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必备：存图方式（邻接表，邻接矩阵），dfs序。 维护：线段树、树状数组、BST。
引入
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\(O(\log n)\)。"><meta property="og:type" content="article"><meta property="og:title" content="树链剖分"><meta property="og:url" content="https://schtonn.github.io/blog/posts/tree-link/index.html"><meta property="og:site_name" content="schtonn"><meta property="og:description" content="前置知识
必备：存图方式（邻接表，邻接矩阵），dfs序。 维护：线段树、树状数组、BST。
引入
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\(O(\log n)\)。"><meta property="og:locale" content="en_US"><meta property="og:image" content="https://img-blog.csdnimg.cn/20191228195815530.png"><meta property="article:published_time" content="2020-03-01T14:41:02.000Z"><meta property="article:modified_time" content="2022-09-24T13:29:39.583Z"><meta property="article:author" content="Alex"><meta property="article:tag" content="graph"><meta property="article:tag" content="struct"><meta property="article:tag" content="tree"><meta name="twitter:card" content="summary"><meta name="twitter:image" content="https://img-blog.csdnimg.cn/20191228195815530.png"><link rel="canonical" href="https://schtonn.github.io/blog/posts/tree-link/"><script id="page-configurations">CONFIG.page={sidebar:"",isHome:!1,isPost:!0,lang:"en"}</script><title>树链剖分 | schtonn</title><noscript><style>.sidebar-inner,.use-motion .brand,.use-motion .collection-header,.use-motion .comments,.use-motion .menu-item,.use-motion 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class="site-subtitle" itemprop="description">schtonn</p></div><div class="site-nav-right"><div class="toggle popup-trigger"></div></div></div><nav class="site-nav"><ul id="menu" class="menu"><li class="menu-item menu-item-home"><a href="/blog/" rel="section"><i class="fa fa-fw fa-home"></i> Home</a></li><li class="menu-item menu-item-tags"><a href="/blog/tags/" rel="section"><i class="fa fa-fw fa-tags"></i> Tags</a></li><li class="menu-item menu-item-archives"><a href="/blog/archives/" rel="section"><i class="fa fa-fw fa-archive"></i> Archives</a></li><li class="menu-item menu-item-games"><a href="/blog/games/" rel="section"><i class="fa fa-fw fa-gamepad"></i> Games</a></li></ul></nav></div></header><div class="back-to-top"><i class="fa fa-arrow-up"></i> <span>0%</span></div><main class="main"><div class="main-inner"><div class="content-wrap"><div class="content post posts-expand"><article itemscope itemtype="http://schema.org/Article" class="post-block" lang="en"><link itemprop="mainEntityOfPage" href="https://schtonn.github.io/blog/posts/tree-link/"><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"><h1 class="post-title" itemprop="name headline"> 树链剖分</h1><div class="post-meta"><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-o"></i></span> <span class="post-meta-item-text">Posted on</span> <time title="Created: 2020-Mar-01 22:41:02" itemprop="dateCreated datePublished" datetime="2020-03-01T22:41:02+08:00">2020-Mar-01</time></span><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-check-o"></i></span> <span class="post-meta-item-text">Edited on</span> <time title="Modified: 2022-Sep-24 21:29:39" itemprop="dateModified" datetime="2022-09-24T21:29:39+08:00">2022-Sep-24</time></span><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-comment-o"></i></span> <span class="post-meta-item-text">Valine:</span><a title="valine" href="/blog/posts/tree-link/#valine-comments" itemprop="discussionUrl"><span class="post-comments-count valine-comment-count" data-xid="/blog/posts/tree-link/" itemprop="commentCount"></span></a></span></div></header><div class="post-body" itemprop="articleBody"><h2 id="前置知识">前置知识</h2><p>必备：存图方式（邻接表，邻接矩阵），dfs序。 维护：线段树、树状数组、BST。</p><h2 id="引入">引入</h2><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>。<a id="more"></a></p><h2 id="剖分方式">剖分方式</h2><p>对于每一个节点，它的子节点中<strong>子树的节点数最大的</strong>为重儿子，连接到重儿子的边称为重边。例如：</p><p><img data-src="https://img-blog.csdnimg.cn/20191228195815530.png"></p><p>加粗节点为重儿子。除重儿子和重边外的节点和边均为轻儿子或轻边。根不是重儿子也不是轻儿子，他根本就不是儿子！</p><p>以轻儿子或者根为起点的，由重边连接的一条连续的链称为重链。特别地，若一个叶子结点是轻儿子，那么便有一条以该叶子结点为起点的长度为1的重链。上图中，1-3-7-9是一条重链，6一个节点也是一条重链。</p><h2 id="预处理">预处理</h2><p>树链剖分的预处理本质上就是2个dfs。</p><h3 id="dfs-1">dfs 1</h3><p>一共完成四项任务：</p><ul><li>标记节点深度：<code>dep[]</code></li><li>标记节点的父节点：<code>fa[]</code></li><li>标记节点的子树大小：<code>siz[]</code></li><li>标记节点的重儿子编号：<code>son[]</code></li></ul><p>代码：</p><figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="keyword">void</span> <span class="title">dfs_1</span><span class="params">(<span class="keyword">int</span> u,<span class="keyword">int</span> f)</span></span>{</span><br><span class="line"> siz[u]=<span class="number">1</span>;</span><br><span class="line"> <span class="keyword">int</span> maxson=<span class="number">-1</span>;</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=head[u];i!=<span class="number">-1</span>;i=edge[i].nxt){</span><br><span class="line"> <span class="keyword">int</span> v=edge[i].v;</span><br><span class="line"> <span class="keyword">if</span>(v==f) <span class="keyword">continue</span>;</span><br><span class="line"> fa[v]=u;</span><br><span class="line"> dep[v]=dep[u]+<span class="number">1</span>;</span><br><span class="line"> dfs_1(v,u);</span><br><span class="line"> siz[u]+=siz[v];</span><br><span class="line"> <span class="keyword">if</span>(siz[v]>siz[son[u]])son[u]=v;</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure><p></p><h3 id="dfs-2">dfs 2</h3><p>以先重后轻为优先级的dfs。完成三项任务：</p><ul><li>标记dfs序（先重后轻）：<code>idx[]</code></li><li>标记dfs序对应的节点：<code>rnk[]</code></li><li>标记节点所在重链的顶端：<code>top[]</code></li></ul><p>代码：</p><figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="keyword">void</span> <span class="title">dfs_2</span><span class="params">(<span class="keyword">int</span> u,<span class="keyword">int</span> tp)</span></span>{</span><br><span class="line"> idx[u]=++dfn;</span><br><span class="line"> rnk[dfn]=a[u];</span><br><span class="line"> top[u]=tp;</span><br><span class="line"> <span class="keyword">if</span>(!son[u])<span class="keyword">return</span>;</span><br><span class="line"> dfs_2(son[u],tp);</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=head[u];i!=<span class="number">-1</span>;i=edge[i].nxt){</span><br><span class="line"> <span class="keyword">if</span>(!idx[edge[i].v]){</span><br><span class="line"> dfs_2(edge[i].v,edge[i].v);</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure><p></p><h2 id="维护">维护</h2><p>这里以洛谷的<a href="https://www.luogu.com.cn/problem/P3384" target="_blank" rel="noopener">P3384</a>为例，要求维护四种操作：</p><ul><li>操作1： 格式： 1 x y z 表示将树从x到y结点最短路径上所有节点的值都加上z</li><li>操作2： 格式： 2 x y 表示求树从x到y结点最短路径上所有节点的值之和</li><li>操作3： 格式： 3 x z 表示将以x为根节点的子树内所有节点值都加上z</li><li>操作4： 格式： 4 x 表示求以x为根节点的子树内所有节点值之和</li></ul><ol type="1"><li><p>要处理两点间的路径时：</p><p>首先找到两个节点中较深的那个点，然后将对该点所在重链进行处理，并将该点移动至所在链顶端节点<strong>的父节点</strong>（相当于一段一段地处理）。因为是按照轻重边为优先级做的dfs，所以一条链上的编号一定是连续的。</p><p>循环执行直到两个点在一条链上，这时再处理两个点之间的区间即可。</p></li><li><p>要处理一个点的子树时：</p><p>子树的dfs序一定是连续的区间，直接处理该区间即可。</p></li></ol><p>这样就把树上问题转化成了区间问题。</p><h2 id="完整代码">完整代码</h2><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><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br><span class="line">75</span><br><span class="line">76</span><br><span class="line">77</span><br><span class="line">78</span><br><span class="line">79</span><br><span class="line">80</span><br><span class="line">81</span><br><span class="line">82</span><br><span class="line">83</span><br><span class="line">84</span><br><span class="line">85</span><br><span class="line">86</span><br><span class="line">87</span><br><span class="line">88</span><br><span class="line">89</span><br><span class="line">90</span><br><span class="line">91</span><br><span class="line">92</span><br><span class="line">93</span><br><span class="line">94</span><br><span class="line">95</span><br><span class="line">96</span><br><span class="line">97</span><br><span class="line">98</span><br><span class="line">99</span><br><span class="line">100</span><br><span class="line">101</span><br><span class="line">102</span><br><span class="line">103</span><br><span class="line">104</span><br><span class="line">105</span><br><span class="line">106</span><br><span class="line">107</span><br><span class="line">108</span><br><span class="line">109</span><br><span class="line">110</span><br><span class="line">111</span><br><span class="line">112</span><br><span class="line">113</span><br><span class="line">114</span><br><span class="line">115</span><br><span class="line">116</span><br><span class="line">117</span><br><span class="line">118</span><br><span class="line">119</span><br><span class="line">120</span><br><span class="line">121</span><br><span class="line">122</span><br><span class="line">123</span><br><span class="line">124</span><br><span class="line">125</span><br><span class="line">126</span><br><span class="line">127</span><br><span class="line">128</span><br><span class="line">129</span><br><span class="line">130</span><br><span class="line">131</span><br><span class="line">132</span><br><span class="line">133</span><br><span class="line">134</span><br><span class="line">135</span><br><span class="line">136</span><br><span class="line">137</span><br><span class="line">138</span><br><span class="line">139</span><br><span class="line">140</span><br><span class="line">141</span><br><span class="line">142</span><br><span class="line">143</span><br><span class="line">144</span><br><span class="line">145</span><br><span class="line">146</span><br><span class="line">147</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string">"bits/stdc++.h"</span></span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="built_in">std</span>;</span><br><span class="line"><span class="keyword">const</span> <span class="keyword">int</span> N=<span class="number">2000100</span>;</span><br><span class="line"><span class="meta">#<span class="meta-keyword">define</span> lson id<<1</span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">define</span> rson id<<1|1</span></span><br><span class="line"><span class="function"><span class="keyword">inline</span> <span class="keyword">int</span> <span class="title">read</span><span class="params">()</span></span>{</span><br><span class="line"> <span class="keyword">int</span> c=<span class="number">1</span>,q=<span class="number">0</span>;<span class="keyword">char</span> ch=<span class="string">' '</span>;</span><br><span class="line"> <span class="keyword">while</span>(ch!=<span class="string">'-'</span>&&(ch<<span class="string">'0'</span>||ch><span class="string">'9'</span>))ch=getchar();</span><br><span class="line"> <span class="keyword">if</span>(ch==<span class="string">'-'</span>)c=<span class="number">-1</span>,ch=getchar();</span><br><span class="line"> <span class="keyword">while</span>(ch>=<span class="string">'0'</span>&&ch<=<span class="string">'9'</span>)q=q*<span class="number">10</span>+ch-<span class="string">'0'</span>,ch=getchar();</span><br><span class="line"> <span class="keyword">return</span> c*q;</span><br><span class="line">}</span><br><span class="line"><span class="class"><span class="keyword">struct</span> <span class="title">node</span>{</span></span><br><span class="line"> <span class="keyword">int</span> u,v,nxt;</span><br><span class="line">}e[N];</span><br><span class="line"><span class="keyword">int</span> head[N];</span><br><span class="line"><span class="keyword">int</span> tot=<span class="number">1</span>;</span><br><span class="line"><span class="class"><span class="keyword">struct</span> <span class="title">Tree</span>{</span></span><br><span class="line"> <span class="keyword">int</span> l,r,c,siz,f;</span><br><span class="line">}t[N];</span><br><span class="line"><span class="keyword">int</span> n,m,root,p,dfn=<span class="number">0</span>,rnk[N],a[N];</span><br><span class="line"><span class="function"><span class="keyword">inline</span> <span class="keyword">void</span> <span class="title">add</span><span class="params">(<span class="keyword">int</span> x,<span class="keyword">int</span> y)</span></span>{</span><br><span class="line"> e[tot].u=x;</span><br><span class="line"> e[tot].v=y;</span><br><span class="line"> e[tot].nxt=head[x];</span><br><span class="line"> head[x]=tot++;</span><br><span class="line">}</span><br><span class="line"><span class="keyword">int</span> dep[N],fa[N],son[N],siz[N],top[N],idx[N];</span><br><span class="line"><span class="function"><span class="keyword">void</span> <span class="title">dfs_1</span><span class="params">(<span class="keyword">int</span> u,<span class="keyword">int</span> f)</span></span>{</span><br><span class="line"> siz[u]=<span class="number">1</span>;</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=head[u];i;i=e[i].nxt){</span><br><span class="line"> <span class="keyword">int</span> v=e[i].v;</span><br><span class="line"> <span class="keyword">if</span>(v==f) <span class="keyword">continue</span>;</span><br><span class="line"> fa[v]=u;</span><br><span class="line"> dep[v]=dep[u]+<span class="number">1</span>;</span><br><span class="line"> dfs_1(v,u);</span><br><span class="line"> siz[u]+=siz[v];</span><br><span class="line"> <span class="keyword">if</span>(siz[v]>siz[son[u]])son[u]=v;</span><br><span class="line"> }</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="keyword">void</span> <span class="title">update</span><span class="params">(<span class="keyword">int</span> id)</span></span>{</span><br><span class="line"> t[id].c=(t[lson].c+t[rson].c+p)%p;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="keyword">void</span> <span class="title">Build</span><span class="params">(<span class="keyword">int</span> id,<span class="keyword">int</span> L,<span class="keyword">int</span> R)</span></span>{</span><br><span class="line"> t[id].l=L;t[id].r=R;t[id].siz=R-L+<span class="number">1</span>;</span><br><span class="line"> <span class="keyword">if</span>(L==R){</span><br><span class="line"> t[id].c=rnk[L];</span><br><span class="line"> <span class="keyword">return</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">int</span> mid=(L+R)>><span class="number">1</span>;</span><br><span class="line"> Build(lson,L,mid);</span><br><span class="line"> Build(rson,mid+<span class="number">1</span>,R);</span><br><span class="line"> update(id);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="keyword">void</span> <span class="title">dfs_2</span><span class="params">(<span class="keyword">int</span> u,<span class="keyword">int</span> tp)</span></span>{</span><br><span class="line"> idx[u]=++dfn;</span><br><span class="line"> rnk[dfn]=a[u];</span><br><span class="line"> top[u]=tp;</span><br><span class="line"> <span class="keyword">if</span>(!son[u])<span class="keyword">return</span>;</span><br><span class="line"> dfs_2(son[u],tp);</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=head[u];i;i=e[i].nxt){</span><br><span class="line"> <span class="keyword">if</span>(!idx[e[i].v]){</span><br><span class="line"> dfs_2(e[i].v,e[i].v);</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="keyword">void</span> <span class="title">pushdown</span><span class="params">(<span class="keyword">int</span> id)</span></span>{</span><br><span class="line"> <span class="keyword">if</span>(!t[id].f) <span class="keyword">return</span> ;</span><br><span class="line"> t[lson].c=(t[lson].c+t[lson].siz*t[id].f)%p;</span><br><span class="line"> t[rson].c=(t[rson].c+t[rson].siz*t[id].f)%p;</span><br><span class="line"> t[lson].f=(t[lson].f+t[id].f)%p;</span><br><span class="line"> t[rson].f=(t[rson].f+t[id].f)%p;</span><br><span class="line"> t[id].f=<span class="number">0</span>;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="keyword">void</span> <span class="title">addroute</span><span class="params">(<span class="keyword">int</span> id,<span class="keyword">int</span> L,<span class="keyword">int</span> R,<span class="keyword">int</span> c)</span></span>{</span><br><span class="line"> <span class="keyword">if</span>(L<=t[id].l&&t[id].r<=R){</span><br><span class="line"> t[id].c+=t[id].siz*c;</span><br><span class="line"> t[id].f+=c;</span><br><span class="line"> <span class="keyword">return</span>;</span><br><span class="line"> }</span><br><span class="line"> pushdown(id);</span><br><span class="line"> <span class="keyword">int</span> mid=(t[id].l+t[id].r)>><span class="number">1</span>;</span><br><span class="line"> <span class="keyword">if</span>(L<=mid)addroute(lson,L,R,c);</span><br><span class="line"> <span class="keyword">if</span>(R>mid)addroute(rson,L,R,c);</span><br><span class="line"> update(id);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="keyword">void</span> <span class="title">addtree</span><span class="params">(<span class="keyword">int</span> x,<span class="keyword">int</span> y,<span class="keyword">int</span> c)</span></span>{</span><br><span class="line"> <span class="keyword">while</span>(top[x]!=top[y]){</span><br><span class="line"> <span class="keyword">if</span>(dep[top[x]]<dep[top[y]])swap(x,y);</span><br><span class="line"> addroute(<span class="number">1</span>,idx[top[x]],idx[x],c);</span><br><span class="line"> x=fa[top[x]];</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">if</span>(dep[x]>dep[y])swap(x,y);</span><br><span class="line"> addroute(<span class="number">1</span>,idx[x],idx[y],c);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="keyword">int</span> <span class="title">sumroute</span><span class="params">(<span class="keyword">int</span> id,<span class="keyword">int</span> L,<span class="keyword">int</span> R)</span></span>{</span><br><span class="line"> <span class="keyword">int</span> ans=<span class="number">0</span>;</span><br><span class="line"> <span class="keyword">if</span>(L<=t[id].l&&t[id].r<=R)</span><br><span class="line"> <span class="keyword">return</span> t[id].c;</span><br><span class="line"> pushdown(id);</span><br><span class="line"> <span class="keyword">int</span> mid=(t[id].l+t[id].r)>><span class="number">1</span>;</span><br><span class="line"> <span class="keyword">if</span>(L<=mid) ans=(ans+sumroute(lson,L,R))%p;</span><br><span class="line"> <span class="keyword">if</span>(R>mid) ans=(ans+sumroute(rson,L,R))%p;</span><br><span class="line"> <span class="keyword">return</span> ans;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="keyword">void</span> <span class="title">treesum</span><span class="params">(<span class="keyword">int</span> x,<span class="keyword">int</span> y)</span></span>{</span><br><span class="line"> <span class="keyword">int</span> ans=<span class="number">0</span>;</span><br><span class="line"> <span class="keyword">while</span>(top[x]!=top[y]){</span><br><span class="line"> <span class="keyword">if</span>(dep[top[x]]<dep[top[y]]) swap(x,y);</span><br><span class="line"> ans=(ans+sumroute(<span class="number">1</span>,idx[top[x]],idx[x]))%p;</span><br><span class="line"> x=fa[top[x]];</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">if</span>(dep[x]>dep[y]) swap(x,y);</span><br><span class="line"> ans=(ans+sumroute(<span class="number">1</span>,idx[x],idx[y]))%p;</span><br><span class="line"> <span class="built_in">printf</span>(<span class="string">"%d\n"</span>,ans);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="keyword">int</span> <span class="title">main</span><span class="params">()</span></span>{</span><br><span class="line"> n=read();m=read();root=read();p=read();</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">1</span>;i<=n;i++) a[i]=read();</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">1</span>;i<=n<span class="number">-1</span>;i++){</span><br><span class="line"> <span class="keyword">int</span> x=read(),y=read();</span><br><span class="line"> add(x,y);add(y,x);</span><br><span class="line"> }</span><br><span class="line"> dfs_1(root,root);</span><br><span class="line"> dfs_2(root,root);</span><br><span class="line"> Build(<span class="number">1</span>,<span class="number">1</span>,n);</span><br><span class="line"> <span class="keyword">while</span>(m--){</span><br><span class="line"> <span class="keyword">int</span> op=read(),x,y,z;</span><br><span class="line"> <span class="keyword">if</span>(op==<span class="number">1</span>){ </span><br><span class="line"> x=read();y=read();z=read();z=z%p;</span><br><span class="line"> addtree(x,y,z);</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">else</span> <span class="keyword">if</span>(op==<span class="number">2</span>){</span><br><span class="line"> x=read();y=read();</span><br><span class="line"> treesum(x,y);</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">else</span> <span class="keyword">if</span>(op==<span class="number">3</span>){</span><br><span class="line"> x=read(),z=read();</span><br><span class="line"> addroute(<span class="number">1</span>,idx[x],idx[x]+siz[x]<span class="number">-1</span>,z%p);</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">else</span> <span class="keyword">if</span>(op==<span class="number">4</span>){</span><br><span class="line"> x=read();</span><br><span class="line"> <span class="built_in">printf</span>(<span class="string">"%d\n"</span>,sumroute(<span class="number">1</span>,idx[x],idx[x]+siz[x]<span class="number">-1</span>));</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div><div><ul class="post-copyright"><li class="post-copyright-author"> <strong>Post author:</strong> Alex</li><li class="post-copyright-link"> <strong>Post link:</strong> <a href="https://schtonn.github.io/blog/posts/tree-link/" title="树链剖分">https://schtonn.github.io/blog/posts/tree-link/</a></li><li class="post-copyright-license"> <strong>Copyright Notice:</strong> All 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