Tarjan_Algorithm.cpp

#include<iostream>
#include <list>
#include <stack>
#define NIL -1
using namespace std;

// A class that represents an directed graph
class Graph
{
	int V; // No. of vertices
	list<int> *adj; // A dynamic array of adjacency lists

	// A Recursive DFS based function used by SCC()
	void SCCUtil(int u, int disc[], int low[],
				stack<int> *st, bool stackMember[]);
public:
	Graph(int V); // Constructor
	void addEdge(int v, int w); // function to add an edge to graph
	void SCC(); // prints strongly connected components
};

Graph::Graph(int V)
{
	this->V = V;
	adj = new list<int>[V];
}

void Graph::addEdge(int v, int w)
{
	adj[v].push_back(w);
}

// A recursive function that finds and prints strongly connected
// components using DFS traversal
// u --> The vertex to be visited next
// disc[] --> Stores discovery times of visited vertices
// low[] -- >> earliest visited vertex (the vertex with minimum
//			 discovery time) that can be reached from subtree
//			 rooted with current vertex
// *st -- >> To store all the connected ancestors (could be part
//		 of SCC)
// stackMember[] --> bit/index array for faster check whether
//				 a node is in stack
void Graph::SCCUtil(int u, int disc[], int low[], stack<int> *st,
					bool stackMember[])
{
	// A static variable is used for simplicity, we can avoid use
	// of static variable by passing a pointer.
	static int time = 0;

	// Initialize discovery time and low value
	disc[u] = low[u] = ++time;
	st->push(u);
	stackMember[u] = true;

	// Go through all vertices adjacent to this
	list<int>::iterator i;
	for (i = adj[u].begin(); i != adj[u].end(); ++i)
	{
		int v = *i; // v is current adjacent of 'u'

		// If v is not visited yet, then recur for it
		if (disc[v] == -1)
		{
			SCCUtil(v, disc, low, st, stackMember);

			// Check if the subtree rooted with 'v' has a
			// connection to one of the ancestors of 'u'
			// Case 1 (per above discussion on Disc and Low value)
			low[u] = min(low[u], low[v]);
		}

		// Update low value of 'u' only of 'v' is still in stack
		// (i.e. it's a back edge, not cross edge).
		// Case 2 (per above discussion on Disc and Low value)
		else if (stackMember[v] == true)
			low[u] = min(low[u], disc[v]);
	}

	// head node found, pop the stack and print an SCC
	int w = 0; // To store stack extracted vertices
	if (low[u] == disc[u])
	{
		while (st->top() != u)
		{
			w = (int) st->top();
			cout << w << " ";
			stackMember[w] = false;
			st->pop();
		}
		w = (int) st->top();
		cout << w << "\n";
		stackMember[w] = false;
		st->pop();
	}
}

// The function to do DFS traversal. It uses SCCUtil()
void Graph::SCC()
{
	int *disc = new int[V];
	int *low = new int[V];
	bool *stackMember = new bool[V];
	stack<int> *st = new stack<int>();

	// Initialize disc and low, and stackMember arrays
	for (int i = 0; i < V; i++)
	{
		disc[i] = NIL;
		low[i] = NIL;
		stackMember[i] = false;
	}

	// Call the recursive helper function to find strongly
	// connected components in DFS tree with vertex 'i'
	for (int i = 0; i < V; i++)
		if (disc[i] == NIL)
			SCCUtil(i, disc, low, st, stackMember);
}

// Driver program to test above function
int main()
{
	cout << "\nSCCs in first graph \n";
	Graph g1(5);
	g1.addEdge(1, 0);
	g1.addEdge(0, 2);
	g1.addEdge(2, 1);
	g1.addEdge(0, 3);
	g1.addEdge(3, 4);
	g1.SCC();

	cout << "\nSCCs in second graph \n";
	Graph g2(4);
	g2.addEdge(0, 1);
	g2.addEdge(1, 2);
	g2.addEdge(2, 3);
	g2.SCC();

	cout << "\nSCCs in third graph \n";
	Graph g3(7);
	g3.addEdge(0, 1);
	g3.addEdge(1, 2);
	g3.addEdge(2, 0);
	g3.addEdge(1, 3);
	g3.addEdge(1, 4);
	g3.addEdge(1, 6);
	g3.addEdge(3, 5);
	g3.addEdge(4, 5);
	g3.SCC();

	cout << "\nSCCs in fourth graph \n";
	Graph g4(11);
	g4.addEdge(0,1);g4.addEdge(0,3);
	g4.addEdge(1,2);g4.addEdge(1,4);
	g4.addEdge(2,0);g4.addEdge(2,6);
	g4.addEdge(3,2);
	g4.addEdge(4,5);g4.addEdge(4,6);
	g4.addEdge(5,6);g4.addEdge(5,7);g4.addEdge(5,8);g4.addEdge(5,9);
	g4.addEdge(6,4);
	g4.addEdge(7,9);
	g4.addEdge(8,9);
	g4.addEdge(9,8);
	g4.SCC();

	cout << "\nSCCs in fifth graph \n";
	Graph g5(5);
	g5.addEdge(0,1);
	g5.addEdge(1,2);
	g5.addEdge(2,3);
	g5.addEdge(2,4);
	g5.addEdge(3,0);
	g5.addEdge(4,2);
	g5.SCC();

	return 0;
}