#include "graph_tree/lca.hpp"
#pragma once #include<vector> #include<cmath> #include<tuple> #include"depth.hpp" #include"distance.hpp" #include"graph_template.hpp" #include"../data_structure/arg_rmq.hpp" /** * @brief LCA &lt;O(N),O(1)&gt;(HL分解と同等の速さ) */ class lca{ std::vector<int>data; std::vector<int>comp_data; std::vector<int>start; arg_rmq<int>*st; std::vector<int> __dist; public: lca(){} lca(std::vector<std::vector<int>>v,int s){ data.resize(v.size()*2-1); comp_data.resize(v.size()*2-1); start.resize(v.size()); int i=0; __dist=distance(v,s); auto f=[&](auto f,int n,int p)->void{ start[n]=i; data[i]=n; comp_data[i++]=__dist[n]; for(int t:v[n]){ if(t==p)continue; f(f,t,n); data[i]=n; comp_data[i++]=__dist[n]; } }; f(f,s,-1); st=new arg_rmq<int>(comp_data); } int query(int p,int q){ return data[st->query(std::min(start[p],start[q]),std::max(start[p],start[q])+1).unwrap().first]; } int dist(int p,int q){ return __dist[p]+__dist[q]-2*__dist[query(p,q)]; } };
#line 2 "graph_tree/lca.hpp" #include<vector> #include<cmath> #include<tuple> #line 4 "graph_tree/graph_template.hpp" #include<iostream> /** * @brief グラフテンプレート */ using graph=std::vector<std::vector<int>>; template<typename T> using graph_w=std::vector<std::vector<std::pair<int,T>>>; graph load_graph(int n,int m){graph g(n);for(int i=0;i<m;++i){int s,t;std::cin>>s>>t;--s;--t;g[s].push_back(t);g[t].push_back(s);}return g;} graph load_digraph(int n,int m){graph g(n);for(int i=0;i<m;++i){int s,t;std::cin>>s>>t;--s;--t;g[s].push_back(t);}return g;} graph load_graph0(int n,int m){graph g(n);for(int i=0;i<m;++i){int s,t;std::cin>>s>>t;g[s].push_back(t);g[t].push_back(s);}return g;} graph load_digraph0(int n,int m){graph g(n);for(int i=0;i<m;++i){int s,t;std::cin>>s>>t;g[s].push_back(t);}return g;} graph load_tree(int n){graph g(n);for(int i=0;i<n-1;++i){int s,t;std::cin>>s>>t;--s;--t;g[s].push_back(t);g[t].push_back(s);}return g;} graph load_tree0(int n){graph g(n);for(int i=0;i<n-1;++i){int s,t;std::cin>>s>>t;g[s].push_back(t);g[t].push_back(s);}return g;} graph load_treep(int n){graph g(n);for(int i=0;i<n-1;++i){int t;std::cin>>t;g[i+1].push_back(t);g[t].push_back(i+1);}return g;} template<typename T>graph_w<T> load_graph_weight(int n,int m){graph_w<T> g(n);for(int i=0;i<m;++i){int s,t;T u;std::cin>>s>>t>>u;--s;--t;g[s].emplace_back(t,u);g[t].emplace_back(s,u);}return g;} template<typename T>graph_w<T> load_digraph_weight(int n,int m){graph_w<T> g(n);for(int i=0;i<m;++i){int s,t;T u;std::cin>>s>>t>>u;--s;--t;g[s].emplace_back(t,u);}return g;} template<typename T>graph_w<T> load_graph0_weight(int n,int m){graph_w<T> g(n);for(int i=0;i<m;++i){int s,t;T u;std::cin>>s>>t>>u;g[s].emplace_back(t,u);g[t].emplace_back(s,u);}return g;} template<typename T>graph_w<T> load_digraph0_weight(int n,int m){graph_w<T> g(n);for(int i=0;i<m;++i){int s,t;T u;std::cin>>s>>t>>u;g[s].emplace_back(t,u);}return g;} template<typename T>graph_w<T> load_tree_weight(int n){graph_w<T> g(n);for(int i=0;i<n-1;++i){int s,t;T u;std::cin>>s>>t>>u;--s;--t;g[s].emplace_back(t,u);g[t].emplace_back(s,u);}return g;} template<typename T>graph_w<T> load_tree0_weight(int n){graph_w<T> g(n);for(int i=0;i<n-1;++i){int s,t;T u;std::cin>>s>>t>>u;g[s].emplace_back(t,u);g[t].emplace_back(s,u);}return g;} template<typename T>graph_w<T> load_treep_weight(int n){graph_w<T> g(n);for(int i=0;i<n-1;++i){int t;T u;std::cin>>t>>u;g[i+1].emplace_back(t,u);g[t].emplace_back(i+1,u);}return g;} #line 5 "graph_tree/depth.hpp" /** * @brief 根からの深さ */ std::vector<int> depth(const graph& g,int start){ std::vector<int>memo(g.size()); auto f=[&](auto f,int v,int p)->int{ int mx=0; for(auto t:g[v]){ if(t==p)continue; mx=std::max(mx,f(f,t,v)); } return memo[v]=mx+1; }; f(f,start,-1); return memo; } #line 1 "graph_tree/distance.hpp" std::vector<int> distance(const graph& G,int start){ std::vector<int>memo(G.size()); auto f=[&](auto f,int v,int p,int i)->void{ for(auto t:G[v]){ if(t==p)continue; f(f,t,v,i+1); } memo[v]=i; }; f(f,start,-1,0); return memo; } #line 2 "data_structure/arg_rmq.hpp" #include<assert.h> #line 4 "data_structure/arg_rmq.hpp" #include<stack> #include<numeric> #line 7 "data_structure/arg_rmq.hpp" #include<algorithm> #line 3 "data_structure/small_rmq.hpp" /** * RMQ(small) &lt;O(N),O(1)&gt;(N<=64) */ template<typename T> class small_rmq{ using u64=unsigned long long; std::vector<u64>table; std::vector<T> v; public: small_rmq(std::vector<T> v):v(v){ assert(v.size()<=64); std::vector<int>tmp(v.size()); table.resize(v.size(),0); std::stack<T>stk; for(int i=0;i<(int)v.size();++i){ tmp.resize(v.size()); while(!stk.empty()&&v[stk.top()]>=v[i]){ stk.pop(); } tmp[i]=stk.empty()?-1:stk.top(); stk.emplace(i); } for(int i=0;i<(int)v.size();++i){ if(tmp[i]!=-1)table[i]=table[tmp[i]]|(1ULL<<(tmp[i])); } } T query(int l,int r){ assert(l!=r); const u64 tmp=table[r-1]&~((1ULL<<l)-1); if(tmp==0)return r-1; else return __builtin_ctzll(tmp); } }; #line 3 "data_structure/sparse_table.hpp" #include<functional> #line 2 "alga/maybe.hpp" #include<cassert> /** * @brief Maybe * @see https://ja.wikipedia.org/wiki/%E3%83%A2%E3%83%8A%E3%83%89_(%E3%83%97%E3%83%AD%E3%82%B0%E3%83%A9%E3%83%9F%E3%83%B3%E3%82%B0)#Maybe%E3%83%A2%E3%83%8A%E3%83%89 */ template<typename T> struct maybe{ bool _is_none; T val; maybe():_is_none(true){} maybe(T val):_is_none(false),val(val){} T unwrap()const{ assert(!_is_none); return val; } T unwrap_or(T e)const{ return _is_none?e:val; } bool is_none()const{return _is_none;} bool is_some()const{return !_is_none;} }; template<typename T,typename F> auto expand(F op){ return [&op](const maybe<T>& s,const maybe<T>& t){ if(s.is_none())return t; if(t.is_none())return s; return maybe<T>(op(s.unwrap(),t.unwrap())); }; } #line 7 "data_structure/sparse_table.hpp" /** * @brief SparseTable */ template<typename T,typename F> class sparse_table{ F f; std::vector<std::vector<T>>data; public: sparse_table(std::vector<T> v,F f=F()):f(f){ int n=v.size(),log=log2(n)+1; data.resize(n,std::vector<T>(log)); for(int i=0;i<n;i++)data[i][0]=v[i]; for(int j=1;j<log;j++)for(int i=0;i+(1<<(j-1))<n;i++){ data[i][j]=f(data[i][j-1],data[i+(1<<(j-1))][j-1]); } } maybe<T> get(int l,int r){ if(l==r)return maybe<T>(); if(r<l)std::swap(l,r); int k=std::log2(r-l); return maybe<T>(f(data[l][k],data[r-(1<<k)][k])); } }; #line 3 "functional/argmin.hpp" /** * @brief 最小値とその位置 */ template<typename T,typename E> struct argmin{ std::pair<T,E> operator()(const std::pair<T,E>& s,const std::pair<T,E>& t){ return s.second<=t.second?s:t; } }; #line 11 "data_structure/arg_rmq.hpp" /** * @brief RangeArgminQuery &lt;O(N),O(1)&gt; * @see https://noshi91.hatenablog.com/entry/2018/08/16/125415 */ template<typename T> class arg_rmq{ constexpr static int b=64; std::vector<T>v; std::vector<small_rmq<T>*>backet; sparse_table<std::pair<int,T>,argmin<int,T>>* st=0; public: arg_rmq(std::vector<T>v):v(v){ std::vector<std::pair<int,T>>tmp2; for(int i=0;i<(int)v.size();i+=b){ std::vector<T>tmp; T mn=std::numeric_limits<T>::max(); int idx=-1; for(int j=0;i+j<(int)v.size()&&j<b;j++){ tmp.push_back(v[i+j]); if(mn>v[i+j]){ mn=v[i+j]; idx=i+j; } } tmp2.emplace_back(idx,mn); backet.push_back(new small_rmq<T>(tmp)); } st=new sparse_table<std::pair<int,T>,argmin<int,T>>(tmp2); } maybe<std::pair<int,T>> query(int s,int t){ if(s==t)return maybe<std::pair<int,T>>(); if(s/b==t/b){ int idx=s/b*b+backet[s/b]->query(s%b,t%b); return maybe<std::pair<int,T>>(std::make_pair(idx,v[idx])); } std::pair<int,T> res=std::make_pair(-1,std::numeric_limits<T>::max()); { int idx=s/b*b+backet[s/b]->query(s%b,b); res=argmin<int,T>()(res,std::make_pair(idx,v[idx])); } if(s/b+1!=t/b)res=argmin<int,T>()(res,st->get(s/b+1,t/b).unwrap()); if(t%b!=0){ int idx=t/b*b+backet[t/b]->query(0,t%b); res=argmin<int,T>()(res,std::make_pair(idx,v[idx])); } return maybe<std::pair<int,T>>(res); } }; #line 9 "graph_tree/lca.hpp" /** * @brief LCA &lt;O(N),O(1)&gt;(HL分解と同等の速さ) */ class lca{ std::vector<int>data; std::vector<int>comp_data; std::vector<int>start; arg_rmq<int>*st; std::vector<int> __dist; public: lca(){} lca(std::vector<std::vector<int>>v,int s){ data.resize(v.size()*2-1); comp_data.resize(v.size()*2-1); start.resize(v.size()); int i=0; __dist=distance(v,s); auto f=[&](auto f,int n,int p)->void{ start[n]=i; data[i]=n; comp_data[i++]=__dist[n]; for(int t:v[n]){ if(t==p)continue; f(f,t,n); data[i]=n; comp_data[i++]=__dist[n]; } }; f(f,s,-1); st=new arg_rmq<int>(comp_data); } int query(int p,int q){ return data[st->query(std::min(start[p],start[q]),std::max(start[p],start[q])+1).unwrap().first]; } int dist(int p,int q){ return __dist[p]+__dist[q]-2*__dist[query(p,q)]; } };