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     <meta name="description" content="Chapter 0 LogisticsContent : discrete(combinatorial) algorithm  ,  Theoretical   [minority] Complexity , NP-Completeness Basic Graph Algorithm , DFS &#x2F; BFS Greedy Dynamic Programming Divide and Conquer">
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+  <div class="reading-progress-bar"></div>
+
+  <a href="https://github.com/ZigZagKmp" class="github-corner" title="在 GitHub 上关注我" aria-label="在 GitHub 上关注我" rel="noopener" target="_blank"><svg width="80" height="80" viewBox="0 0 250 250" aria-hidden="true"><path d="M0,0 L115,115 L130,115 L142,142 L250,250 L250,0 Z"></path><path d="M128.3,109.0 C113.8,99.7 119.0,89.6 119.0,89.6 C122.0,82.7 120.5,78.6 120.5,78.6 C119.2,72.0 123.4,76.3 123.4,76.3 C127.3,80.9 125.5,87.3 125.5,87.3 C122.9,97.6 130.6,101.9 134.4,103.2" fill="currentColor" style="transform-origin: 130px 106px;" class="octo-arm"></path><path d="M115.0,115.0 C114.9,115.1 118.7,116.5 119.8,115.4 L133.7,101.6 C136.9,99.2 139.9,98.4 142.2,98.6 C133.8,88.0 127.5,74.4 143.8,58.0 C148.5,53.4 154.0,51.2 159.7,51.0 C160.3,49.4 163.2,43.6 171.4,40.1 C171.4,40.1 176.1,42.5 178.8,56.2 C183.1,58.6 187.2,61.8 190.9,65.4 C194.5,69.0 197.7,73.2 200.1,77.6 C213.8,80.2 216.3,84.9 216.3,84.9 C212.7,93.1 206.9,96.0 205.4,96.6 C205.1,102.4 203.0,107.8 198.3,112.5 C181.9,128.9 168.3,122.5 157.7,114.1 C157.9,116.9 156.7,120.9 152.7,124.9 L141.0,136.5 C139.8,137.7 141.6,141.9 141.8,141.8 Z" fill="currentColor" class="octo-body"></path></svg></a>
 
 <noscript>
   <div class="noscript-warning">Theme NexT works best with JavaScript enabled</div>
@@ -261,7 +333,9 @@ <h3 id="Deploy-to-remote-sites"><a href="#Deploy-to-remote-sites" class="headerl
   <script src="https://cdnjs.cloudflare.com/ajax/libs/animejs/3.2.1/anime.min.js" integrity="sha256-XL2inqUJaslATFnHdJOi9GfQ60on8Wx1C2H8DYiN1xY=" crossorigin="anonymous"></script>
 <script src="/js/comments.js"></script><script src="/js/utils.js"></script><script src="/js/motion.js"></script><script src="/js/next-boot.js"></script>
 
-  
+  <script src="https://cdnjs.cloudflare.com/ajax/libs/hexo-generator-searchdb/1.4.1/search.js" integrity="sha256-1kfA5uHPf65M5cphT2dvymhkuyHPQp5A53EGZOnOLmc=" crossorigin="anonymous"></script>
+<script src="/js/third-party/search/local-search.js"></script>
+
 
 
 
@@ -269,10 +343,17 @@ <h3 id="Deploy-to-remote-sites"><a href="#Deploy-to-remote-sites" class="headerl
 
 
   
+  <script async src="https://busuanzi.ibruce.info/busuanzi/2.3/busuanzi.pure.mini.js"></script>
 
 
 
 
+  
+
+  <script class="next-config" data-name="enableMath" type="application/json">true</script><script class="next-config" data-name="mathjax" type="application/json">{"enable":true,"tags":"none","js":{"url":"https://cdnjs.cloudflare.com/ajax/libs/mathjax/3.2.2/es5/tex-mml-chtml.js","integrity":"sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI="}}</script>
+<script src="/js/third-party/math/mathjax.js"></script>
+
+
 
 </body>
 </html>
diff --git a/404.html b/404.html
index 677dda5..076d30d 100755
--- a/404.html
+++ b/404.html
@@ -17,7 +17,7 @@
 <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.0/css/all.min.css" integrity="sha256-HtsXJanqjKTc8vVQjO4YMhiqFoXkfBsjBWcX91T1jr8=" crossorigin="anonymous">
   <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/animate.css/3.1.1/animate.min.css" integrity="sha256-PR7ttpcvz8qrF57fur/yAx1qXMFJeJFiA6pSzWi0OIE=" crossorigin="anonymous">
 
-<script class="next-config" data-name="main" type="application/json">{"hostname":"zigzagkmp.github.io","root":"/","images":"/images","scheme":"Gemini","darkmode":false,"version":"8.18.1","exturl":false,"sidebar":{"position":"left","display":"post","padding":18,"offset":12},"copycode":{"enable":false,"style":null},"fold":{"enable":false,"height":500},"bookmark":{"enable":false,"color":"#222","save":"auto"},"mediumzoom":false,"lazyload":false,"pangu":false,"comments":{"style":"tabs","active":null,"storage":true,"lazyload":false,"nav":null},"stickytabs":false,"motion":{"enable":true,"async":false,"transition":{"menu_item":"fadeInDown","post_block":"fadeIn","post_header":"fadeInDown","post_body":"fadeInDown","coll_header":"fadeInLeft","sidebar":"fadeInUp"}},"prism":false,"i18n":{"placeholder":"搜索...","empty":"没有找到任何搜索结果：${query}","hits_time":"找到 ${hits} 个搜索结果（用时 ${time} 毫秒）","hits":"找到 ${hits} 个搜索结果"}}</script><script src="/js/config.js"></script>
+<script class="next-config" data-name="main" type="application/json">{"hostname":"zigzagkmp.github.io","root":"/","images":"/images","scheme":"Gemini","darkmode":false,"version":"8.18.1","exturl":false,"sidebar":{"position":"left","display":"post","padding":18,"offset":12},"copycode":{"enable":true,"style":null},"fold":{"enable":true,"height":500},"bookmark":{"enable":false,"color":"#222","save":"auto"},"mediumzoom":false,"lazyload":false,"pangu":false,"comments":{"style":"tabs","active":null,"storage":true,"lazyload":false,"nav":null},"stickytabs":false,"motion":{"enable":true,"async":false,"transition":{"menu_item":"fadeInDown","post_block":"fadeIn","post_header":"fadeInDown","post_body":"fadeInDown","coll_header":"fadeInLeft","sidebar":"fadeInUp"}},"prism":false,"i18n":{"placeholder":"搜索...","empty":"没有找到任何搜索结果：${query}","hits_time":"找到 ${hits} 个搜索结果（用时 ${time} 毫秒）","hits":"找到 ${hits} 个搜索结果"},"path":"/search.xml","localsearch":{"enable":true,"trigger":"auto","top_n_per_article":1,"unescape":false,"preload":false}}</script><script src="/js/config.js"></script>
 
     <meta property="og:type" content="website">
 <meta property="og:title" content="ZigZagKmp&#39;s Blog">
@@ -61,6 +61,9 @@
       <header class="header" itemscope itemtype="http://schema.org/WPHeader"><div class="site-brand-container">
   <div class="site-nav-toggle">
     <div class="toggle" aria-label="切换导航栏" role="button">
+        <span class="toggle-line"></span>
+        <span class="toggle-line"></span>
+        <span class="toggle-line"></span>
     </div>
   </div>
 
@@ -76,15 +79,46 @@
 
   <div class="site-nav-right">
     <div class="toggle popup-trigger" aria-label="搜索" role="button">
+        <i class="fa fa-search fa-fw fa-lg"></i>
     </div>
   </div>
 </div>
 
 
 
+<nav class="site-nav">
+  <ul class="main-menu menu"><li class="menu-item menu-item-home"><a href="/" rel="section"><i class="fa fa-home fa-fw"></i>首页</a></li><li class="menu-item menu-item-about"><a href="/about/" rel="section"><i class="fa fa-user fa-fw"></i>关于</a></li><li class="menu-item menu-item-tags"><a href="/tags/" rel="section"><i class="fa fa-tags fa-fw"></i>标签</a></li><li class="menu-item menu-item-categories"><a href="/categories/" rel="section"><i class="fa fa-th fa-fw"></i>分类</a></li><li class="menu-item menu-item-archives"><a href="/archives/" rel="section"><i class="fa fa-archive fa-fw"></i>归档</a></li>
+      <li class="menu-item menu-item-search">
+        <a role="button" class="popup-trigger"><i class="fa fa-search fa-fw"></i>搜索
+        </a>
+      </li>
+  </ul>
+</nav>
 
 
 
+  <div class="search-pop-overlay">
+    <div class="popup search-popup"><div class="search-header">
+  <span class="search-icon">
+    <i class="fa fa-search"></i>
+  </span>
+  <div class="search-input-container">
+    <input autocomplete="off" autocapitalize="off" maxlength="80"
+           placeholder="搜索..." spellcheck="false"
+           type="search" class="search-input">
+  </div>
+  <span class="popup-btn-close" role="button">
+    <i class="fa fa-times-circle"></i>
+  </span>
+</div>
+<div class="search-result-container no-result">
+  <div class="search-result-icon">
+    <i class="fa fa-spinner fa-pulse fa-5x"></i>
+  </div>
+</div>
+
+    </div>
+  </div>
 
 </header>
         
@@ -109,6 +143,8 @@
 
         <div class="site-overview-wrap sidebar-panel">
           <div class="site-author animated" itemprop="author" itemscope itemtype="http://schema.org/Person">
+    <img class="site-author-image" itemprop="image" alt="ZigZagKmp"
+      src="/images/avatar/avatar.jpg">
   <p class="site-author-name" itemprop="name">ZigZagKmp</p>
   <div class="site-description" itemprop="description"></div>
 </div>
@@ -122,9 +158,21 @@
       </div>
   </nav>
 </div>
+  <div class="links-of-author animated">
+      <span class="links-of-author-item">
+        <a href="https://github.com/ZigZagKmp" title="GitHub → https:&#x2F;&#x2F;github.com&#x2F;ZigZagKmp" rel="noopener me" target="_blank"><i class="fab fa-github fa-fw"></i>GitHub</a>
+      </span>
+      <span class="links-of-author-item">
+        <a href="mailto:zigzagkmp@qq.com" title="E-Mail → mailto:zigzagkmp@qq.com" rel="noopener me" target="_blank"><i class="fa fa-envelope fa-fw"></i>E-Mail</a>
+      </span>
+  </div>
 
         </div>
       </div>
+        <div class="back-to-top animated" role="button" aria-label="返回顶部">
+          <i class="fa fa-arrow-up"></i>
+          <span>0%</span>
+        </div>
     </div>
 
     
@@ -177,6 +225,24 @@ <h1 class="post-title" itemprop="name headline">
     </span>
     <span class="author" itemprop="copyrightHolder">ZigZagKmp</span>
   </div>
+<div class="busuanzi-count">
+    <span class="post-meta-item" id="busuanzi_container_site_uv">
+      <span class="post-meta-item-icon">
+        <i class="fa fa-user"></i>
+      </span>
+      <span class="site-uv" title="总访客量">
+        <span id="busuanzi_value_site_uv"></span>
+      </span>
+    </span>
+    <span class="post-meta-item" id="busuanzi_container_site_pv">
+      <span class="post-meta-item-icon">
+        <i class="fa fa-eye"></i>
+      </span>
+      <span class="site-pv" title="总访问量">
+        <span id="busuanzi_value_site_pv"></span>
+      </span>
+    </span>
+</div>
   <div class="powered-by">由 <a href="https://hexo.io/" rel="noopener" target="_blank">Hexo</a> & <a href="https://theme-next.js.org/" rel="noopener" target="_blank">NexT.Gemini</a> 强力驱动
   </div>
 
@@ -184,10 +250,9 @@ <h1 class="post-title" itemprop="name headline">
   </footer>
 
   
-  <div class="back-to-top" role="button" aria-label="返回顶部">
-    <i class="fa fa-arrow-up fa-lg"></i>
-    <span>0%</span>
-  </div>
+  <div class="reading-progress-bar"></div>
+
+  <a href="https://github.com/ZigZagKmp" class="github-corner" title="在 GitHub 上关注我" aria-label="在 GitHub 上关注我" rel="noopener" target="_blank"><svg width="80" height="80" viewBox="0 0 250 250" aria-hidden="true"><path d="M0,0 L115,115 L130,115 L142,142 L250,250 L250,0 Z"></path><path d="M128.3,109.0 C113.8,99.7 119.0,89.6 119.0,89.6 C122.0,82.7 120.5,78.6 120.5,78.6 C119.2,72.0 123.4,76.3 123.4,76.3 C127.3,80.9 125.5,87.3 125.5,87.3 C122.9,97.6 130.6,101.9 134.4,103.2" fill="currentColor" style="transform-origin: 130px 106px;" class="octo-arm"></path><path d="M115.0,115.0 C114.9,115.1 118.7,116.5 119.8,115.4 L133.7,101.6 C136.9,99.2 139.9,98.4 142.2,98.6 C133.8,88.0 127.5,74.4 143.8,58.0 C148.5,53.4 154.0,51.2 159.7,51.0 C160.3,49.4 163.2,43.6 171.4,40.1 C171.4,40.1 176.1,42.5 178.8,56.2 C183.1,58.6 187.2,61.8 190.9,65.4 C194.5,69.0 197.7,73.2 200.1,77.6 C213.8,80.2 216.3,84.9 216.3,84.9 C212.7,93.1 206.9,96.0 205.4,96.6 C205.1,102.4 203.0,107.8 198.3,112.5 C181.9,128.9 168.3,122.5 157.7,114.1 C157.9,116.9 156.7,120.9 152.7,124.9 L141.0,136.5 C139.8,137.7 141.6,141.9 141.8,141.8 Z" fill="currentColor" class="octo-body"></path></svg></a>
 
 <noscript>
   <div class="noscript-warning">Theme NexT works best with JavaScript enabled</div>
@@ -198,7 +263,9 @@ <h1 class="post-title" itemprop="name headline">
   <script src="https://cdnjs.cloudflare.com/ajax/libs/animejs/3.2.1/anime.min.js" integrity="sha256-XL2inqUJaslATFnHdJOi9GfQ60on8Wx1C2H8DYiN1xY=" crossorigin="anonymous"></script>
 <script src="/js/comments.js"></script><script src="/js/utils.js"></script><script src="/js/motion.js"></script><script src="/js/next-boot.js"></script>
 
-  
+  <script src="https://cdnjs.cloudflare.com/ajax/libs/hexo-generator-searchdb/1.4.1/search.js" integrity="sha256-1kfA5uHPf65M5cphT2dvymhkuyHPQp5A53EGZOnOLmc=" crossorigin="anonymous"></script>
+<script src="/js/third-party/search/local-search.js"></script>
+
 
 
 
@@ -206,8 +273,15 @@ <h1 class="post-title" itemprop="name headline">
 
 
   
+  <script async src="https://busuanzi.ibruce.info/busuanzi/2.3/busuanzi.pure.mini.js"></script>
+
+
 
 
+  
+
+  <script class="next-config" data-name="enableMath" type="application/json">true</script><script class="next-config" data-name="mathjax" type="application/json">{"enable":true,"tags":"none","js":{"url":"https://cdnjs.cloudflare.com/ajax/libs/mathjax/3.2.2/es5/tex-mml-chtml.js","integrity":"sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI="}}</script>
+<script src="/js/third-party/math/mathjax.js"></script>
 
 
 
diff --git a/about/index.html b/about/index.html
index f6ee21d..350ab8a 100755
--- a/about/index.html
+++ b/about/index.html
@@ -17,7 +17,7 @@
 <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.0/css/all.min.css" integrity="sha256-HtsXJanqjKTc8vVQjO4YMhiqFoXkfBsjBWcX91T1jr8=" crossorigin="anonymous">
   <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/animate.css/3.1.1/animate.min.css" integrity="sha256-PR7ttpcvz8qrF57fur/yAx1qXMFJeJFiA6pSzWi0OIE=" crossorigin="anonymous">
 
-<script class="next-config" data-name="main" type="application/json">{"hostname":"zigzagkmp.github.io","root":"/","images":"/images","scheme":"Gemini","darkmode":false,"version":"8.18.1","exturl":false,"sidebar":{"position":"left","display":"post","padding":18,"offset":12},"copycode":{"enable":false,"style":null},"fold":{"enable":false,"height":500},"bookmark":{"enable":false,"color":"#222","save":"auto"},"mediumzoom":false,"lazyload":false,"pangu":false,"comments":{"style":"tabs","active":null,"storage":true,"lazyload":false,"nav":null},"stickytabs":false,"motion":{"enable":true,"async":false,"transition":{"menu_item":"fadeInDown","post_block":"fadeIn","post_header":"fadeInDown","post_body":"fadeInDown","coll_header":"fadeInLeft","sidebar":"fadeInUp"}},"prism":false,"i18n":{"placeholder":"搜索...","empty":"没有找到任何搜索结果：${query}","hits_time":"找到 ${hits} 个搜索结果（用时 ${time} 毫秒）","hits":"找到 ${hits} 个搜索结果"}}</script><script src="/js/config.js"></script>
+<script class="next-config" data-name="main" type="application/json">{"hostname":"zigzagkmp.github.io","root":"/","images":"/images","scheme":"Gemini","darkmode":false,"version":"8.18.1","exturl":false,"sidebar":{"position":"left","display":"post","padding":18,"offset":12},"copycode":{"enable":true,"style":null},"fold":{"enable":true,"height":500},"bookmark":{"enable":false,"color":"#222","save":"auto"},"mediumzoom":false,"lazyload":false,"pangu":false,"comments":{"style":"tabs","active":null,"storage":true,"lazyload":false,"nav":null},"stickytabs":false,"motion":{"enable":true,"async":false,"transition":{"menu_item":"fadeInDown","post_block":"fadeIn","post_header":"fadeInDown","post_body":"fadeInDown","coll_header":"fadeInLeft","sidebar":"fadeInUp"}},"prism":false,"i18n":{"placeholder":"搜索...","empty":"没有找到任何搜索结果：${query}","hits_time":"找到 ${hits} 个搜索结果（用时 ${time} 毫秒）","hits":"找到 ${hits} 个搜索结果"},"path":"/search.xml","localsearch":{"enable":true,"trigger":"auto","top_n_per_article":1,"unescape":false,"preload":false}}</script><script src="/js/config.js"></script>
 
     <meta property="og:type" content="website">
 <meta property="og:title" content="about">
@@ -61,6 +61,9 @@
       <header class="header" itemscope itemtype="http://schema.org/WPHeader"><div class="site-brand-container">
   <div class="site-nav-toggle">
     <div class="toggle" aria-label="切换导航栏" role="button">
+        <span class="toggle-line"></span>
+        <span class="toggle-line"></span>
+        <span class="toggle-line"></span>
     </div>
   </div>
 
@@ -76,15 +79,46 @@
 
   <div class="site-nav-right">
     <div class="toggle popup-trigger" aria-label="搜索" role="button">
+        <i class="fa fa-search fa-fw fa-lg"></i>
     </div>
   </div>
 </div>
 
 
 
+<nav class="site-nav">
+  <ul class="main-menu menu"><li class="menu-item menu-item-home"><a href="/" rel="section"><i class="fa fa-home fa-fw"></i>首页</a></li><li class="menu-item menu-item-about"><a href="/about/" rel="section"><i class="fa fa-user fa-fw"></i>关于</a></li><li class="menu-item menu-item-tags"><a href="/tags/" rel="section"><i class="fa fa-tags fa-fw"></i>标签</a></li><li class="menu-item menu-item-categories"><a href="/categories/" rel="section"><i class="fa fa-th fa-fw"></i>分类</a></li><li class="menu-item menu-item-archives"><a href="/archives/" rel="section"><i class="fa fa-archive fa-fw"></i>归档</a></li>
+      <li class="menu-item menu-item-search">
+        <a role="button" class="popup-trigger"><i class="fa fa-search fa-fw"></i>搜索
+        </a>
+      </li>
+  </ul>
+</nav>
 
 
 
+  <div class="search-pop-overlay">
+    <div class="popup search-popup"><div class="search-header">
+  <span class="search-icon">
+    <i class="fa fa-search"></i>
+  </span>
+  <div class="search-input-container">
+    <input autocomplete="off" autocapitalize="off" maxlength="80"
+           placeholder="搜索..." spellcheck="false"
+           type="search" class="search-input">
+  </div>
+  <span class="popup-btn-close" role="button">
+    <i class="fa fa-times-circle"></i>
+  </span>
+</div>
+<div class="search-result-container no-result">
+  <div class="search-result-icon">
+    <i class="fa fa-spinner fa-pulse fa-5x"></i>
+  </div>
+</div>
+
+    </div>
+  </div>
 
 </header>
         
@@ -109,6 +143,8 @@
 
         <div class="site-overview-wrap sidebar-panel">
           <div class="site-author animated" itemprop="author" itemscope itemtype="http://schema.org/Person">
+    <img class="site-author-image" itemprop="image" alt="ZigZagKmp"
+      src="/images/avatar/avatar.jpg">
   <p class="site-author-name" itemprop="name">ZigZagKmp</p>
   <div class="site-description" itemprop="description"></div>
 </div>
@@ -122,9 +158,21 @@
       </div>
   </nav>
 </div>
+  <div class="links-of-author animated">
+      <span class="links-of-author-item">
+        <a href="https://github.com/ZigZagKmp" title="GitHub → https:&#x2F;&#x2F;github.com&#x2F;ZigZagKmp" rel="noopener me" target="_blank"><i class="fab fa-github fa-fw"></i>GitHub</a>
+      </span>
+      <span class="links-of-author-item">
+        <a href="mailto:zigzagkmp@qq.com" title="E-Mail → mailto:zigzagkmp@qq.com" rel="noopener me" target="_blank"><i class="fa fa-envelope fa-fw"></i>E-Mail</a>
+      </span>
+  </div>
 
         </div>
       </div>
+        <div class="back-to-top animated" role="button" aria-label="返回顶部">
+          <i class="fa fa-arrow-up"></i>
+          <span>0%</span>
+        </div>
     </div>
 
     
@@ -177,6 +225,24 @@ <h1 class="post-title" itemprop="name headline">about
     </span>
     <span class="author" itemprop="copyrightHolder">ZigZagKmp</span>
   </div>
+<div class="busuanzi-count">
+    <span class="post-meta-item" id="busuanzi_container_site_uv">
+      <span class="post-meta-item-icon">
+        <i class="fa fa-user"></i>
+      </span>
+      <span class="site-uv" title="总访客量">
+        <span id="busuanzi_value_site_uv"></span>
+      </span>
+    </span>
+    <span class="post-meta-item" id="busuanzi_container_site_pv">
+      <span class="post-meta-item-icon">
+        <i class="fa fa-eye"></i>
+      </span>
+      <span class="site-pv" title="总访问量">
+        <span id="busuanzi_value_site_pv"></span>
+      </span>
+    </span>
+</div>
   <div class="powered-by">由 <a href="https://hexo.io/" rel="noopener" target="_blank">Hexo</a> & <a href="https://theme-next.js.org/" rel="noopener" target="_blank">NexT.Gemini</a> 强力驱动
   </div>
 
@@ -184,10 +250,9 @@ <h1 class="post-title" itemprop="name headline">about
   </footer>
 
   
-  <div class="back-to-top" role="button" aria-label="返回顶部">
-    <i class="fa fa-arrow-up fa-lg"></i>
-    <span>0%</span>
-  </div>
+  <div class="reading-progress-bar"></div>
+
+  <a href="https://github.com/ZigZagKmp" class="github-corner" title="在 GitHub 上关注我" aria-label="在 GitHub 上关注我" rel="noopener" target="_blank"><svg width="80" height="80" viewBox="0 0 250 250" aria-hidden="true"><path d="M0,0 L115,115 L130,115 L142,142 L250,250 L250,0 Z"></path><path d="M128.3,109.0 C113.8,99.7 119.0,89.6 119.0,89.6 C122.0,82.7 120.5,78.6 120.5,78.6 C119.2,72.0 123.4,76.3 123.4,76.3 C127.3,80.9 125.5,87.3 125.5,87.3 C122.9,97.6 130.6,101.9 134.4,103.2" fill="currentColor" style="transform-origin: 130px 106px;" class="octo-arm"></path><path d="M115.0,115.0 C114.9,115.1 118.7,116.5 119.8,115.4 L133.7,101.6 C136.9,99.2 139.9,98.4 142.2,98.6 C133.8,88.0 127.5,74.4 143.8,58.0 C148.5,53.4 154.0,51.2 159.7,51.0 C160.3,49.4 163.2,43.6 171.4,40.1 C171.4,40.1 176.1,42.5 178.8,56.2 C183.1,58.6 187.2,61.8 190.9,65.4 C194.5,69.0 197.7,73.2 200.1,77.6 C213.8,80.2 216.3,84.9 216.3,84.9 C212.7,93.1 206.9,96.0 205.4,96.6 C205.1,102.4 203.0,107.8 198.3,112.5 C181.9,128.9 168.3,122.5 157.7,114.1 C157.9,116.9 156.7,120.9 152.7,124.9 L141.0,136.5 C139.8,137.7 141.6,141.9 141.8,141.8 Z" fill="currentColor" class="octo-body"></path></svg></a>
 
 <noscript>
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@@ -198,7 +263,9 @@ <h1 class="post-title" itemprop="name headline">about
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 <script src="/js/comments.js"></script><script src="/js/utils.js"></script><script src="/js/motion.js"></script><script src="/js/next-boot.js"></script>
 
-  
+  <script src="https://cdnjs.cloudflare.com/ajax/libs/hexo-generator-searchdb/1.4.1/search.js" integrity="sha256-1kfA5uHPf65M5cphT2dvymhkuyHPQp5A53EGZOnOLmc=" crossorigin="anonymous"></script>
+<script src="/js/third-party/search/local-search.js"></script>
+
 
 
 
@@ -206,8 +273,15 @@ <h1 class="post-title" itemprop="name headline">about
 
 
   
+  <script async src="https://busuanzi.ibruce.info/busuanzi/2.3/busuanzi.pure.mini.js"></script>
+
+
 
 
+  
+
+  <script class="next-config" data-name="enableMath" type="application/json">true</script><script class="next-config" data-name="mathjax" type="application/json">{"enable":true,"tags":"none","js":{"url":"https://cdnjs.cloudflare.com/ajax/libs/mathjax/3.2.2/es5/tex-mml-chtml.js","integrity":"sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI="}}</script>
+<script src="/js/third-party/math/mathjax.js"></script>
 
 
 
diff --git a/archives/2023/10/index.html b/archives/2023/10/index.html
index 16649f7..147b153 100755
--- a/archives/2023/10/index.html
+++ b/archives/2023/10/index.html
@@ -17,7 +17,7 @@
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-<script class="next-config" data-name="main" type="application/json">{"hostname":"zigzagkmp.github.io","root":"/","images":"/images","scheme":"Gemini","darkmode":false,"version":"8.18.1","exturl":false,"sidebar":{"position":"left","display":"post","padding":18,"offset":12},"copycode":{"enable":false,"style":null},"fold":{"enable":false,"height":500},"bookmark":{"enable":false,"color":"#222","save":"auto"},"mediumzoom":false,"lazyload":false,"pangu":false,"comments":{"style":"tabs","active":null,"storage":true,"lazyload":false,"nav":null},"stickytabs":false,"motion":{"enable":true,"async":false,"transition":{"menu_item":"fadeInDown","post_block":"fadeIn","post_header":"fadeInDown","post_body":"fadeInDown","coll_header":"fadeInLeft","sidebar":"fadeInUp"}},"prism":false,"i18n":{"placeholder":"搜索...","empty":"没有找到任何搜索结果：${query}","hits_time":"找到 ${hits} 个搜索结果（用时 ${time} 毫秒）","hits":"找到 ${hits} 个搜索结果"}}</script><script src="/js/config.js"></script>
+<script class="next-config" data-name="main" type="application/json">{"hostname":"zigzagkmp.github.io","root":"/","images":"/images","scheme":"Gemini","darkmode":false,"version":"8.18.1","exturl":false,"sidebar":{"position":"left","display":"post","padding":18,"offset":12},"copycode":{"enable":true,"style":null},"fold":{"enable":true,"height":500},"bookmark":{"enable":false,"color":"#222","save":"auto"},"mediumzoom":false,"lazyload":false,"pangu":false,"comments":{"style":"tabs","active":null,"storage":true,"lazyload":false,"nav":null},"stickytabs":false,"motion":{"enable":true,"async":false,"transition":{"menu_item":"fadeInDown","post_block":"fadeIn","post_header":"fadeInDown","post_body":"fadeInDown","coll_header":"fadeInLeft","sidebar":"fadeInUp"}},"prism":false,"i18n":{"placeholder":"搜索...","empty":"没有找到任何搜索结果：${query}","hits_time":"找到 ${hits} 个搜索结果（用时 ${time} 毫秒）","hits":"找到 ${hits} 个搜索结果"},"path":"/search.xml","localsearch":{"enable":true,"trigger":"auto","top_n_per_article":1,"unescape":false,"preload":false}}</script><script src="/js/config.js"></script>
 
     <meta property="og:type" content="website">
 <meta property="og:title" content="ZigZagKmp&#39;s Blog">
@@ -58,6 +58,9 @@
       <header class="header" itemscope itemtype="http://schema.org/WPHeader"><div class="site-brand-container">
   <div class="site-nav-toggle">
     <div class="toggle" aria-label="切换导航栏" role="button">
+        <span class="toggle-line"></span>
+        <span class="toggle-line"></span>
+        <span class="toggle-line"></span>
     </div>
   </div>
 
@@ -73,15 +76,46 @@ <h1 class="site-title">ZigZagKmp's Blog</h1>
 
   <div class="site-nav-right">
     <div class="toggle popup-trigger" aria-label="搜索" role="button">
+        <i class="fa fa-search fa-fw fa-lg"></i>
     </div>
   </div>
 </div>
 
 
 
+<nav class="site-nav">
+  <ul class="main-menu menu"><li class="menu-item menu-item-home"><a href="/" rel="section"><i class="fa fa-home fa-fw"></i>首页</a></li><li class="menu-item menu-item-about"><a href="/about/" rel="section"><i class="fa fa-user fa-fw"></i>关于</a></li><li class="menu-item menu-item-tags"><a href="/tags/" rel="section"><i class="fa fa-tags fa-fw"></i>标签</a></li><li class="menu-item menu-item-categories"><a href="/categories/" rel="section"><i class="fa fa-th fa-fw"></i>分类</a></li><li class="menu-item menu-item-archives"><a href="/archives/" rel="section"><i class="fa fa-archive fa-fw"></i>归档</a></li>
+      <li class="menu-item menu-item-search">
+        <a role="button" class="popup-trigger"><i class="fa fa-search fa-fw"></i>搜索
+        </a>
+      </li>
+  </ul>
+</nav>
 
 
 
+  <div class="search-pop-overlay">
+    <div class="popup search-popup"><div class="search-header">
+  <span class="search-icon">
+    <i class="fa fa-search"></i>
+  </span>
+  <div class="search-input-container">
+    <input autocomplete="off" autocapitalize="off" maxlength="80"
+           placeholder="搜索..." spellcheck="false"
+           type="search" class="search-input">
+  </div>
+  <span class="popup-btn-close" role="button">
+    <i class="fa fa-times-circle"></i>
+  </span>
+</div>
+<div class="search-result-container no-result">
+  <div class="search-result-icon">
+    <i class="fa fa-spinner fa-pulse fa-5x"></i>
+  </div>
+</div>
+
+    </div>
+  </div>
 
 </header>
         
@@ -106,6 +140,8 @@ <h1 class="site-title">ZigZagKmp's Blog</h1>
 
         <div class="site-overview-wrap sidebar-panel">
           <div class="site-author animated" itemprop="author" itemscope itemtype="http://schema.org/Person">
+    <img class="site-author-image" itemprop="image" alt="ZigZagKmp"
+      src="/images/avatar/avatar.jpg">
   <p class="site-author-name" itemprop="name">ZigZagKmp</p>
   <div class="site-description" itemprop="description"></div>
 </div>
@@ -119,9 +155,21 @@ <h1 class="site-title">ZigZagKmp's Blog</h1>
       </div>
   </nav>
 </div>
+  <div class="links-of-author animated">
+      <span class="links-of-author-item">
+        <a href="https://github.com/ZigZagKmp" title="GitHub → https:&#x2F;&#x2F;github.com&#x2F;ZigZagKmp" rel="noopener me" target="_blank"><i class="fab fa-github fa-fw"></i>GitHub</a>
+      </span>
+      <span class="links-of-author-item">
+        <a href="mailto:zigzagkmp@qq.com" title="E-Mail → mailto:zigzagkmp@qq.com" rel="noopener me" target="_blank"><i class="fa fa-envelope fa-fw"></i>E-Mail</a>
+      </span>
+  </div>
 
         </div>
       </div>
+        <div class="back-to-top animated" role="button" aria-label="返回顶部">
+          <i class="fa fa-arrow-up"></i>
+          <span>0%</span>
+        </div>
     </div>
 
     
@@ -208,6 +256,24 @@ <h1 class="site-title">ZigZagKmp's Blog</h1>
     </span>
     <span class="author" itemprop="copyrightHolder">ZigZagKmp</span>
   </div>
+<div class="busuanzi-count">
+    <span class="post-meta-item" id="busuanzi_container_site_uv">
+      <span class="post-meta-item-icon">
+        <i class="fa fa-user"></i>
+      </span>
+      <span class="site-uv" title="总访客量">
+        <span id="busuanzi_value_site_uv"></span>
+      </span>
+    </span>
+    <span class="post-meta-item" id="busuanzi_container_site_pv">
+      <span class="post-meta-item-icon">
+        <i class="fa fa-eye"></i>
+      </span>
+      <span class="site-pv" title="总访问量">
+        <span id="busuanzi_value_site_pv"></span>
+      </span>
+    </span>
+</div>
   <div class="powered-by">由 <a href="https://hexo.io/" rel="noopener" target="_blank">Hexo</a> & <a href="https://theme-next.js.org/" rel="noopener" target="_blank">NexT.Gemini</a> 强力驱动
   </div>
 
@@ -215,10 +281,9 @@ <h1 class="site-title">ZigZagKmp's Blog</h1>
   </footer>
 
   
-  <div class="back-to-top" role="button" aria-label="返回顶部">
-    <i class="fa fa-arrow-up fa-lg"></i>
-    <span>0%</span>
-  </div>
+  <div class="reading-progress-bar"></div>
+
+  <a href="https://github.com/ZigZagKmp" class="github-corner" title="在 GitHub 上关注我" aria-label="在 GitHub 上关注我" rel="noopener" target="_blank"><svg width="80" height="80" viewBox="0 0 250 250" aria-hidden="true"><path d="M0,0 L115,115 L130,115 L142,142 L250,250 L250,0 Z"></path><path d="M128.3,109.0 C113.8,99.7 119.0,89.6 119.0,89.6 C122.0,82.7 120.5,78.6 120.5,78.6 C119.2,72.0 123.4,76.3 123.4,76.3 C127.3,80.9 125.5,87.3 125.5,87.3 C122.9,97.6 130.6,101.9 134.4,103.2" fill="currentColor" style="transform-origin: 130px 106px;" class="octo-arm"></path><path d="M115.0,115.0 C114.9,115.1 118.7,116.5 119.8,115.4 L133.7,101.6 C136.9,99.2 139.9,98.4 142.2,98.6 C133.8,88.0 127.5,74.4 143.8,58.0 C148.5,53.4 154.0,51.2 159.7,51.0 C160.3,49.4 163.2,43.6 171.4,40.1 C171.4,40.1 176.1,42.5 178.8,56.2 C183.1,58.6 187.2,61.8 190.9,65.4 C194.5,69.0 197.7,73.2 200.1,77.6 C213.8,80.2 216.3,84.9 216.3,84.9 C212.7,93.1 206.9,96.0 205.4,96.6 C205.1,102.4 203.0,107.8 198.3,112.5 C181.9,128.9 168.3,122.5 157.7,114.1 C157.9,116.9 156.7,120.9 152.7,124.9 L141.0,136.5 C139.8,137.7 141.6,141.9 141.8,141.8 Z" fill="currentColor" class="octo-body"></path></svg></a>
 
 <noscript>
   <div class="noscript-warning">Theme NexT works best with JavaScript enabled</div>
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 <script src="/js/comments.js"></script><script src="/js/utils.js"></script><script src="/js/motion.js"></script><script src="/js/next-boot.js"></script>
 
-  
+  <script src="https://cdnjs.cloudflare.com/ajax/libs/hexo-generator-searchdb/1.4.1/search.js" integrity="sha256-1kfA5uHPf65M5cphT2dvymhkuyHPQp5A53EGZOnOLmc=" crossorigin="anonymous"></script>
+<script src="/js/third-party/search/local-search.js"></script>
+
 
 
 
@@ -237,8 +304,15 @@ <h1 class="site-title">ZigZagKmp's Blog</h1>
 
 
   
+  <script async src="https://busuanzi.ibruce.info/busuanzi/2.3/busuanzi.pure.mini.js"></script>
+
+
 
 
+  
+
+  <script class="next-config" data-name="enableMath" type="application/json">true</script><script class="next-config" data-name="mathjax" type="application/json">{"enable":true,"tags":"none","js":{"url":"https://cdnjs.cloudflare.com/ajax/libs/mathjax/3.2.2/es5/tex-mml-chtml.js","integrity":"sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI="}}</script>
+<script src="/js/third-party/math/mathjax.js"></script>
 
 
 
diff --git a/archives/2023/index.html b/archives/2023/index.html
index 1a05fb0..2923757 100755
--- a/archives/2023/index.html
+++ b/archives/2023/index.html
@@ -17,7 +17,7 @@
 <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.0/css/all.min.css" integrity="sha256-HtsXJanqjKTc8vVQjO4YMhiqFoXkfBsjBWcX91T1jr8=" crossorigin="anonymous">
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+<script class="next-config" data-name="main" type="application/json">{"hostname":"zigzagkmp.github.io","root":"/","images":"/images","scheme":"Gemini","darkmode":false,"version":"8.18.1","exturl":false,"sidebar":{"position":"left","display":"post","padding":18,"offset":12},"copycode":{"enable":true,"style":null},"fold":{"enable":true,"height":500},"bookmark":{"enable":false,"color":"#222","save":"auto"},"mediumzoom":false,"lazyload":false,"pangu":false,"comments":{"style":"tabs","active":null,"storage":true,"lazyload":false,"nav":null},"stickytabs":false,"motion":{"enable":true,"async":false,"transition":{"menu_item":"fadeInDown","post_block":"fadeIn","post_header":"fadeInDown","post_body":"fadeInDown","coll_header":"fadeInLeft","sidebar":"fadeInUp"}},"prism":false,"i18n":{"placeholder":"搜索...","empty":"没有找到任何搜索结果：${query}","hits_time":"找到 ${hits} 个搜索结果（用时 ${time} 毫秒）","hits":"找到 ${hits} 个搜索结果"},"path":"/search.xml","localsearch":{"enable":true,"trigger":"auto","top_n_per_article":1,"unescape":false,"preload":false}}</script><script src="/js/config.js"></script>
 
     <meta property="og:type" content="website">
 <meta property="og:title" content="ZigZagKmp&#39;s Blog">
@@ -58,6 +58,9 @@
       <header class="header" itemscope itemtype="http://schema.org/WPHeader"><div class="site-brand-container">
   <div class="site-nav-toggle">
     <div class="toggle" aria-label="切换导航栏" role="button">
+        <span class="toggle-line"></span>
+        <span class="toggle-line"></span>
+        <span class="toggle-line"></span>
     </div>
   </div>
 
@@ -73,15 +76,46 @@ <h1 class="site-title">ZigZagKmp's Blog</h1>
 
   <div class="site-nav-right">
     <div class="toggle popup-trigger" aria-label="搜索" role="button">
+        <i class="fa fa-search fa-fw fa-lg"></i>
     </div>
   </div>
 </div>
 
 
 
+<nav class="site-nav">
+  <ul class="main-menu menu"><li class="menu-item menu-item-home"><a href="/" rel="section"><i class="fa fa-home fa-fw"></i>首页</a></li><li class="menu-item menu-item-about"><a href="/about/" rel="section"><i class="fa fa-user fa-fw"></i>关于</a></li><li class="menu-item menu-item-tags"><a href="/tags/" rel="section"><i class="fa fa-tags fa-fw"></i>标签</a></li><li class="menu-item menu-item-categories"><a href="/categories/" rel="section"><i class="fa fa-th fa-fw"></i>分类</a></li><li class="menu-item menu-item-archives"><a href="/archives/" rel="section"><i class="fa fa-archive fa-fw"></i>归档</a></li>
+      <li class="menu-item menu-item-search">
+        <a role="button" class="popup-trigger"><i class="fa fa-search fa-fw"></i>搜索
+        </a>
+      </li>
+  </ul>
+</nav>
 
 
 
+  <div class="search-pop-overlay">
+    <div class="popup search-popup"><div class="search-header">
+  <span class="search-icon">
+    <i class="fa fa-search"></i>
+  </span>
+  <div class="search-input-container">
+    <input autocomplete="off" autocapitalize="off" maxlength="80"
+           placeholder="搜索..." spellcheck="false"
+           type="search" class="search-input">
+  </div>
+  <span class="popup-btn-close" role="button">
+    <i class="fa fa-times-circle"></i>
+  </span>
+</div>
+<div class="search-result-container no-result">
+  <div class="search-result-icon">
+    <i class="fa fa-spinner fa-pulse fa-5x"></i>
+  </div>
+</div>
+
+    </div>
+  </div>
 
 </header>
         
@@ -106,6 +140,8 @@ <h1 class="site-title">ZigZagKmp's Blog</h1>
 
         <div class="site-overview-wrap sidebar-panel">
           <div class="site-author animated" itemprop="author" itemscope itemtype="http://schema.org/Person">
+    <img class="site-author-image" itemprop="image" alt="ZigZagKmp"
+      src="/images/avatar/avatar.jpg">
   <p class="site-author-name" itemprop="name">ZigZagKmp</p>
   <div class="site-description" itemprop="description"></div>
 </div>
@@ -119,9 +155,21 @@ <h1 class="site-title">ZigZagKmp's Blog</h1>
       </div>
   </nav>
 </div>
+  <div class="links-of-author animated">
+      <span class="links-of-author-item">
+        <a href="https://github.com/ZigZagKmp" title="GitHub → https:&#x2F;&#x2F;github.com&#x2F;ZigZagKmp" rel="noopener me" target="_blank"><i class="fab fa-github fa-fw"></i>GitHub</a>
+      </span>
+      <span class="links-of-author-item">
+        <a href="mailto:zigzagkmp@qq.com" title="E-Mail → mailto:zigzagkmp@qq.com" rel="noopener me" target="_blank"><i class="fa fa-envelope fa-fw"></i>E-Mail</a>
+      </span>
+  </div>
 
         </div>
       </div>
+        <div class="back-to-top animated" role="button" aria-label="返回顶部">
+          <i class="fa fa-arrow-up"></i>
+          <span>0%</span>
+        </div>
     </div>
 
     
@@ -208,6 +256,24 @@ <h1 class="site-title">ZigZagKmp's Blog</h1>
     </span>
     <span class="author" itemprop="copyrightHolder">ZigZagKmp</span>
   </div>
+<div class="busuanzi-count">
+    <span class="post-meta-item" id="busuanzi_container_site_uv">
+      <span class="post-meta-item-icon">
+        <i class="fa fa-user"></i>
+      </span>
+      <span class="site-uv" title="总访客量">
+        <span id="busuanzi_value_site_uv"></span>
+      </span>
+    </span>
+    <span class="post-meta-item" id="busuanzi_container_site_pv">
+      <span class="post-meta-item-icon">
+        <i class="fa fa-eye"></i>
+      </span>
+      <span class="site-pv" title="总访问量">
+        <span id="busuanzi_value_site_pv"></span>
+      </span>
+    </span>
+</div>
   <div class="powered-by">由 <a href="https://hexo.io/" rel="noopener" target="_blank">Hexo</a> & <a href="https://theme-next.js.org/" rel="noopener" target="_blank">NexT.Gemini</a> 强力驱动
   </div>
 
@@ -215,10 +281,9 @@ <h1 class="site-title">ZigZagKmp's Blog</h1>
   </footer>
 
   
-  <div class="back-to-top" role="button" aria-label="返回顶部">
-    <i class="fa fa-arrow-up fa-lg"></i>
-    <span>0%</span>
-  </div>
+  <div class="reading-progress-bar"></div>
+
+  <a href="https://github.com/ZigZagKmp" class="github-corner" title="在 GitHub 上关注我" aria-label="在 GitHub 上关注我" rel="noopener" target="_blank"><svg width="80" height="80" viewBox="0 0 250 250" aria-hidden="true"><path d="M0,0 L115,115 L130,115 L142,142 L250,250 L250,0 Z"></path><path d="M128.3,109.0 C113.8,99.7 119.0,89.6 119.0,89.6 C122.0,82.7 120.5,78.6 120.5,78.6 C119.2,72.0 123.4,76.3 123.4,76.3 C127.3,80.9 125.5,87.3 125.5,87.3 C122.9,97.6 130.6,101.9 134.4,103.2" fill="currentColor" style="transform-origin: 130px 106px;" class="octo-arm"></path><path d="M115.0,115.0 C114.9,115.1 118.7,116.5 119.8,115.4 L133.7,101.6 C136.9,99.2 139.9,98.4 142.2,98.6 C133.8,88.0 127.5,74.4 143.8,58.0 C148.5,53.4 154.0,51.2 159.7,51.0 C160.3,49.4 163.2,43.6 171.4,40.1 C171.4,40.1 176.1,42.5 178.8,56.2 C183.1,58.6 187.2,61.8 190.9,65.4 C194.5,69.0 197.7,73.2 200.1,77.6 C213.8,80.2 216.3,84.9 216.3,84.9 C212.7,93.1 206.9,96.0 205.4,96.6 C205.1,102.4 203.0,107.8 198.3,112.5 C181.9,128.9 168.3,122.5 157.7,114.1 C157.9,116.9 156.7,120.9 152.7,124.9 L141.0,136.5 C139.8,137.7 141.6,141.9 141.8,141.8 Z" fill="currentColor" class="octo-body"></path></svg></a>
 
 <noscript>
   <div class="noscript-warning">Theme NexT works best with JavaScript enabled</div>
@@ -229,7 +294,9 @@ <h1 class="site-title">ZigZagKmp's Blog</h1>
   <script src="https://cdnjs.cloudflare.com/ajax/libs/animejs/3.2.1/anime.min.js" integrity="sha256-XL2inqUJaslATFnHdJOi9GfQ60on8Wx1C2H8DYiN1xY=" crossorigin="anonymous"></script>
 <script src="/js/comments.js"></script><script src="/js/utils.js"></script><script src="/js/motion.js"></script><script src="/js/next-boot.js"></script>
 
-  
+  <script src="https://cdnjs.cloudflare.com/ajax/libs/hexo-generator-searchdb/1.4.1/search.js" integrity="sha256-1kfA5uHPf65M5cphT2dvymhkuyHPQp5A53EGZOnOLmc=" crossorigin="anonymous"></script>
+<script src="/js/third-party/search/local-search.js"></script>
+
 
 
 
@@ -237,8 +304,15 @@ <h1 class="site-title">ZigZagKmp's Blog</h1>
 
 
   
+  <script async src="https://busuanzi.ibruce.info/busuanzi/2.3/busuanzi.pure.mini.js"></script>
+
+
 
 
+  
+
+  <script class="next-config" data-name="enableMath" type="application/json">true</script><script class="next-config" data-name="mathjax" type="application/json">{"enable":true,"tags":"none","js":{"url":"https://cdnjs.cloudflare.com/ajax/libs/mathjax/3.2.2/es5/tex-mml-chtml.js","integrity":"sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI="}}</script>
+<script src="/js/third-party/math/mathjax.js"></script>
 
 
 
diff --git a/archives/index.html b/archives/index.html
index 991c24a..b5655c8 100755
--- a/archives/index.html
+++ b/archives/index.html
@@ -17,7 +17,7 @@
 <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.0/css/all.min.css" integrity="sha256-HtsXJanqjKTc8vVQjO4YMhiqFoXkfBsjBWcX91T1jr8=" crossorigin="anonymous">
   <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/animate.css/3.1.1/animate.min.css" integrity="sha256-PR7ttpcvz8qrF57fur/yAx1qXMFJeJFiA6pSzWi0OIE=" crossorigin="anonymous">
 
-<script class="next-config" data-name="main" type="application/json">{"hostname":"zigzagkmp.github.io","root":"/","images":"/images","scheme":"Gemini","darkmode":false,"version":"8.18.1","exturl":false,"sidebar":{"position":"left","display":"post","padding":18,"offset":12},"copycode":{"enable":false,"style":null},"fold":{"enable":false,"height":500},"bookmark":{"enable":false,"color":"#222","save":"auto"},"mediumzoom":false,"lazyload":false,"pangu":false,"comments":{"style":"tabs","active":null,"storage":true,"lazyload":false,"nav":null},"stickytabs":false,"motion":{"enable":true,"async":false,"transition":{"menu_item":"fadeInDown","post_block":"fadeIn","post_header":"fadeInDown","post_body":"fadeInDown","coll_header":"fadeInLeft","sidebar":"fadeInUp"}},"prism":false,"i18n":{"placeholder":"搜索...","empty":"没有找到任何搜索结果：${query}","hits_time":"找到 ${hits} 个搜索结果（用时 ${time} 毫秒）","hits":"找到 ${hits} 个搜索结果"}}</script><script src="/js/config.js"></script>
+<script class="next-config" data-name="main" type="application/json">{"hostname":"zigzagkmp.github.io","root":"/","images":"/images","scheme":"Gemini","darkmode":false,"version":"8.18.1","exturl":false,"sidebar":{"position":"left","display":"post","padding":18,"offset":12},"copycode":{"enable":true,"style":null},"fold":{"enable":true,"height":500},"bookmark":{"enable":false,"color":"#222","save":"auto"},"mediumzoom":false,"lazyload":false,"pangu":false,"comments":{"style":"tabs","active":null,"storage":true,"lazyload":false,"nav":null},"stickytabs":false,"motion":{"enable":true,"async":false,"transition":{"menu_item":"fadeInDown","post_block":"fadeIn","post_header":"fadeInDown","post_body":"fadeInDown","coll_header":"fadeInLeft","sidebar":"fadeInUp"}},"prism":false,"i18n":{"placeholder":"搜索...","empty":"没有找到任何搜索结果：${query}","hits_time":"找到 ${hits} 个搜索结果（用时 ${time} 毫秒）","hits":"找到 ${hits} 个搜索结果"},"path":"/search.xml","localsearch":{"enable":true,"trigger":"auto","top_n_per_article":1,"unescape":false,"preload":false}}</script><script src="/js/config.js"></script>
 
     <meta property="og:type" content="website">
 <meta property="og:title" content="ZigZagKmp&#39;s Blog">
@@ -58,6 +58,9 @@
       <header class="header" itemscope itemtype="http://schema.org/WPHeader"><div class="site-brand-container">
   <div class="site-nav-toggle">
     <div class="toggle" aria-label="切换导航栏" role="button">
+        <span class="toggle-line"></span>
+        <span class="toggle-line"></span>
+        <span class="toggle-line"></span>
     </div>
   </div>
 
@@ -73,15 +76,46 @@ <h1 class="site-title">ZigZagKmp's Blog</h1>
 
   <div class="site-nav-right">
     <div class="toggle popup-trigger" aria-label="搜索" role="button">
+        <i class="fa fa-search fa-fw fa-lg"></i>
     </div>
   </div>
 </div>
 
 
 
+<nav class="site-nav">
+  <ul class="main-menu menu"><li class="menu-item menu-item-home"><a href="/" rel="section"><i class="fa fa-home fa-fw"></i>首页</a></li><li class="menu-item menu-item-about"><a href="/about/" rel="section"><i class="fa fa-user fa-fw"></i>关于</a></li><li class="menu-item menu-item-tags"><a href="/tags/" rel="section"><i class="fa fa-tags fa-fw"></i>标签</a></li><li class="menu-item menu-item-categories"><a href="/categories/" rel="section"><i class="fa fa-th fa-fw"></i>分类</a></li><li class="menu-item menu-item-archives"><a href="/archives/" rel="section"><i class="fa fa-archive fa-fw"></i>归档</a></li>
+      <li class="menu-item menu-item-search">
+        <a role="button" class="popup-trigger"><i class="fa fa-search fa-fw"></i>搜索
+        </a>
+      </li>
+  </ul>
+</nav>
 
 
 
+  <div class="search-pop-overlay">
+    <div class="popup search-popup"><div class="search-header">
+  <span class="search-icon">
+    <i class="fa fa-search"></i>
+  </span>
+  <div class="search-input-container">
+    <input autocomplete="off" autocapitalize="off" maxlength="80"
+           placeholder="搜索..." spellcheck="false"
+           type="search" class="search-input">
+  </div>
+  <span class="popup-btn-close" role="button">
+    <i class="fa fa-times-circle"></i>
+  </span>
+</div>
+<div class="search-result-container no-result">
+  <div class="search-result-icon">
+    <i class="fa fa-spinner fa-pulse fa-5x"></i>
+  </div>
+</div>
+
+    </div>
+  </div>
 
 </header>
         
@@ -106,6 +140,8 @@ <h1 class="site-title">ZigZagKmp's Blog</h1>
 
         <div class="site-overview-wrap sidebar-panel">
           <div class="site-author animated" itemprop="author" itemscope itemtype="http://schema.org/Person">
+    <img class="site-author-image" itemprop="image" alt="ZigZagKmp"
+      src="/images/avatar/avatar.jpg">
   <p class="site-author-name" itemprop="name">ZigZagKmp</p>
   <div class="site-description" itemprop="description"></div>
 </div>
@@ -119,9 +155,21 @@ <h1 class="site-title">ZigZagKmp's Blog</h1>
       </div>
   </nav>
 </div>
+  <div class="links-of-author animated">
+      <span class="links-of-author-item">
+        <a href="https://github.com/ZigZagKmp" title="GitHub → https:&#x2F;&#x2F;github.com&#x2F;ZigZagKmp" rel="noopener me" target="_blank"><i class="fab fa-github fa-fw"></i>GitHub</a>
+      </span>
+      <span class="links-of-author-item">
+        <a href="mailto:zigzagkmp@qq.com" title="E-Mail → mailto:zigzagkmp@qq.com" rel="noopener me" target="_blank"><i class="fa fa-envelope fa-fw"></i>E-Mail</a>
+      </span>
+  </div>
 
         </div>
       </div>
+        <div class="back-to-top animated" role="button" aria-label="返回顶部">
+          <i class="fa fa-arrow-up"></i>
+          <span>0%</span>
+        </div>
     </div>
 
     
@@ -208,6 +256,24 @@ <h1 class="site-title">ZigZagKmp's Blog</h1>
     </span>
     <span class="author" itemprop="copyrightHolder">ZigZagKmp</span>
   </div>
+<div class="busuanzi-count">
+    <span class="post-meta-item" id="busuanzi_container_site_uv">
+      <span class="post-meta-item-icon">
+        <i class="fa fa-user"></i>
+      </span>
+      <span class="site-uv" title="总访客量">
+        <span id="busuanzi_value_site_uv"></span>
+      </span>
+    </span>
+    <span class="post-meta-item" id="busuanzi_container_site_pv">
+      <span class="post-meta-item-icon">
+        <i class="fa fa-eye"></i>
+      </span>
+      <span class="site-pv" title="总访问量">
+        <span id="busuanzi_value_site_pv"></span>
+      </span>
+    </span>
+</div>
   <div class="powered-by">由 <a href="https://hexo.io/" rel="noopener" target="_blank">Hexo</a> & <a href="https://theme-next.js.org/" rel="noopener" target="_blank">NexT.Gemini</a> 强力驱动
   </div>
 
@@ -215,10 +281,9 @@ <h1 class="site-title">ZigZagKmp's Blog</h1>
   </footer>
 
   
-  <div class="back-to-top" role="button" aria-label="返回顶部">
-    <i class="fa fa-arrow-up fa-lg"></i>
-    <span>0%</span>
-  </div>
+  <div class="reading-progress-bar"></div>
+
+  <a href="https://github.com/ZigZagKmp" class="github-corner" title="在 GitHub 上关注我" aria-label="在 GitHub 上关注我" rel="noopener" target="_blank"><svg width="80" height="80" viewBox="0 0 250 250" aria-hidden="true"><path d="M0,0 L115,115 L130,115 L142,142 L250,250 L250,0 Z"></path><path d="M128.3,109.0 C113.8,99.7 119.0,89.6 119.0,89.6 C122.0,82.7 120.5,78.6 120.5,78.6 C119.2,72.0 123.4,76.3 123.4,76.3 C127.3,80.9 125.5,87.3 125.5,87.3 C122.9,97.6 130.6,101.9 134.4,103.2" fill="currentColor" style="transform-origin: 130px 106px;" class="octo-arm"></path><path d="M115.0,115.0 C114.9,115.1 118.7,116.5 119.8,115.4 L133.7,101.6 C136.9,99.2 139.9,98.4 142.2,98.6 C133.8,88.0 127.5,74.4 143.8,58.0 C148.5,53.4 154.0,51.2 159.7,51.0 C160.3,49.4 163.2,43.6 171.4,40.1 C171.4,40.1 176.1,42.5 178.8,56.2 C183.1,58.6 187.2,61.8 190.9,65.4 C194.5,69.0 197.7,73.2 200.1,77.6 C213.8,80.2 216.3,84.9 216.3,84.9 C212.7,93.1 206.9,96.0 205.4,96.6 C205.1,102.4 203.0,107.8 198.3,112.5 C181.9,128.9 168.3,122.5 157.7,114.1 C157.9,116.9 156.7,120.9 152.7,124.9 L141.0,136.5 C139.8,137.7 141.6,141.9 141.8,141.8 Z" fill="currentColor" class="octo-body"></path></svg></a>
 
 <noscript>
   <div class="noscript-warning">Theme NexT works best with JavaScript enabled</div>
@@ -229,7 +294,9 @@ <h1 class="site-title">ZigZagKmp's Blog</h1>
   <script src="https://cdnjs.cloudflare.com/ajax/libs/animejs/3.2.1/anime.min.js" integrity="sha256-XL2inqUJaslATFnHdJOi9GfQ60on8Wx1C2H8DYiN1xY=" crossorigin="anonymous"></script>
 <script src="/js/comments.js"></script><script src="/js/utils.js"></script><script src="/js/motion.js"></script><script src="/js/next-boot.js"></script>
 
-  
+  <script src="https://cdnjs.cloudflare.com/ajax/libs/hexo-generator-searchdb/1.4.1/search.js" integrity="sha256-1kfA5uHPf65M5cphT2dvymhkuyHPQp5A53EGZOnOLmc=" crossorigin="anonymous"></script>
+<script src="/js/third-party/search/local-search.js"></script>
+
 
 
 
@@ -237,8 +304,15 @@ <h1 class="site-title">ZigZagKmp's Blog</h1>
 
 
   
+  <script async src="https://busuanzi.ibruce.info/busuanzi/2.3/busuanzi.pure.mini.js"></script>
+
+
 
 
+  
+
+  <script class="next-config" data-name="enableMath" type="application/json">true</script><script class="next-config" data-name="mathjax" type="application/json">{"enable":true,"tags":"none","js":{"url":"https://cdnjs.cloudflare.com/ajax/libs/mathjax/3.2.2/es5/tex-mml-chtml.js","integrity":"sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI="}}</script>
+<script src="/js/third-party/math/mathjax.js"></script>
 
 
 
diff --git a/categories/index.html b/categories/index.html
index 1d40721..ee87652 100755
--- a/categories/index.html
+++ b/categories/index.html
@@ -17,7 +17,7 @@
 <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.0/css/all.min.css" integrity="sha256-HtsXJanqjKTc8vVQjO4YMhiqFoXkfBsjBWcX91T1jr8=" crossorigin="anonymous">
   <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/animate.css/3.1.1/animate.min.css" integrity="sha256-PR7ttpcvz8qrF57fur/yAx1qXMFJeJFiA6pSzWi0OIE=" crossorigin="anonymous">
 
-<script class="next-config" data-name="main" type="application/json">{"hostname":"zigzagkmp.github.io","root":"/","images":"/images","scheme":"Gemini","darkmode":false,"version":"8.18.1","exturl":false,"sidebar":{"position":"left","display":"post","padding":18,"offset":12},"copycode":{"enable":false,"style":null},"fold":{"enable":false,"height":500},"bookmark":{"enable":false,"color":"#222","save":"auto"},"mediumzoom":false,"lazyload":false,"pangu":false,"comments":{"style":"tabs","active":null,"storage":true,"lazyload":false,"nav":null},"stickytabs":false,"motion":{"enable":true,"async":false,"transition":{"menu_item":"fadeInDown","post_block":"fadeIn","post_header":"fadeInDown","post_body":"fadeInDown","coll_header":"fadeInLeft","sidebar":"fadeInUp"}},"prism":false,"i18n":{"placeholder":"搜索...","empty":"没有找到任何搜索结果：${query}","hits_time":"找到 ${hits} 个搜索结果（用时 ${time} 毫秒）","hits":"找到 ${hits} 个搜索结果"}}</script><script src="/js/config.js"></script>
+<script class="next-config" data-name="main" type="application/json">{"hostname":"zigzagkmp.github.io","root":"/","images":"/images","scheme":"Gemini","darkmode":false,"version":"8.18.1","exturl":false,"sidebar":{"position":"left","display":"post","padding":18,"offset":12},"copycode":{"enable":true,"style":null},"fold":{"enable":true,"height":500},"bookmark":{"enable":false,"color":"#222","save":"auto"},"mediumzoom":false,"lazyload":false,"pangu":false,"comments":{"style":"tabs","active":null,"storage":true,"lazyload":false,"nav":null},"stickytabs":false,"motion":{"enable":true,"async":false,"transition":{"menu_item":"fadeInDown","post_block":"fadeIn","post_header":"fadeInDown","post_body":"fadeInDown","coll_header":"fadeInLeft","sidebar":"fadeInUp"}},"prism":false,"i18n":{"placeholder":"搜索...","empty":"没有找到任何搜索结果：${query}","hits_time":"找到 ${hits} 个搜索结果（用时 ${time} 毫秒）","hits":"找到 ${hits} 个搜索结果"},"path":"/search.xml","localsearch":{"enable":true,"trigger":"auto","top_n_per_article":1,"unescape":false,"preload":false}}</script><script src="/js/config.js"></script>
 
     <meta property="og:type" content="website">
 <meta property="og:title" content="categories">
@@ -61,6 +61,9 @@
       <header class="header" itemscope itemtype="http://schema.org/WPHeader"><div class="site-brand-container">
   <div class="site-nav-toggle">
     <div class="toggle" aria-label="切换导航栏" role="button">
+        <span class="toggle-line"></span>
+        <span class="toggle-line"></span>
+        <span class="toggle-line"></span>
     </div>
   </div>
 
@@ -76,15 +79,46 @@
 
   <div class="site-nav-right">
     <div class="toggle popup-trigger" aria-label="搜索" role="button">
+        <i class="fa fa-search fa-fw fa-lg"></i>
     </div>
   </div>
 </div>
 
 
 
+<nav class="site-nav">
+  <ul class="main-menu menu"><li class="menu-item menu-item-home"><a href="/" rel="section"><i class="fa fa-home fa-fw"></i>首页</a></li><li class="menu-item menu-item-about"><a href="/about/" rel="section"><i class="fa fa-user fa-fw"></i>关于</a></li><li class="menu-item menu-item-tags"><a href="/tags/" rel="section"><i class="fa fa-tags fa-fw"></i>标签</a></li><li class="menu-item menu-item-categories"><a href="/categories/" rel="section"><i class="fa fa-th fa-fw"></i>分类</a></li><li class="menu-item menu-item-archives"><a href="/archives/" rel="section"><i class="fa fa-archive fa-fw"></i>归档</a></li>
+      <li class="menu-item menu-item-search">
+        <a role="button" class="popup-trigger"><i class="fa fa-search fa-fw"></i>搜索
+        </a>
+      </li>
+  </ul>
+</nav>
 
 
 
+  <div class="search-pop-overlay">
+    <div class="popup search-popup"><div class="search-header">
+  <span class="search-icon">
+    <i class="fa fa-search"></i>
+  </span>
+  <div class="search-input-container">
+    <input autocomplete="off" autocapitalize="off" maxlength="80"
+           placeholder="搜索..." spellcheck="false"
+           type="search" class="search-input">
+  </div>
+  <span class="popup-btn-close" role="button">
+    <i class="fa fa-times-circle"></i>
+  </span>
+</div>
+<div class="search-result-container no-result">
+  <div class="search-result-icon">
+    <i class="fa fa-spinner fa-pulse fa-5x"></i>
+  </div>
+</div>
+
+    </div>
+  </div>
 
 </header>
         
@@ -109,6 +143,8 @@
 
         <div class="site-overview-wrap sidebar-panel">
           <div class="site-author animated" itemprop="author" itemscope itemtype="http://schema.org/Person">
+    <img class="site-author-image" itemprop="image" alt="ZigZagKmp"
+      src="/images/avatar/avatar.jpg">
   <p class="site-author-name" itemprop="name">ZigZagKmp</p>
   <div class="site-description" itemprop="description"></div>
 </div>
@@ -122,9 +158,21 @@
       </div>
   </nav>
 </div>
+  <div class="links-of-author animated">
+      <span class="links-of-author-item">
+        <a href="https://github.com/ZigZagKmp" title="GitHub → https:&#x2F;&#x2F;github.com&#x2F;ZigZagKmp" rel="noopener me" target="_blank"><i class="fab fa-github fa-fw"></i>GitHub</a>
+      </span>
+      <span class="links-of-author-item">
+        <a href="mailto:zigzagkmp@qq.com" title="E-Mail → mailto:zigzagkmp@qq.com" rel="noopener me" target="_blank"><i class="fa fa-envelope fa-fw"></i>E-Mail</a>
+      </span>
+  </div>
 
         </div>
       </div>
+        <div class="back-to-top animated" role="button" aria-label="返回顶部">
+          <i class="fa fa-arrow-up"></i>
+          <span>0%</span>
+        </div>
     </div>
 
     
@@ -177,6 +225,24 @@ <h1 class="post-title" itemprop="name headline">categories
     </span>
     <span class="author" itemprop="copyrightHolder">ZigZagKmp</span>
   </div>
+<div class="busuanzi-count">
+    <span class="post-meta-item" id="busuanzi_container_site_uv">
+      <span class="post-meta-item-icon">
+        <i class="fa fa-user"></i>
+      </span>
+      <span class="site-uv" title="总访客量">
+        <span id="busuanzi_value_site_uv"></span>
+      </span>
+    </span>
+    <span class="post-meta-item" id="busuanzi_container_site_pv">
+      <span class="post-meta-item-icon">
+        <i class="fa fa-eye"></i>
+      </span>
+      <span class="site-pv" title="总访问量">
+        <span id="busuanzi_value_site_pv"></span>
+      </span>
+    </span>
+</div>
   <div class="powered-by">由 <a href="https://hexo.io/" rel="noopener" target="_blank">Hexo</a> & <a href="https://theme-next.js.org/" rel="noopener" target="_blank">NexT.Gemini</a> 强力驱动
   </div>
 
@@ -184,10 +250,9 @@ <h1 class="post-title" itemprop="name headline">categories
   </footer>
 
   
-  <div class="back-to-top" role="button" aria-label="返回顶部">
-    <i class="fa fa-arrow-up fa-lg"></i>
-    <span>0%</span>
-  </div>
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 </body>
diff --git a/search.xml b/search.xml
new file mode 100755
index 0000000..b1d47f5
--- /dev/null
+++ b/search.xml
@@ -0,0 +1,161 @@
+<?xml version="1.0" encoding="utf-8"?>
+<search>
+  <entry>
+    <title>Algorithm Design Note 1</title>
+    <url>/2023/10/05/Algorithm-Design-Note-1/</url>
+    <content><![CDATA[<h2 id="Chapter-0-Logistics"><a href="#Chapter-0-Logistics" class="headerlink" title="Chapter 0 Logistics"></a>Chapter 0 Logistics</h2><p><strong>Content</strong> : discrete(combinatorial) algorithm  ,  Theoretical </p>
+<ul>
+<li>[minority] Complexity , NP-Completeness</li>
+<li>Basic Graph Algorithm , DFS / BFS</li>
+<li>Greedy</li>
+<li>Dynamic Programming</li>
+<li>Divide and Conquer</li>
+<li>NP-completeness Theory</li>
+<li>Approximation Algorithm</li>
+<li>Randomized Algorithm (Probability Analysis)</li>
+<li><ul>
+<li>Computational Geometry</li>
+</ul>
+</li>
+<li><ul>
+<li>Streaming Algorithm (online)</li>
+</ul>
+</li>
+</ul>
+<p><strong>Textbook</strong> : [Kleinberg&amp;Tardos] Algorithm Design </p>
+<p><strong>Reference Book</strong> : [CLRS] Intro to Algorithm</p>
+<h2 id="Chapter-1"><a href="#Chapter-1" class="headerlink" title="Chapter 1"></a>Chapter 1</h2><h3 id="1-1-Stable-matching"><a href="#1-1-Stable-matching" class="headerlink" title="1.1 Stable matching"></a>1.1 Stable matching</h3><ol>
+<li><p>Def</p>
+<ul>
+<li><p>Input : $boys=\{B_1,\cdots,B_n\} , girls=\{G_1,\cdots,G_n\}$</p>
+<p>Preference List : $BP_i$ : a permutation of $girls$ , $GP_i$ : a permutation of $boys$</p>
+</li>
+<li><p>output : a stable matching </p>
+</li>
+<li><p>stable matching : no unstable pairs</p>
+</li>
+<li><p>unstable pair : $(B_i,G_j)$ s.t.  $M(B_i)$ after $G_j$ in $BP_i$ and $M(G_j)$ after $B_i$ in $GP_j$</p>
+</li>
+</ul>
+</li>
+<li><p>Efficient Algorithm : Gale &amp; Shapley Algorithm ( propose-reject )</p>
+<figure class="highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="keyword">while</span>( exists sb. single )&#123;</span><br><span class="line">    A &lt;- an arbitrary single boy</span><br><span class="line">    X &lt;- <span class="function">first girl A has <span class="keyword">not</span> proposed yet</span></span><br><span class="line"><span class="function">    <span class="title">if</span> <span class="params">( X is single )</span></span></span><br><span class="line"><span class="function">        A-X engage</span></span><br><span class="line"><span class="function">    <span class="keyword">else</span></span></span><br><span class="line"><span class="function">        <span class="title">if</span> <span class="params">( A is better than M(X) )</span></span></span><br><span class="line"><span class="function">            A-X engage</span></span><br><span class="line"><span class="function">        <span class="keyword">else</span></span></span><br><span class="line"><span class="function">            X reject A</span></span><br><span class="line"><span class="function">&#125;</span></span><br></pre></td></tr></table></figure>
+</li>
+<li><p>Analysis</p>
+<ol>
+<li><p>Proof of Termination </p>
+<ol>
+<li>For girl : once engaged , engaged forever </li>
+<li>For one boy : If used all preference list : then all girls must be engaged</li>
+</ol>
+</li>
+<li><p>Proof of Correctness</p>
+<p>Prove by Contradiction</p>
+<p>$(B_i,G_j)$ : an unstable pair</p>
+<p>$B_i$ preference list : $\cdots G_j \cdots M(B_i)$</p>
+<p>$G_j$ preference list : $\cdots B_i \cdots Z=M(G_j)$</p>
+<p>$\therefore$ $G_j$ rejected $B_i$ , but $G_j$ should not reject $B_i$ compared with $Z$</p>
+</li>
+<li><p>Running Time : $\mathcal O(n^2)$ ( All boys used up their preference list)</p>
+</li>
+</ol>
+</li>
+<li><p>Random ver.</p>
+<ol>
+<li><p>def : $BP_i$ , $GP_i$ are all random permutations (uniformly distributed) </p>
+</li>
+<li><p>How to get a uniformly distributed random permutation ?</p>
+<p>draw-likely process</p>
+</li>
+<li><p>THM : $\mathbb E[T]\le n\cdot H_n$  ($\mathbb E[T]=\mathcal O(n\log n)$)</p>
+</li>
+<li><p>Proof </p>
+<ol>
+<li><p>key observation : </p>
+<p>G-S’ : each time a boy propose to a random girl not proposed yet</p>
+<p><strong>This is equivalent as generate a uniformly distributed random permutation</strong></p>
+<p>G-S’’ : each time a boy propose to a random girl (can be proposed yet)</p>
+<p>$\therefore $ $T(G-S)=T(G-S’)\le T(G-S’’)$</p>
+</li>
+<li><p>Coupon Collector Problem ( Bins-Balls ) </p>
+<p>$n$ bins , each time throw a ball to a random bin . </p>
+<p>Q : $\mathbb E[\text{balls}]$ s.t. every bin is nonempty .</p>
+<p>A : $\mathbb E[\text{balls}]=n\cdot H_n$</p>
+<p>Construct Sequence $a_i\in \{0,1\}$ , $a_i=1\Leftrightarrow$ a ball falls in an empty bin</p>
+<p>Exactly $n$ number of $1$s . -&gt; $n$ segments like $0\cdots 01$</p>
+<script type="math/tex; mode=display">
+\begin{aligned}
+\mathbb E[T]&=\mathbb E\left[\sum_{i=1}^n \text{len of i-th segment}\right]\\
+&=\sum_{i=1}^n\mathbb E\left[ \text{len of i-th segment}\right]\\
+&=\sum_{i=1}^n \frac{1}{\Pr\{\text{in i-th seg , choosed empty bin}\}}\\
+&=\sum_{i=1}^n \frac{n}{n-i+1}\\
+&=n\cdot H_n
+\end{aligned}</script></li>
+<li><p>Consider boy -&gt; ball , girl -&gt; bin</p>
+<p>G-S’’ -&gt; Bins-Balls Problem</p>
+</li>
+<li><ul>
+<li><p>Concentration inequality for Coupon Collection Running Time</p>
+<p>Same as Chernoff Bound</p>
+</li>
+</ul>
+</li>
+</ol>
+</li>
+</ol>
+</li>
+</ol>
+<h3 id="1-2-BFS-amp-DFS"><a href="#1-2-BFS-amp-DFS" class="headerlink" title="1.2 BFS &amp; DFS"></a>1.2 BFS &amp; DFS</h3><ol>
+<li><p>BFS</p>
+<figure class="highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="comment">// bfs</span></span><br><span class="line">q.<span class="built_in">clear</span>();</span><br><span class="line"><span class="keyword">for</span>(u in Vertices)&#123;</span><br><span class="line">    dep[u]=inf;</span><br><span class="line">    prev[u]=<span class="literal">NULL</span>;</span><br><span class="line">    col[u]=white;</span><br><span class="line">&#125;</span><br><span class="line"></span><br><span class="line">dep[s]=<span class="number">0</span>;</span><br><span class="line">prev[s]=<span class="literal">NULL</span>;</span><br><span class="line">col[s]=grey;</span><br><span class="line">q.<span class="built_in">push</span>(s);</span><br><span class="line"></span><br><span class="line"><span class="keyword">while</span>(!q.<span class="built_in">empty</span>())&#123;</span><br><span class="line">    u=q.<span class="built_in">front</span>();q.<span class="built_in">pop</span>();</span><br><span class="line">    <span class="keyword">for</span>(v in <span class="built_in">Neighbour</span>(u) )&#123;</span><br><span class="line">        <span class="keyword">if</span>(col[v]==white)&#123;</span><br><span class="line">            dep[v]=dep[u]+<span class="number">1</span>;</span><br><span class="line">            prev[v]=u;</span><br><span class="line">            col[v]=grey;</span><br><span class="line">            q.<span class="built_in">push</span>(v);</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line">    col[v]=black;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
+<p>BFS Tree Property : no edges with depth difference $\ge 2$ .</p>
+</li>
+<li><p>DFS</p>
+<figure class="highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="function">function <span class="title">dfs</span><span class="params">(u)</span></span>&#123;</span><br><span class="line">    ++time;</span><br><span class="line">    discover[u]=time;</span><br><span class="line">    col[u]=grey;</span><br><span class="line">    <span class="keyword">for</span>(v in <span class="built_in">Neighbour</span>(u) )&#123;</span><br><span class="line">        <span class="keyword">if</span>(col[v]==white)&#123;</span><br><span class="line">            <span class="built_in">dfs</span>(v)</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line">    col[u]=black;</span><br><span class="line">    ++time;</span><br><span class="line">    finish[u]=time;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
+<p>DFS Tree Properties</p>
+<p>Time stamp intervals</p>
+<ol>
+<li>non-crossing : only non-intersect / totally include</li>
+<li>Tree Structure $\Leftrightarrow$ Time stamp intervals Structure </li>
+</ol>
+</li>
+<li><p>Connectivity</p>
+<ol>
+<li><p>undirected graph : connected component</p>
+</li>
+<li><p>directed graph : strongly connected component (SCC)</p>
+<p>every vertex can reach other vertex</p>
+</li>
+<li><p>directed acyclic graph (DAG)</p>
+<p>i.e. no directed cycle</p>
+<p>i.e. no SCC has $\ge 2$ vertices</p>
+<ul>
+<li>DAG has a topological order</li>
+</ul>
+</li>
+<li><p>A useful view of directed graph : a DAG of SCC</p>
+<p>a.k.a. 缩点</p>
+</li>
+<li><p>DAG has a topological order</p>
+<p>get topological order : use bfs/dfs starting from $in_deg=0$ </p>
+</li>
+</ol>
+</li>
+</ol>
+]]></content>
+  </entry>
+  <entry>
+    <title>Hello World</title>
+    <url>/2023/10/05/hello-world/</url>
+    <content><![CDATA[<p>Welcome to <a href="https://hexo.io/">Hexo</a>! This is your very first post. Check <a href="https://hexo.io/docs/">documentation</a> for more info. If you get any problems when using Hexo, you can find the answer in <a href="https://hexo.io/docs/troubleshooting.html">troubleshooting</a> or you can ask me on <a href="https://github.com/hexojs/hexo/issues">GitHub</a>.</p>
+<h2 id="Quick-Start"><a href="#Quick-Start" class="headerlink" title="Quick Start"></a>Quick Start</h2><h3 id="Create-a-new-post"><a href="#Create-a-new-post" class="headerlink" title="Create a new post"></a>Create a new post</h3><figure class="highlight bash"><table><tr><td class="code"><pre><span class="line">$ hexo new <span class="string">&quot;My New Post&quot;</span></span><br></pre></td></tr></table></figure>
+<p>More info: <a href="https://hexo.io/docs/writing.html">Writing</a></p>
+<h3 id="Run-server"><a href="#Run-server" class="headerlink" title="Run server"></a>Run server</h3><figure class="highlight bash"><table><tr><td class="code"><pre><span class="line">$ hexo server</span><br></pre></td></tr></table></figure>
+<p>More info: <a href="https://hexo.io/docs/server.html">Server</a></p>
+<h3 id="Generate-static-files"><a href="#Generate-static-files" class="headerlink" title="Generate static files"></a>Generate static files</h3><figure class="highlight bash"><table><tr><td class="code"><pre><span class="line">$ hexo generate</span><br></pre></td></tr></table></figure>
+<p>More info: <a href="https://hexo.io/docs/generating.html">Generating</a></p>
+<h3 id="Deploy-to-remote-sites"><a href="#Deploy-to-remote-sites" class="headerlink" title="Deploy to remote sites"></a>Deploy to remote sites</h3><figure class="highlight bash"><table><tr><td class="code"><pre><span class="line">$ hexo deploy</span><br></pre></td></tr></table></figure>
+<p>More info: <a href="https://hexo.io/docs/one-command-deployment.html">Deployment</a></p>
+]]></content>
+  </entry>
+</search>
diff --git a/tags/index.html b/tags/index.html
index 1736a70..948f0fb 100755
--- a/tags/index.html
+++ b/tags/index.html
@@ -17,7 +17,7 @@
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+<script class="next-config" data-name="main" type="application/json">{"hostname":"zigzagkmp.github.io","root":"/","images":"/images","scheme":"Gemini","darkmode":false,"version":"8.18.1","exturl":false,"sidebar":{"position":"left","display":"post","padding":18,"offset":12},"copycode":{"enable":true,"style":null},"fold":{"enable":true,"height":500},"bookmark":{"enable":false,"color":"#222","save":"auto"},"mediumzoom":false,"lazyload":false,"pangu":false,"comments":{"style":"tabs","active":null,"storage":true,"lazyload":false,"nav":null},"stickytabs":false,"motion":{"enable":true,"async":false,"transition":{"menu_item":"fadeInDown","post_block":"fadeIn","post_header":"fadeInDown","post_body":"fadeInDown","coll_header":"fadeInLeft","sidebar":"fadeInUp"}},"prism":false,"i18n":{"placeholder":"搜索...","empty":"没有找到任何搜索结果：${query}","hits_time":"找到 ${hits} 个搜索结果（用时 ${time} 毫秒）","hits":"找到 ${hits} 个搜索结果"},"path":"/search.xml","localsearch":{"enable":true,"trigger":"auto","top_n_per_article":1,"unescape":false,"preload":false}}</script><script src="/js/config.js"></script>
 
     <meta property="og:type" content="website">
 <meta property="og:title" content="tags">
@@ -61,6 +61,9 @@
       <header class="header" itemscope itemtype="http://schema.org/WPHeader"><div class="site-brand-container">
   <div class="site-nav-toggle">
     <div class="toggle" aria-label="切换导航栏" role="button">
+        <span class="toggle-line"></span>
+        <span class="toggle-line"></span>
+        <span class="toggle-line"></span>
     </div>
   </div>
 
@@ -76,15 +79,46 @@
 
   <div class="site-nav-right">
     <div class="toggle popup-trigger" aria-label="搜索" role="button">
+        <i class="fa fa-search fa-fw fa-lg"></i>
     </div>
   </div>
 </div>
 
 
 
+<nav class="site-nav">
+  <ul class="main-menu menu"><li class="menu-item menu-item-home"><a href="/" rel="section"><i class="fa fa-home fa-fw"></i>首页</a></li><li class="menu-item menu-item-about"><a href="/about/" rel="section"><i class="fa fa-user fa-fw"></i>关于</a></li><li class="menu-item menu-item-tags"><a href="/tags/" rel="section"><i class="fa fa-tags fa-fw"></i>标签</a></li><li class="menu-item menu-item-categories"><a href="/categories/" rel="section"><i class="fa fa-th fa-fw"></i>分类</a></li><li class="menu-item menu-item-archives"><a href="/archives/" rel="section"><i class="fa fa-archive fa-fw"></i>归档</a></li>
+      <li class="menu-item menu-item-search">
+        <a role="button" class="popup-trigger"><i class="fa fa-search fa-fw"></i>搜索
+        </a>
+      </li>
+  </ul>
+</nav>
 
 
 
+  <div class="search-pop-overlay">
+    <div class="popup search-popup"><div class="search-header">
+  <span class="search-icon">
+    <i class="fa fa-search"></i>
+  </span>
+  <div class="search-input-container">
+    <input autocomplete="off" autocapitalize="off" maxlength="80"
+           placeholder="搜索..." spellcheck="false"
+           type="search" class="search-input">
+  </div>
+  <span class="popup-btn-close" role="button">
+    <i class="fa fa-times-circle"></i>
+  </span>
+</div>
+<div class="search-result-container no-result">
+  <div class="search-result-icon">
+    <i class="fa fa-spinner fa-pulse fa-5x"></i>
+  </div>
+</div>
+
+    </div>
+  </div>
 
 </header>
         
@@ -109,6 +143,8 @@
 
         <div class="site-overview-wrap sidebar-panel">
           <div class="site-author animated" itemprop="author" itemscope itemtype="http://schema.org/Person">
+    <img class="site-author-image" itemprop="image" alt="ZigZagKmp"
+      src="/images/avatar/avatar.jpg">
   <p class="site-author-name" itemprop="name">ZigZagKmp</p>
   <div class="site-description" itemprop="description"></div>
 </div>
@@ -122,9 +158,21 @@
       </div>
   </nav>
 </div>
+  <div class="links-of-author animated">
+      <span class="links-of-author-item">
+        <a href="https://github.com/ZigZagKmp" title="GitHub → https:&#x2F;&#x2F;github.com&#x2F;ZigZagKmp" rel="noopener me" target="_blank"><i class="fab fa-github fa-fw"></i>GitHub</a>
+      </span>
+      <span class="links-of-author-item">
+        <a href="mailto:zigzagkmp@qq.com" title="E-Mail → mailto:zigzagkmp@qq.com" rel="noopener me" target="_blank"><i class="fa fa-envelope fa-fw"></i>E-Mail</a>
+      </span>
+  </div>
 
         </div>
       </div>
+        <div class="back-to-top animated" role="button" aria-label="返回顶部">
+          <i class="fa fa-arrow-up"></i>
+          <span>0%</span>
+        </div>
     </div>
 
     
@@ -177,6 +225,24 @@ <h1 class="post-title" itemprop="name headline">tags
     </span>
     <span class="author" itemprop="copyrightHolder">ZigZagKmp</span>
   </div>
+<div class="busuanzi-count">
+    <span class="post-meta-item" id="busuanzi_container_site_uv">
+      <span class="post-meta-item-icon">
+        <i class="fa fa-user"></i>
+      </span>
+      <span class="site-uv" title="总访客量">
+        <span id="busuanzi_value_site_uv"></span>
+      </span>
+    </span>
+    <span class="post-meta-item" id="busuanzi_container_site_pv">
+      <span class="post-meta-item-icon">
+        <i class="fa fa-eye"></i>
+      </span>
+      <span class="site-pv" title="总访问量">
+        <span id="busuanzi_value_site_pv"></span>
+      </span>
+    </span>
+</div>
   <div class="powered-by">由 <a href="https://hexo.io/" rel="noopener" target="_blank">Hexo</a> & <a href="https://theme-next.js.org/" rel="noopener" target="_blank">NexT.Gemini</a> 强力驱动
   </div>
 
@@ -184,10 +250,9 @@ <h1 class="post-title" itemprop="name headline">tags
   </footer>
 
   
-  <div class="back-to-top" role="button" aria-label="返回顶部">
-    <i class="fa fa-arrow-up fa-lg"></i>
-    <span>0%</span>
-  </div>
+  <div class="reading-progress-bar"></div>
+
+  <a href="https://github.com/ZigZagKmp" class="github-corner" title="在 GitHub 上关注我" aria-label="在 GitHub 上关注我" rel="noopener" target="_blank"><svg width="80" height="80" viewBox="0 0 250 250" aria-hidden="true"><path d="M0,0 L115,115 L130,115 L142,142 L250,250 L250,0 Z"></path><path d="M128.3,109.0 C113.8,99.7 119.0,89.6 119.0,89.6 C122.0,82.7 120.5,78.6 120.5,78.6 C119.2,72.0 123.4,76.3 123.4,76.3 C127.3,80.9 125.5,87.3 125.5,87.3 C122.9,97.6 130.6,101.9 134.4,103.2" fill="currentColor" style="transform-origin: 130px 106px;" class="octo-arm"></path><path d="M115.0,115.0 C114.9,115.1 118.7,116.5 119.8,115.4 L133.7,101.6 C136.9,99.2 139.9,98.4 142.2,98.6 C133.8,88.0 127.5,74.4 143.8,58.0 C148.5,53.4 154.0,51.2 159.7,51.0 C160.3,49.4 163.2,43.6 171.4,40.1 C171.4,40.1 176.1,42.5 178.8,56.2 C183.1,58.6 187.2,61.8 190.9,65.4 C194.5,69.0 197.7,73.2 200.1,77.6 C213.8,80.2 216.3,84.9 216.3,84.9 C212.7,93.1 206.9,96.0 205.4,96.6 C205.1,102.4 203.0,107.8 198.3,112.5 C181.9,128.9 168.3,122.5 157.7,114.1 C157.9,116.9 156.7,120.9 152.7,124.9 L141.0,136.5 C139.8,137.7 141.6,141.9 141.8,141.8 Z" fill="currentColor" class="octo-body"></path></svg></a>
 
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   <div class="noscript-warning">Theme NexT works best with JavaScript enabled</div>
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 <script src="/js/comments.js"></script><script src="/js/utils.js"></script><script src="/js/motion.js"></script><script src="/js/next-boot.js"></script>
 
-  
+  <script src="https://cdnjs.cloudflare.com/ajax/libs/hexo-generator-searchdb/1.4.1/search.js" integrity="sha256-1kfA5uHPf65M5cphT2dvymhkuyHPQp5A53EGZOnOLmc=" crossorigin="anonymous"></script>
+<script src="/js/third-party/search/local-search.js"></script>
+
 
 
 
@@ -206,8 +273,15 @@ <h1 class="post-title" itemprop="name headline">tags
 
 
   
+  <script async src="https://busuanzi.ibruce.info/busuanzi/2.3/busuanzi.pure.mini.js"></script>
+
+
 
 
+  
+
+  <script class="next-config" data-name="enableMath" type="application/json">true</script><script class="next-config" data-name="mathjax" type="application/json">{"enable":true,"tags":"none","js":{"url":"https://cdnjs.cloudflare.com/ajax/libs/mathjax/3.2.2/es5/tex-mml-chtml.js","integrity":"sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI="}}</script>
+<script src="/js/third-party/math/mathjax.js"></script>