class="fa fa-user"></i>
  810. </span>
  811. <span class="author" itemprop="copyrightHolder">Alex Xiang</span>
  812. </div>
  813. </div>
  814. </footer>
  815. </div>
  816. <script src="/lib/anime.min.js"></script>
  817. <script src="//cdn.jsdelivr.net/npm/lozad@1/dist/lozad.min.js"></script>
  818. <script src="/lib/velocity/velocity.min.js"></script>
  819. <script src="/lib/velocity/velocity.ui.min.js"></script>
  820. <script src="/js/utils.js"></script>
  821. <script src="/js/motion.js"></script>
  822. <script src="/js/schemes/muse.js"></script>
  823. <script src="/js/next-boot.js"></script>
  824. <script>
  825. (function(){
  826. var bp = document.createElement('script');
  827. var curProtocol = window.location.protocol.split(':')[0];
  828. bp.src = (curProtocol === 'https') ? 'https://zz.bdstatic.com/linksubmit/push.js' : 'http://push.zhanzhang.baidu.com/push.js';
  829. var s = document.getElementsByTagName("script")[0];
  830. s.parentNode.insertBefore(bp, s);
  831. })();
  832. </script>
  833. <link rel="stylesheet" href="//cdn.jsdelivr.net/npm/katex@0/dist/katex.min.css">
  834. <script>
  835. NexT.utils.loadComments(document.querySelector('#valine-comments'), () => {
  836. NexT.utils.getScript('//unpkg.com/valine/dist/Valine.min.js', () => {
  837. var GUEST = ['nick', 'mail', 'link'];
  838. var guest = 'nick,mail,link';
  839. guest = guest.split(',').filter(item => {
  840. return GUEST.includes(item);
  841. });
  842. new Valine({
  843. el : '#valine-comments',
  844. verify : true,
  845. notify : true,
  846. appId : 'BmologYYnRqCv0SLHDeDdA17-gzGzoHsz',
  847. appKey : 'w9mVebFMdCmY6Nh9vfcBGaGt',
  848. placeholder: "Write your comment...",
  849. avatar : 'mm',
  850. meta : guest,
  851. pageSize : '10' || 10,
  852. visitor : false,
  853. lang : 'en' || 'zh-cn',
  854. path : location.pathname,
  855. recordIP : false,
  856. serverURLs : ''
  857. });
  858. }, window.Valine);
  859. });
  860. </script>
  861. </body>
  862. </html>