fix: something

content/data-structure/SegmentTreeBeats.hpp

@@ -1,4 +1,5 @@
 #pragma once
+#include "../template/Header.hpp"
 
 /**
  * Author: Teetat T.

content/data-structure/StaticTopTree.hpp

@@ -0,0 +1,159 @@
+#pragma once
+#include "../template/Header.hpp"
+
+/**
+ * Author: Teetat T.
+ * Date: 2024-08-17
+ * License: CC0
+ * Description: Static Top Tree
+ * Status: Tested
+ */
+
+enum Type{Compress,Rake,AddEdge,AddVertex,Vertex};
+
+struct StaticTopTree{
+    int n,node_id;
+    int root,stt_root;
+    vector<vector<int>> &adj;
+    vector<int> hv;
+    vector<int> lch,rch,par;
+    vector<Type> type;
+    StaticTopTree(vector<vector<int>> &_adj,int _root):adj(_adj){
+        n=adj.size();
+        root=_root;
+        node_id=n;
+        hv.assign(n,-1);
+        lch.assign(4*n,-1);
+        rch.assign(4*n,-1);
+        par.assign(4*n,-1);
+        type.assign(4*n,Type::Vertex);
+        dfs(root);
+        stt_root=compress(root).first;
+    }
+    int dfs(int u){
+        int mx=0,sz=1;
+        for(auto v:adj[u]){
+            int x=dfs(v);
+            sz+=x;
+            if(x>mx){
+                hv[u]=v;
+                mx=x;
+            }
+        }
+        return sz;
+    }
+    int add(int i,int l,int r,Type t){
+        if(i==-1)i=node_id++;
+        lch[i]=l,rch[i]=r,par[i]=-1,type[i]=t;
+        if(l!=-1)par[l]=i;
+        if(r!=-1)par[r]=i;
+        return i;
+    }
+    pair<int,int> merge(vector<pair<int,int>> a,Type t){
+        if(a.size()==1)return a[0];
+        int tot=0;
+        vector<pair<int,int>> l,r;
+        for(auto [i,s]:a)tot+=s;
+        for(auto [i,s]:a){
+            if(tot>s)l.emplace_back(i,s);
+            else r.emplace_back(i,s);
+            tot-=s*2;
+        }
+        auto [i,si]=merge(l,t);
+        auto [j,sj]=merge(r,t);
+        return {add(-1,i,j,t),si+sj};
+    }
+    pair<int,int> compress(int i){
+        vector<pair<int,int>> a{add_vertex(i)};
+        while(hv[i]!=-1)a.emplace_back(add_vertex(i=hv[i]));
+        return merge(a,Type::Compress);
+    }
+    pair<int,int> rake(int i){
+        vector<pair<int,int>> a;
+        for(auto j:adj[i])if(j!=hv[i])a.emplace_back(add_edge(j));
+        return a.empty()?make_pair(-1,0):merge(a,Type::Rake);
+    }
+    pair<int,int> add_edge(int i){
+        auto [j,s]=compress(i);
+        return {add(-1,j,-1,Type::AddEdge),s};
+    }
+    pair<int,int> add_vertex(int i){
+        auto [j,s]=rake(i);
+        return {add(i,j,-1,j==-1?Type::Vertex:Type::AddVertex),s+1};
+    }
+};
+
+const int N=2e5+5;
+
+int n,q;
+ll a[N];
+vector<vector<int>> adj;
+
+using Path = pair<ll,ll>;
+using Point = ll;
+
+Path compress(Path p,Path ch){
+    auto [a,b]=ch;
+    auto [c,d]=p;
+    return {a*c%MOD,(b*c+d)%MOD};
+}
+
+Point rake(Point l,Point r){
+    return l*r%MOD;
+}
+
+Path add_vertex(Point x,int i){
+    return {x,a[i]};
+}
+
+Point add_edge(Path x){
+    return x.second;
+}
+
+Path vertex(int i){
+    return {1LL,a[i]};
+}
+
+Path path[4*N];
+Point point[4*N];
+
+void example(){
+    cin.tie(nullptr)->sync_with_stdio(false);
+    cin >> n >> q;
+    adj.resize(n);
+    for(int i=1;i<n;i++){
+        int p;
+        cin >> p;
+        adj[p-1].emplace_back(i);
+    }
+    for(int i=0;i<n;i++)cin >> a[i];
+    StaticTopTree stt(adj,0);
+    auto update=[&](int i){
+        if(stt.type[i]==Type::Compress){
+            path[i]=compress(path[stt.lch[i]],path[stt.rch[i]]);
+        }else if(stt.type[i]==Type::Rake){
+            point[i]=rake(point[stt.lch[i]],point[stt.rch[i]]);
+        }else if(stt.type[i]==Type::AddVertex){
+            path[i]=add_vertex(point[stt.lch[i]],i);
+        }else if(stt.type[i]==Type::AddEdge){
+            point[i]=add_edge(path[stt.lch[i]]);
+        }else{
+            path[i]=vertex(i);
+        }
+    };
+    function<void(int)> dfs=[&](int u){
+        if(u==-1)return;
+        dfs(stt.lch[u]);
+        dfs(stt.rch[u]);
+        update(u);
+    };
+    dfs(stt.stt_root);
+    while(q--){
+        int v,x;
+        cin >> v >> x;
+        v--;
+        a[v]=x;
+        for(;v!=-1;v=stt.par[v])update(v);
+        cout << path[stt.stt_root].second << "\n";
+    }
+}

content/data-structure/chapter.tex

@@ -16,3 +16,4 @@ \chapter{Data Structures}
 \kactlimport{LazyReversibleSplayTree.hpp}
 \kactlimport{LinkCutTreeBase.hpp}
 \kactlimport{LazyLinkCutTree.hpp}
+\ksactlimport{StaticTopTree.hpp}