Find a vertex that all other vertices can be reached from in a digraph

Question

Given a directed graph, how can we determine whether or not there exists a vertex v, from which all other vertices are reachable. the algorithm should be as efficient as possibl

Answer 1

The solution can be found by taking the concept from Kosaraju's algorithm for Strongly Connected Components. The idea is based on the following fact:

If there exists a vertex (or vertices), from which all other vertices are reachable, then this vertex would have the maximum finish time in a DFS traversal. So, the solution would look like:

// Utility function to find mother vertex 
//(vertex from which all other vertices are reachable)

public void findMotherVertex() {
    int motherVertex=0;

    for (int i=0;i

The above algorithm takes O(V+E) time to solve the problem.