Artifact 1f3d1cfa1b9a8b8a251abf74979b2be32b887f89
//-------------------------------------------------------------
// Strongly Connected Component of a Directed Graph
// O(E)
//
// Verified by
// - SRM 499 Div1 LV3
//
// Using "Spagetthi Source"'s one path algorithm
//-------------------------------------------------------------
template<typename T>
class IdGen
{
map<T, int> v2id_;
vector<T> id2v_;
public:
int v2id(const T& v) {
if( !v2id_.count(v) ) { v2id_[v] = size(); id2v_.push_back(v); }
return v2id_[v];
}
const T& id2v(int i) const { return id2v_[i]; }
int size() const { return id2v_.size(); }
};
template<typename Vert>
class SCC
{
IdGen<Vert> idgen;
vector< vector<int> > G;
public:
void addVert( Vert s_ )
{
int s = idgen.v2id(s_);
if( s >= G.size() ) G.resize(s+1);
}
void addEdge( Vert s_, Vert t_ )
{
int s = idgen.v2id(s_), t = idgen.v2id(t_);
if( max(s,t) >= G.size() ) G.resize(max(s,t)+1);
G[s].push_back(t);
}
void scc()
{
int N = G.size();
dfs_no.assign(N, 0);
dfs_lo.assign(N, 0);
pending = stack<int>();
scc_id.assign(N, -1);
scc_list.clear();
scc_children.clear();
for(int v=0; v<N; ++v)
dfs(v);
}
vector<int> scc_id; // which scc does the vert belong to?
vector< vector<int> > scc_list; // list of nodes in the scc
vector< vector<int> > scc_children; // forest relationship of sccs
private:
int no;
vector<int> dfs_no; // 1-origin dfs-visit ID
vector<int> dfs_lo; // the least ID in the vert's scc
stack<int> pending; // current unclassigied verts
void dfs(int v)
{
// visit v if not yet
if( dfs_no[v] )
return;
dfs_no[v] = dfs_lo[v] = ++no;
pending.push(v);
// visit children
for(int i=0; i<G[v].size(); ++i) {
int u = G[v][i];
dfs( u );
if( scc_id[u] == -1 )
dfs_lo[v] = min( dfs_lo[v], dfs_lo[u] );
}
// when v is the representative of scc
if( dfs_no[v] == dfs_lo[v] ) {
vector<int> scc;
for(;;) {
int w = pending.top(); pending.pop();
scc.push_back(w);
scc_id[w] = scc_list.size();
if( w == v ) break;
}
scc_list.push_back(scc);
set<int> children;
for(int j=0; j<scc.size(); ++j)
for(int i=0; i<G[scc[j]].size(); ++i)
children.insert( scc_id[G[scc[j]][i]] );
children.erase(scc_id[v]);
scc_children.push_back( vector<int>(children.begin(), children.end()) );
}
}
};