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content="/blog/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content="blog"></span><script type="text/javascript" src="/blog/js/md5.js"></script><script></script><script>document.oncopy=function(e){window.event&&(e=window.event);try{var t=e.srcElement;return"INPUT"==t.tagName&&"text"==t.type.toLowerCase()||"TEXTAREA"==t.tagName}catch(e){return!1}}</script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="schtonn"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/blog/posts/matrix-pow-ext/" class="post-title-link" itemprop="url">矩阵快速幂扩展应用</a></h2><div class="post-meta"><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-o"></i></span> <span class="post-meta-item-text">Posted on</span> <time title="Created: 2021-May-16 21:38:21" itemprop="dateCreated datePublished" datetime="2021-05-16T21:38:21+08:00">2021-May-16</time></span><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-check-o"></i></span> <span class="post-meta-item-text">Edited on</span> <time title="Modified: 2022-Oct-19 23:02:06" itemprop="dateModified" datetime="2022-10-19T23:02:06+08:00">2022-Oct-19</time></span></div></header><div class="post-body" itemprop="articleBody"><h2 id="前置知识">前置知识</h2><p><a href="/blog/posts/matrix-pow">矩阵快速幂</a>，聪明的头脑。</p><h2 id="引入">引入</h2><p>这篇文章旨在记录丰富的矩阵快速幂应用。</p><div class="post-button"> <a class="btn" href="/blog/posts/matrix-pow-ext/#more" rel="contents">Read more &raquo;</a></div></div><footer class="post-footer"><div class="post-eof"></div></footer></article><article itemscope itemtype="http://schema.org/Article" class="post-block" lang="en"><link itemprop="mainEntityOfPage" href="https://schtonn.github.io/blog/posts/fermat/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/blog/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content="blog"></span><script type="text/javascript" src="/blog/js/md5.js"></script><script></script><script>document.oncopy=function(e){window.event&&(e=window.event);try{var t=e.srcElement;return"INPUT"==t.tagName&&"text"==t.type.toLowerCase()||"TEXTAREA"==t.tagName}catch(e){return!1}}</script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="schtonn"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/blog/posts/fermat/" class="post-title-link" itemprop="url">费马小定理</a></h2><div class="post-meta"><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-o"></i></span> <span class="post-meta-item-text">Posted on</span> <time title="Created: 2021-May-01 14:06:02" itemprop="dateCreated datePublished" datetime="2021-05-01T14:06:02+08:00">2021-May-01</time></span><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-check-o"></i></span> <span class="post-meta-item-text">Edited on</span> <time title="Modified: 2022-Oct-19 23:33:49" itemprop="dateModified" datetime="2022-10-19T23:33:49+08:00">2022-Oct-19</time></span></div></header><div class="post-body" itemprop="articleBody"><h2 id="前置知识">前置知识</h2><p>取模</p><h2 id="引入">引入</h2><p>对于 <span class="math inline">\(p\in\mathbb{P},a\in\mathbb{N}^+\)</span> 且 <span class="math inline">\((a,p)=1\)</span>，也就是 <span class="math inline">\(p\)</span> 为素数且正整数 <span class="math inline">\(a\)</span> 与 <span class="math inline">\(p\)</span> 互质，有： <span class="math display">\[a^{p-1}\equiv1\pmod p\]</span></p><div class="post-button"> <a class="btn" href="/blog/posts/fermat/#more" rel="contents">Read more &raquo;</a></div></div><footer class="post-footer"><div class="post-eof"></div></footer></article><article itemscope itemtype="http://schema.org/Article" class="post-block" lang="en"><link itemprop="mainEntityOfPage" href="https://schtonn.github.io/blog/posts/ac-auto/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/blog/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content="blog"></span><script type="text/javascript" src="/blog/js/md5.js"></script><script></script><script>document.oncopy=function(e){window.event&&(e=window.event);try{var t=e.srcElement;return"INPUT"==t.tagName&&"text"==t.type.toLowerCase()||"TEXTAREA"==t.tagName}catch(e){return!1}}</script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="schtonn"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/blog/posts/ac-auto/" class="post-title-link" itemprop="url">AC 自动机</a></h2><div class="post-meta"><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-o"></i></span> <span class="post-meta-item-text">Posted on</span> <time title="Created: 2021-Apr-22 21:11:50" itemprop="dateCreated datePublished" datetime="2021-04-22T21:11:50+08:00">2021-Apr-22</time></span><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-check-o"></i></span> <span class="post-meta-item-text">Edited on</span> <time title="Modified: 2022-Sep-24 21:31:03" itemprop="dateModified" datetime="2022-09-24T21:31:03+08:00">2022-Sep-24</time></span></div></header><div class="post-body" itemprop="articleBody"><h2 id="前置知识">前置知识</h2><p><a href="/blog/posts/KMP">KMP</a>，<a href="/blog/posts/trie">trie</a></p><h2 id="引入">引入</h2><p>往简单了说，AC自动机其实就是在字典树上搞KMP思想。它能够快速实现在一个文本串中匹配多个模式串。</p><div class="post-button"> <a class="btn" href="/blog/posts/ac-auto/#more" rel="contents">Read more &raquo;</a></div></div><footer class="post-footer"><div class="post-eof"></div></footer></article><article itemscope itemtype="http://schema.org/Article" class="post-block" lang="en"><link itemprop="mainEntityOfPage" href="https://schtonn.github.io/blog/posts/trie/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/blog/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content="blog"></span><script type="text/javascript" src="/blog/js/md5.js"></script><script></script><script>document.oncopy=function(e){window.event&&(e=window.event);try{var t=e.srcElement;return"INPUT"==t.tagName&&"text"==t.type.toLowerCase()||"TEXTAREA"==t.tagName}catch(e){return!1}}</script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="schtonn"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/blog/posts/trie/" class="post-title-link" itemprop="url">字典树</a></h2><div class="post-meta"><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-o"></i></span> <span class="post-meta-item-text">Posted on</span> <time title="Created: 2021-Apr-22 20:53:00" itemprop="dateCreated datePublished" datetime="2021-04-22T20:53:00+08:00">2021-Apr-22</time></span><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-check-o"></i></span> <span class="post-meta-item-text">Edited on</span> <time title="Modified: 2022-Sep-26 23:01:08" itemprop="dateModified" datetime="2022-09-26T23:01:08+08:00">2022-Sep-26</time></span></div></header><div class="post-body" itemprop="articleBody"><h3 id="前置知识">前置知识</h3><p>字符串，图论基础</p><h3 id="引入">引入</h3><p>trie-字典树，就是一棵可以拿来当字典用的树，它的思考和实现都非常简单。例如，<code>hello</code>，<code>her</code>，<code>hers</code>，<code>his</code> 生成的字典树如下：</p><div class="post-button"> <a class="btn" href="/blog/posts/trie/#more" rel="contents">Read more &raquo;</a></div></div><footer class="post-footer"><div class="post-eof"></div></footer></article><article itemscope itemtype="http://schema.org/Article" class="post-block" lang="en"><link itemprop="mainEntityOfPage" href="https://schtonn.github.io/blog/posts/fft/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/blog/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content="blog"></span><script type="text/javascript" src="/blog/js/md5.js"></script><script></script><script>document.oncopy=function(e){window.event&&(e=window.event);try{var t=e.srcElement;return"INPUT"==t.tagName&&"text"==t.type.toLowerCase()||"TEXTAREA"==t.tagName}catch(e){return!1}}</script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="schtonn"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/blog/posts/fft/" class="post-title-link" itemprop="url">FFT</a></h2><div class="post-meta"><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-o"></i></span> <span class="post-meta-item-text">Posted on</span> <time title="Created: 2021-Apr-18 20:09:52" itemprop="dateCreated datePublished" datetime="2021-04-18T20:09:52+08:00">2021-Apr-18</time></span><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-check-o"></i></span> <span class="post-meta-item-text">Edited on</span> <time title="Modified: 2022-Oct-19 23:02:06" itemprop="dateModified" datetime="2022-10-19T23:02:06+08:00">2022-Oct-19</time></span></div></header><div class="post-body" itemprop="articleBody"><h2 id="前置知识">前置知识</h2><p>复数域的运算，基础运算记号。</p><h2 id="引入">引入</h2><p>FFT-快速傅里叶变换是一种能够快速实现 DFT 和 IDFT 的算法，常用于快速求多项式相乘。</p><div class="post-button"> <a class="btn" href="/blog/posts/fft/#more" rel="contents">Read more &raquo;</a></div></div><footer class="post-footer"><div class="post-eof"></div></footer></article><article itemscope itemtype="http://schema.org/Article" class="post-block" lang="en"><link itemprop="mainEntityOfPage" href="https://schtonn.github.io/blog/posts/matrix-pow-complex/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/blog/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content="blog"></span><script type="text/javascript" src="/blog/js/md5.js"></script><script></script><script>document.oncopy=function(e){window.event&&(e=window.event);try{var t=e.srcElement;return"INPUT"==t.tagName&&"text"==t.type.toLowerCase()||"TEXTAREA"==t.tagName}catch(e){return!1}}</script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="schtonn"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/blog/posts/matrix-pow-complex/" class="post-title-link" itemprop="url">复杂矩阵快速幂</a></h2><div class="post-meta"><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-o"></i></span> <span class="post-meta-item-text">Posted on</span> <time title="Created: 2021-Apr-13 22:29:35" itemprop="dateCreated datePublished" datetime="2021-04-13T22:29:35+08:00">2021-Apr-13</time></span><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-check-o"></i></span> <span class="post-meta-item-text">Edited on</span> <time title="Modified: 2022-Oct-19 23:02:06" itemprop="dateModified" datetime="2022-10-19T23:02:06+08:00">2022-Oct-19</time></span></div></header><div class="post-body" itemprop="articleBody"><h2 id="前置知识">前置知识</h2><p><a href="/blog/posts/matrix-pow">矩阵快速幂</a>。这是一点比较复杂的应用。</p><div class="post-button"> <a class="btn" href="/blog/posts/matrix-pow-complex/#more" rel="contents">Read more &raquo;</a></div></div><footer class="post-footer"><div class="post-eof"></div></footer></article><article itemscope itemtype="http://schema.org/Article" class="post-block" lang="en"><link itemprop="mainEntityOfPage" href="https://schtonn.github.io/blog/posts/rabbit/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/blog/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content="blog"></span><script type="text/javascript" src="/blog/js/md5.js"></script><script></script><script>document.oncopy=function(e){window.event&&(e=window.event);try{var t=e.srcElement;return"INPUT"==t.tagName&&"text"==t.type.toLowerCase()||"TEXTAREA"==t.tagName}catch(e){return!1}}</script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="schtonn"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/blog/posts/rabbit/" class="post-title-link" itemprop="url">兔农</a></h2><div class="post-meta"><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-o"></i></span> <span class="post-meta-item-text">Posted on</span> <time title="Created: 2021-Apr-13 22:27:26" itemprop="dateCreated datePublished" datetime="2021-04-13T22:27:26+08:00">2021-Apr-13</time></span><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-check-o"></i></span> <span class="post-meta-item-text">Edited on</span> <time title="Modified: 2022-Oct-19 23:02:06" itemprop="dateModified" datetime="2022-10-19T23:02:06+08:00">2022-Oct-19</time></span></div></header><div class="post-body" itemprop="articleBody"><h2 id="前置知识">前置知识</h2><p><a href="/blog/posts/matrix-pow">矩阵快速幂</a>，扩展欧几里得求逆元，基本的找规律能力。</p><h2 id="题面">题面</h2><p>(<a href="https://www.luogu.com.cn/problem/P2020" target="_blank" rel="noopener">luogu P2020</a>)</p><div class="post-button"> <a class="btn" href="/blog/posts/rabbit/#more" rel="contents">Read more &raquo;</a></div></div><footer class="post-footer"><div class="post-eof"></div></footer></article><article itemscope itemtype="http://schema.org/Article" class="post-block" lang="en"><link itemprop="mainEntityOfPage" href="https://schtonn.github.io/blog/posts/gen-func/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/blog/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content="blog"></span><script type="text/javascript" src="/blog/js/md5.js"></script><script></script><script>document.oncopy=function(e){window.event&&(e=window.event);try{var t=e.srcElement;return"INPUT"==t.tagName&&"text"==t.type.toLowerCase()||"TEXTAREA"==t.tagName}catch(e){return!1}}</script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="schtonn"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/blog/posts/gen-func/" class="post-title-link" itemprop="url">生成函数</a></h2><div class="post-meta"><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-o"></i></span> <span class="post-meta-item-text">Posted on</span> <time title="Created: 2021-Feb-16 21:38:17" itemprop="dateCreated datePublished" datetime="2021-02-16T21:38:17+08:00">2021-Feb-16</time></span><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-check-o"></i></span> <span class="post-meta-item-text">Edited on</span> <time title="Modified: 2022-Oct-19 23:02:06" itemprop="dateModified" datetime="2022-10-19T23:02:06+08:00">2022-Oct-19</time></span></div></header><div class="post-body" itemprop="articleBody"><p>。。。我最近写数学越来越多了，人都麻了</p><h2 id="前置知识">前置知识</h2><p>好像没啥，看得懂公式就行了。</p><h2 id="引入">引入</h2><p>一般的生成函数会和某个数列 <span class="math inline">\(a_0,a_1,\dots,a_n\)</span> 建立关系，它是一个多项式函数，其中每一项的系数等于对应数列每一位的值，这样的函数有时候也叫形式幂级数。</p><div class="post-button"> <a class="btn" href="/blog/posts/gen-func/#more" rel="contents">Read more &raquo;</a></div></div><footer class="post-footer"><div class="post-eof"></div></footer></article><article itemscope itemtype="http://schema.org/Article" class="post-block" lang="en"><link itemprop="mainEntityOfPage" href="https://schtonn.github.io/blog/posts/CRT/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/blog/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content="blog"></span><script type="text/javascript" src="/blog/js/md5.js"></script><script></script><script>document.oncopy=function(e){window.event&&(e=window.event);try{var t=e.srcElement;return"INPUT"==t.tagName&&"text"==t.type.toLowerCase()||"TEXTAREA"==t.tagName}catch(e){return!1}}</script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="schtonn"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/blog/posts/CRT/" class="post-title-link" itemprop="url">中国剩余定理</a></h2><div class="post-meta"><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-o"></i></span> <span class="post-meta-item-text">Posted on</span> <time title="Created: 2021-Jan-02 14:47:52" itemprop="dateCreated datePublished" datetime="2021-01-02T14:47:52+08:00">2021-Jan-02</time></span><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-check-o"></i></span> <span class="post-meta-item-text">Edited on</span> <time title="Modified: 2022-Oct-19 23:02:06" itemprop="dateModified" datetime="2022-10-19T23:02:06+08:00">2022-Oct-19</time></span></div></header><div class="post-body" itemprop="articleBody"><h2 id="前置知识">前置知识</h2><p>同余，逆元等数论基础。</p><h2 id="引入">引入</h2><p>我们来看这样一个问题：有物不知其数，三三数之剩二，五五数之剩三，七七数之剩二。问物几何？——《孙子算经》</p><p>即： <span class="math display">\[ \left\{ \begin{aligned} x&amp;\equiv 2\pmod {3}\\ x&amp;\equiv 3\pmod {5}\\ x&amp;\equiv 2\pmod {7} \end{aligned} \right.\tag{1.0} \]</span></p><div class="post-button"> <a class="btn" href="/blog/posts/CRT/#more" rel="contents">Read more &raquo;</a></div></div><footer class="post-footer"><div class="post-eof"></div></footer></article><article itemscope itemtype="http://schema.org/Article" class="post-block" lang="en"><link itemprop="mainEntityOfPage" href="https://schtonn.github.io/blog/posts/combination/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/blog/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content="blog"></span><script type="text/javascript" src="/blog/js/md5.js"></script><script></script><script>document.oncopy=function(e){window.event&&(e=window.event);try{var t=e.srcElement;return"INPUT"==t.tagName&&"text"==t.type.toLowerCase()||"TEXTAREA"==t.tagName}catch(e){return!1}}</script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="schtonn"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/blog/posts/combination/" class="post-title-link" itemprop="url">求组合数</a></h2><div class="post-meta"><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-o"></i></span> <span class="post-meta-item-text">Posted on</span> <time title="Created: 2021-Jan-01 20:26:59" itemprop="dateCreated datePublished" datetime="2021-01-01T20:26:59+08:00">2021-Jan-01</time></span><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-check-o"></i></span> <span class="post-meta-item-text">Edited on</span> <time title="Modified: 2022-Oct-19 23:02:06" itemprop="dateModified" datetime="2022-10-19T23:02:06+08:00">2022-Oct-19</time></span></div></header><div class="post-body" itemprop="articleBody"><h2 id="前置知识">前置知识</h2><p>中国剩余定理，</p><h2 id="引入">引入</h2><p>从 <span class="math inline">\(n\)</span> 个不同元素中取出 <span class="math inline">\(m\)</span> 个元素的组合数，即 <span class="math inline">\(C_n^m\)</span>，是从 <span class="math inline">\(n\)</span> 个不同元素中，取出 <span class="math inline">\(m\)</span> 个元素所形成的组合个数。</p><p>我们需要使用各种方式求 <span class="math inline">\(C_n^m\)</span>，每个方式难度，速度和空间都有不同。</p><div class="post-button"> <a class="btn" href="/blog/posts/combination/#more" rel="contents">Read more &raquo;</a></div></div><footer class="post-footer"><div class="post-eof"></div></footer></article><nav class="pagination"><a class="extend prev" rel="prev" href="/blog/"><i class="fa fa-angle-left" aria-label="Previous page"></i></a> <a class="page-number" href="/blog/">1</a><span class="page-number current">2</span><a class="page-number" href="/blog/page/3/">3</a><a class="page-number" href="/blog/page/4/">4</a><a class="extend next" rel="next" href="/blog/page/3/"><i class="fa fa-angle-right" aria-label="Next 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