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

import java.util.*;

public class FindMotherVertex {
    public static void main(String[] arg) {
        List edges = Arrays.asList(
            new Edges(0, 1), new Edges(0, 2),
            new Edges(1, 3),
            new Edges(4, 1),
            new Edges(5, 2), new Edges(5, 6),
            new Edges(6, 4),
            new Edges(6, 0)
        );
        findMotherVertex(graph);

    }
    public static void findMotherVertex(Graph graph) {
        int motherVertex =  0;
        boolean[] visited = new boolean[7];

        for (int i=0;i<7;i++) {  
            if (visited[i] == false) {  //marked - boolean array storing visited vertices
                DFS(graph,i,visited);
                motherVertex= i;
            }

        }

        //Check for this vertex if all other vertices have been already visited
        //Otherwise no mother vertex exists

        for (int i=0;i<6;i++) {
            if (!visited[i]){ visited[i] = false;}

        }

        System.out.println("Mother vertex is : " + motherVertex);
    }

    public static void DFS(Graph graph, int v,boolean[] visited) {

        //create a stack used to do DFS
        Stack stack = new Stack<>();
        stack.add(v);
        //Run While queue is empty

        while (!stack.isEmpty()) {
            //Pop vertex from stack
            v = stack.pop();

            if (visited[v])
                continue;
            visited[v] = true;
            System.out.print("(" + v + ")" + "===>");
// do for every edge
            List list = graph.adj.get(v);
            for (int i = list.size() - 1; i >= 0; i--) {
                int u = list.get(i);
                if (!visited[u]) ;
                stack.push(u);
            }
        }

    }


    static class Graph {

        //List of List to represent Adajacency List
        List> adj = new ArrayList<>();
        //Constructor to construct Graph

        public Graph(List edges) {
            //Allocate memory for adjacency List
            for (int i = 0; i < edges.size(); i++) {
                adj.add(i, new ArrayList<>());
            }

            //Add edges to the undirected Graph
            for (Edges curr : edges) {
                adj.get(curr.src).add(curr.desc);


            }

        }

    }
}