/* Implementation of Kosaraju's Algorithm to find out the strongly connected
components (SCCs) in a graph. Author:Anirban166
*/
#include <iostream>
#include <stack>
#include <vector>
/**
* Iterative function/method to print graph:
* @param a adjacency list representation of the graph
* @param V number of vertices
* @return void
**/
void print(const std::vector<std::vector<int> > &a, int V) {
for (int i = 0; i < V; i++) {
if (!a[i].empty()) {
std::cout << "i=" << i << "-->";
}
for (int j : a[i]) {
std::cout << j << " ";
}
if (!a[i].empty()) {
std::cout << std::endl;
}
}
}
/**
* //Recursive function/method to push vertices into stack passed as parameter:
* @param v vertices
* @param st stack passed by reference
* @param vis array to keep track of visited nodes (boolean type)
* @param adj adjacency list representation of the graph
* @return void
**/
void push_vertex(int v, std::stack<int> *st, std::vector<bool> *vis,
const std::vector<std::vector<int> > &adj) {
(*vis)[v] = true;
for (auto i = adj[v].begin(); i != adj[v].end(); i++) {
if ((*vis)[*i] == false) {
push_vertex(*i, st, vis, adj);
}
}
st->push(v);
}
/**
* //Recursive function/method to implement depth first traversal(dfs):
* @param v vertices
* @param vis array to keep track of visited nodes (boolean type)
* @param grev graph with reversed edges
* @return void
**/
void dfs(int v, std::vector<bool> *vis,
const std::vector<std::vector<int> > &grev) {
(*vis)[v] = true;
// cout<<v<<" ";
for (auto i = grev[v].begin(); i != grev[v].end(); i++) {
if ((*vis)[*i] == false) {
dfs(*i, vis, grev);
}
}
}
// function/method to implement Kosaraju's Algorithm:
/**
* Info about the method
* @param V vertices in graph
* @param adj array of vectors that represent a graph (adjacency list/array)
* @return int ( 0, 1, 2..and so on, only unsigned values as either there can be
no SCCs i.e. none(0) or there will be x no. of SCCs (x>0)) i.e. it returns the
count of (number of) strongly connected components (SCCs) in the graph.
(variable 'count_scc' within function)
**/
int kosaraju(int V, const std::vector<std::vector<int> > &adj) {
std::vector<bool> vis(V, false);
std::stack<int> st;
for (int v = 0; v < V; v++) {
if (vis[v] == false) {
push_vertex(v, &st, &vis, adj);
}
}
// making new graph (grev) with reverse edges as in adj[]:
std::vector<std::vector<int> > grev(V);
for (int i = 0; i < V + 1; i++) {
for (auto j = adj[i].begin(); j != adj[i].end(); j++) {
grev[*j].push_back(i);
}
}
// cout<<"grev="<<endl; ->debug statement
// print(grev,V); ->debug statement
// reinitialise visited to 0
for (int i = 0; i < V; i++) vis[i] = false;
int count_scc = 0;
while (!st.empty()) {
int t = st.top();
st.pop();
if (vis[t] == false) {
dfs(t, &vis, grev);
count_scc++;
}
}
// cout<<"count_scc="<<count_scc<<endl; //in case you want to print here
// itself, uncomment & change return type of function to void.
return count_scc;
}
// All critical/corner cases have been taken care of.
// Input your required values: (not hardcoded)
int main() {
int t = 0;
std::cin >> t;
while (t--) {
int a = 0, b = 0; // a->number of nodes, b->directed edges.
std::cin >> a >> b;
int m = 0, n = 0;
std::vector<std::vector<int> > adj(a + 1);
for (int i = 0; i < b; i++) // take total b inputs of 2 vertices each
// required to form an edge.
{
std::cin >> m >> n; // take input m,n denoting edge from m->n.
adj[m].push_back(n);
}
// pass number of nodes and adjacency array as parameters to function:
std::cout << kosaraju(a, adj) << std::endl;
}
return 0;
}