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          <h3 id="前置知识">前置知识</h3>
<p>数组，结构体，二叉树</p>
<h3 id="引入">引入</h3>
<p>有时候我们会遇到一些大规模的区间查找和区间修改问题，比如让你维护一个 <span class="math inline">\(10^5\)</span> 长度的数列，要求操作有区间求和、区间加（区间每个数加上一个值），让你在一秒内完成 <span class="math inline">\(10^5\)</span> 次操作。 暴力是肯定不行的，数据范围太大，会超时。 所以我们就有一种专门解决大范围区间修改查询的数据结构：线段树。</p>
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          <p>引自：《信息学奥赛之-数学一本通》 揍是这样： <span class="math display">\[\operatorname{F}(n)=\dfrac{\sqrt{5}}{5}\cdot\left[\left(1+\sqrt{5}\right)^n-\left(1-\sqrt{5}\right)^n\right]\]</span> 代码揍这么简单： <figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="keyword">int</span> <span class="title">ferbo</span><span class="params">(<span class="keyword">int</span> n)</span></span>&#123;</span><br><span class="line">	<span class="keyword">return</span> (<span class="built_in">sqrt</span>(<span class="number">5</span>)/<span class="number">5</span>)*(<span class="built_in">pow</span>((<span class="number">1</span>+<span class="built_in">sqrt</span>(<span class="number">5</span>))/<span class="number">2</span>,n)-<span class="built_in">pow</span>((<span class="number">1</span>-<span class="built_in">sqrt</span>(<span class="number">5</span>))/<span class="number">2</span>,n));</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure> 要是再加个快速幂就更棒了（够快了，懒得写）</p>

      
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          <h3 id="前置知识">前置知识</h3>
<p>存图方式（<a href="http://baidu.physton.com/?q=邻接表" target="_blank" rel="noopener" title="简单">邻接表</a>，<a href="http://baidu.physton.com/?q=邻接矩阵" target="_blank" rel="noopener" title="都太简单了">邻接矩阵</a>）,图的遍历（<a href="http://baidu.physton.com/?q=dfs" target="_blank" rel="noopener" title="简单">dfs</a>，<a href="http://baidu.physton.com/?q=bfs" target="_blank" rel="noopener" title="简单">bfs</a>）</p>
<h3 id="引入">引入</h3>
<p>我们举个例子吧： 有一个毒瘤水管工，他会造水管，有一天他造了一个水管网络，就像一个图。其中有一个点只有出边，就是起点，还有一个点只有入边，是终点。 点之间有一些管子，这些管子都有单位时间内的容量，现在毒瘤水管工想知道，他的管子在<strong>单位时间内</strong>在起点终点之间最多能流多少水。
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          <h3 id="前置知识">前置知识</h3>
<p>存图方式（<a href="http://baidu.physton.com/?q=邻接表" target="_blank" rel="noopener" title="简单">邻接表</a>，<a href="http://baidu.physton.com/?q=邻接矩阵" target="_blank" rel="noopener" title="都太简单了，没有一个打得过的">邻接矩阵</a>），<a href="https://schtonn.github.io/2020/03/01/union-find" target="_blank" rel="noopener">并查集</a>。 不会的快进入链接学习吧！</p>
<h3 id="引入">引入</h3>
<p>生成树，就是从一个图中选中<span class="math inline">\(n-1\)</span>条边，使得这些边构成一棵树，并包含图中的所有节点。 最小生成树，就是找到一种生成树，使得这个生成树的边权和最小。
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            <a href="/2020/03/01/union-find/" class="post-title-link" itemprop="url">并查集</a>
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          <h3 id="前置知识">前置知识</h3>
<p>哈哈，简单到爆，没有。</p>
<h3 id="引入">引入</h3>
<p>并查集是一种快到爆炸的集合算法，可以进行两项基本操作：合并两个集合（并）、查询两个参数是否在一个集合内（查）。这也是它名字的由来。
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          <h3 id="前置知识">前置知识</h3>
<p>必备：存图方式（<a href="http://baidu.physton.com/?q=邻接表" target="_blank" rel="noopener" title="简单">邻接表</a>，<a href="http://baidu.physton.com/?q=邻接矩阵" target="_blank" rel="noopener" title="都太简单了，没有一个打得过的">邻接矩阵</a>），<a href="http://baidu.physton.com/?q=dfs%E5%BA%8F" target="_blank" rel="noopener">dfs序</a>。 维护：<a href="http://baidu.physton.com/?q=%E7%BA%BF%E6%AE%B5%E6%A0%91" target="_blank" rel="noopener">线段树</a>、<a href="http://baidu.physton.com/?q=%E6%A0%91%E7%8A%B6%E6%95%B0%E7%BB%84" target="_blank" rel="noopener">树状数组</a>、<a href="http://baidu.physton.com/?q=BST" target="_blank" rel="noopener">BST</a>。 不会的快进入链接学习吧！</p>
<h3 id="引入">引入</h3>
<p>树链剖分，简单来说就是把树分割成链，然后维护每一条链。一般的维护算法有线段树，树状数组和BST。复杂度为<span class="math inline">\(O(log n)\)</span>。
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