b57cc94f1b 2011-10-08        kinaba: 
b57cc94f1b 2011-10-08        kinaba: //-------------------------------------------------------------
b57cc94f1b 2011-10-08        kinaba: // Strongly Connected Component of a Directed Graph
b57cc94f1b 2011-10-08        kinaba: //   O(E)
b57cc94f1b 2011-10-08        kinaba: //
b57cc94f1b 2011-10-08        kinaba: // Verified by
b57cc94f1b 2011-10-08        kinaba: //   - SRM 499 Div1 LV3
b57cc94f1b 2011-10-08        kinaba: //
109f2a9050 2012-09-08        kinaba: // Using "Spagetthi Source"'s one pass algorithm
b57cc94f1b 2011-10-08        kinaba: //-------------------------------------------------------------
b57cc94f1b 2011-10-08        kinaba: 
b57cc94f1b 2011-10-08        kinaba: template<typename T>
b57cc94f1b 2011-10-08        kinaba: class IdGen
b57cc94f1b 2011-10-08        kinaba: {
b57cc94f1b 2011-10-08        kinaba: 	map<T, int> v2id_;
b57cc94f1b 2011-10-08        kinaba: 	vector<T>   id2v_;
b57cc94f1b 2011-10-08        kinaba: public:
b57cc94f1b 2011-10-08        kinaba: 	int v2id(const T& v) {
b57cc94f1b 2011-10-08        kinaba: 		if( !v2id_.count(v) ) { v2id_[v] = size(); id2v_.push_back(v); }
b57cc94f1b 2011-10-08        kinaba: 		return v2id_[v];
b57cc94f1b 2011-10-08        kinaba: 	}
b57cc94f1b 2011-10-08        kinaba: 	const T& id2v(int i) const { return id2v_[i]; }
b57cc94f1b 2011-10-08        kinaba: 	int size() const { return id2v_.size(); }
b57cc94f1b 2011-10-08        kinaba: };
b57cc94f1b 2011-10-08        kinaba: 
b57cc94f1b 2011-10-08        kinaba: template<typename Vert>
b57cc94f1b 2011-10-08        kinaba: class SCC
b57cc94f1b 2011-10-08        kinaba: {
b57cc94f1b 2011-10-08        kinaba: 	IdGen<Vert> idgen;
b57cc94f1b 2011-10-08        kinaba: 	vector< vector<int> > G;
b57cc94f1b 2011-10-08        kinaba: 
b57cc94f1b 2011-10-08        kinaba: public:
b57cc94f1b 2011-10-08        kinaba: 	void addVert( Vert s_ )
b57cc94f1b 2011-10-08        kinaba: 	{
b57cc94f1b 2011-10-08        kinaba: 		int s = idgen.v2id(s_);
b57cc94f1b 2011-10-08        kinaba: 		if( s >= G.size() ) G.resize(s+1);
b57cc94f1b 2011-10-08        kinaba: 	}
b57cc94f1b 2011-10-08        kinaba: 
b57cc94f1b 2011-10-08        kinaba: 	void addEdge( Vert s_, Vert t_ )
b57cc94f1b 2011-10-08        kinaba: 	{
b57cc94f1b 2011-10-08        kinaba: 		int s = idgen.v2id(s_), t = idgen.v2id(t_);
b57cc94f1b 2011-10-08        kinaba: 		if( max(s,t) >= G.size() ) G.resize(max(s,t)+1);
b57cc94f1b 2011-10-08        kinaba: 		G[s].push_back(t);
b57cc94f1b 2011-10-08        kinaba: 	}
b57cc94f1b 2011-10-08        kinaba: 
b57cc94f1b 2011-10-08        kinaba: 	void scc()
b57cc94f1b 2011-10-08        kinaba: 	{
b57cc94f1b 2011-10-08        kinaba: 		int N = G.size();
1c5fa6584e 2015-11-27        kinaba: 		no = 0; // whatever small enough
b57cc94f1b 2011-10-08        kinaba: 		dfs_no.assign(N, 0);
b57cc94f1b 2011-10-08        kinaba: 		dfs_lo.assign(N, 0);
b57cc94f1b 2011-10-08        kinaba: 		pending = stack<int>();
b57cc94f1b 2011-10-08        kinaba: 		scc_id.assign(N, -1);
b57cc94f1b 2011-10-08        kinaba: 		scc_list.clear();
b57cc94f1b 2011-10-08        kinaba: 		scc_children.clear();
b57cc94f1b 2011-10-08        kinaba: 		for(int v=0; v<N; ++v)
b57cc94f1b 2011-10-08        kinaba: 			dfs(v);
b57cc94f1b 2011-10-08        kinaba: 	}
b57cc94f1b 2011-10-08        kinaba: 
b57cc94f1b 2011-10-08        kinaba: 	vector<int> scc_id; // which scc does the vert belong to?
b57cc94f1b 2011-10-08        kinaba: 	vector< vector<int> > scc_list;     // list of nodes in the scc
b57cc94f1b 2011-10-08        kinaba: 	vector< vector<int> > scc_children; // forest relationship of sccs
b57cc94f1b 2011-10-08        kinaba: 
b57cc94f1b 2011-10-08        kinaba: private:
b57cc94f1b 2011-10-08        kinaba: 	int no;
b57cc94f1b 2011-10-08        kinaba: 	vector<int> dfs_no; // 1-origin dfs-visit ID
b57cc94f1b 2011-10-08        kinaba: 	vector<int> dfs_lo; // the least ID in the vert's scc
b57cc94f1b 2011-10-08        kinaba: 	stack<int> pending; // current unclassigied verts
b57cc94f1b 2011-10-08        kinaba: 
b57cc94f1b 2011-10-08        kinaba: 	void dfs(int v)
b57cc94f1b 2011-10-08        kinaba: 	{
b57cc94f1b 2011-10-08        kinaba: 		// visit v if not yet
b57cc94f1b 2011-10-08        kinaba: 		if( dfs_no[v] )
b57cc94f1b 2011-10-08        kinaba: 			return;
b57cc94f1b 2011-10-08        kinaba: 		dfs_no[v] = dfs_lo[v] = ++no;
b57cc94f1b 2011-10-08        kinaba: 		pending.push(v);
b57cc94f1b 2011-10-08        kinaba: 
b57cc94f1b 2011-10-08        kinaba: 		// visit children
b57cc94f1b 2011-10-08        kinaba: 		for(int i=0; i<G[v].size(); ++i) {
b57cc94f1b 2011-10-08        kinaba: 			int u = G[v][i];
b57cc94f1b 2011-10-08        kinaba: 			dfs( u );
b57cc94f1b 2011-10-08        kinaba: 			if( scc_id[u] == -1 )
b57cc94f1b 2011-10-08        kinaba: 				dfs_lo[v] = min( dfs_lo[v], dfs_lo[u] );
b57cc94f1b 2011-10-08        kinaba: 		}
b57cc94f1b 2011-10-08        kinaba: 
b57cc94f1b 2011-10-08        kinaba: 		// when v is the representative of scc
b57cc94f1b 2011-10-08        kinaba: 		if( dfs_no[v] == dfs_lo[v] ) {
b57cc94f1b 2011-10-08        kinaba: 			vector<int> scc;
b57cc94f1b 2011-10-08        kinaba: 			for(;;) {
b57cc94f1b 2011-10-08        kinaba: 				int w = pending.top(); pending.pop();
b57cc94f1b 2011-10-08        kinaba: 				scc.push_back(w);
b57cc94f1b 2011-10-08        kinaba: 				scc_id[w] = scc_list.size();
b57cc94f1b 2011-10-08        kinaba: 				if( w == v ) break;
b57cc94f1b 2011-10-08        kinaba: 			}
b57cc94f1b 2011-10-08        kinaba: 			scc_list.push_back(scc);
b57cc94f1b 2011-10-08        kinaba: 
b57cc94f1b 2011-10-08        kinaba: 			set<int> children;
b57cc94f1b 2011-10-08        kinaba: 			for(int j=0; j<scc.size(); ++j)
b57cc94f1b 2011-10-08        kinaba: 				for(int i=0; i<G[scc[j]].size(); ++i)
b57cc94f1b 2011-10-08        kinaba: 					children.insert( scc_id[G[scc[j]][i]] );
b57cc94f1b 2011-10-08        kinaba: 			children.erase(scc_id[v]);
b57cc94f1b 2011-10-08        kinaba: 			scc_children.push_back( vector<int>(children.begin(), children.end()) );
b57cc94f1b 2011-10-08        kinaba: 		}
b57cc94f1b 2011-10-08        kinaba: 	}
b57cc94f1b 2011-10-08        kinaba: };