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View the Project on GitHub mugen1337/procon
#include "Graph2/StronglyConnectedComponents.hpp"
SCC belong[i] : iが属するSCC group[i] : SCC_iに入っている頂点たち compressed : SCCごと分解したグラフが入る.DAGだけど,元グラフが連結じゃないなら連結ではないところに注意.また,多重辺が生える実装になっている.
もしトポソ順が欲しいのであれば, rep(i,(int)scc.compressed.size()) for(auto j:scc.group[i]) ord.push_back(j); とかやるとよい.
#include "./GraphTemplate.hpp" // scc.belong[i] : strongly connected components i belongs // scc.group[i] : vertice i-th strongly connected component has // scc.compressed : compressed Graph, DAG // Longest Path verified : https://atcoder.jp/contests/abc135/submissions/19684261 template<typename T=int> struct StronglyConnectedComponents{ private: Graph<T> g,rg; vector<int> check; void dfs(int cur,vector<int> &ord){ for(auto &to:g[cur])if(!check[to]){ check[to]=true; dfs(to,ord); } ord.push_back(cur); } void rdfs(int cur,int p){ for(auto &to:rg[cur])if(belong[to]==-1){ belong[to]=p; rdfs(to,p); } } void build(){ vector<int> ord; for(int i=0;i<(int)g.size();i++)if(!check[i]){ check[i]=true; dfs(i,ord); } int ptr=0;; for(int i=(int)ord.size()-1;i>=0;i--)if(belong[ord[i]]==-1){ belong[ord[i]]=ptr; rdfs(ord[i],ptr);ptr++; } compressed.resize(ptr); group.resize(ptr); for(int i=0;i<(int)g.size();i++){ int u=belong[i]; group[u].push_back(i); for(auto &e:g[i]){ int v=belong[e]; if(u!=v) compressed.add_directed_edge(u,v,e.w); } } return ; } public: vector<int> belong; vector<vector<int>> group; Graph<T> compressed; StronglyConnectedComponents(Graph<T> &g):g(g),rg(g.size()),check(g.size()),belong(g.size(),-1){ for(int i=0;i<(int)g.size();i++)for(auto &e:g[i]) rg.add_directed_edge(e.to,e.from,e.w); build(); } // topological sort vector<int> get_DAG_order(){ vector<int> ret; for(int i=0;i<(int)group.size();i++)for(auto &j:group[i]) ret.push_back(j); return ret; } // g is not DAG or contain self-loop, return inf T LongestPath(){ for(int i=0;i<(int)g.size();i++){ for(auto &e:g[i]){ if(belong[i]==belong[e]) return -1; } } vector<int> ord=get_DAG_order(); vector<T> dp(g.size(),0); for(auto i:ord)for(auto &e:g[i]) dp[e]=max(dp[e],dp[i]+e.w); return (*max_element(begin(dp),end(dp))); } };
#line 1 "Graph2/GraphTemplate.hpp" // graph template // ref : https://ei1333.github.io/library/graph/graph-template.hpp template<typename T=int> struct Edge{ int from,to; T w; int idx; Edge()=default; Edge(int from,int to,T w=1,int idx=-1):from(from),to(to),w(w),idx(idx){} operator int() const{return to;} }; template<typename T=int> struct Graph{ vector<vector<Edge<T>>> g; int V,E; Graph()=default; Graph(int n):g(n),V(n),E(0){} int size(){ return (int)g.size(); } void resize(int k){ g.resize(k); V=k; } inline const vector<Edge<T>> &operator[](int k)const{ return (g.at(k)); } inline vector<Edge<T>> &operator[](int k){ return (g.at(k)); } void add_directed_edge(int from,int to,T cost=1){ g[from].emplace_back(from,to,cost,E++); } void add_edge(int from,int to,T cost=1){ g[from].emplace_back(from,to,cost,E); g[to].emplace_back(to,from,cost,E++); } void read(int m,int pad=-1,bool weighted=false,bool directed=false){ for(int i=0;i<m;i++){ int u,v;cin>>u>>v; u+=pad,v+=pad; T w=T(1); if(weighted) cin>>w; if(directed) add_directed_edge(u,v,w); else add_edge(u,v,w); } } }; #line 2 "Graph2/StronglyConnectedComponents.hpp" // scc.belong[i] : strongly connected components i belongs // scc.group[i] : vertice i-th strongly connected component has // scc.compressed : compressed Graph, DAG // Longest Path verified : https://atcoder.jp/contests/abc135/submissions/19684261 template<typename T=int> struct StronglyConnectedComponents{ private: Graph<T> g,rg; vector<int> check; void dfs(int cur,vector<int> &ord){ for(auto &to:g[cur])if(!check[to]){ check[to]=true; dfs(to,ord); } ord.push_back(cur); } void rdfs(int cur,int p){ for(auto &to:rg[cur])if(belong[to]==-1){ belong[to]=p; rdfs(to,p); } } void build(){ vector<int> ord; for(int i=0;i<(int)g.size();i++)if(!check[i]){ check[i]=true; dfs(i,ord); } int ptr=0;; for(int i=(int)ord.size()-1;i>=0;i--)if(belong[ord[i]]==-1){ belong[ord[i]]=ptr; rdfs(ord[i],ptr);ptr++; } compressed.resize(ptr); group.resize(ptr); for(int i=0;i<(int)g.size();i++){ int u=belong[i]; group[u].push_back(i); for(auto &e:g[i]){ int v=belong[e]; if(u!=v) compressed.add_directed_edge(u,v,e.w); } } return ; } public: vector<int> belong; vector<vector<int>> group; Graph<T> compressed; StronglyConnectedComponents(Graph<T> &g):g(g),rg(g.size()),check(g.size()),belong(g.size(),-1){ for(int i=0;i<(int)g.size();i++)for(auto &e:g[i]) rg.add_directed_edge(e.to,e.from,e.w); build(); } // topological sort vector<int> get_DAG_order(){ vector<int> ret; for(int i=0;i<(int)group.size();i++)for(auto &j:group[i]) ret.push_back(j); return ret; } // g is not DAG or contain self-loop, return inf T LongestPath(){ for(int i=0;i<(int)g.size();i++){ for(auto &e:g[i]){ if(belong[i]==belong[e]) return -1; } } vector<int> ord=get_DAG_order(); vector<T> dp(g.size(),0); for(auto i:ord)for(auto &e:g[i]) dp[e]=max(dp[e],dp[i]+e.w); return (*max_element(begin(dp),end(dp))); } };