Transitive Closure of a Graph using DFS

TransitiveClosure.java

// Given a directed graph, find out if a vertex v is reachable from another vertex u for all vertex pairs (u, v) in the given graph.
import java.util.LinkedList;

class Graph
{
    int V; // No. of vertices
    boolean [][]tc; // To store transitive closure
    LinkedList<Integer> adj[]; // array of adjacency lists
    
    public Graph(int V)
    {
        this.V = V;
        adj = new LinkedList[V];

        tc = new boolean[V][V];
        for (int i=0; i<V; i++)
        {
            tc[i] = new boolean[V];
            adj[i] = new LinkedList<Integer>();
            for(int j =0 ;j < V; j++)
                tc[i][j] = false;
        }
    }

    // function to add an edge to graph
    public void addEdge(int v, int w) 
    { 
        adj[v].addLast(w); 
    }

    // prints transitive closure matrix
    public void transitiveClosure()
    {
        // Call the recursive helper function to print DFS
        // traversal starting from all vertices one by one
        for (int i = 0; i < V; i++)
            DFSUtil(i, i); // Every vertex is reachable from self.

        for (int i=0; i<V; i++)
        {
            for (int j=0; j<V; j++)
                System.out.print( tc[i][j] + " ");
            System.out.println();
        }
    }


    public void DFSUtil(int s, int v)
    {
        // Mark reachability from s to t as true.
        System.out.println(" s: " + s + " v: " + v);
        tc[s][v] = true;
        for (Integer i : adj[v])
            if (tc[s][i] == false)
                DFSUtil(s, i);
    }
    
    public static void main(String[] args)
    {
        // Create a graph given in the above diagram
        Graph g = new Graph(4);
        g.addEdge(0, 1);
        g.addEdge(0, 2);
        g.addEdge(1, 2);
        g.addEdge(2, 0);
        g.addEdge(2, 3);
        g.addEdge(3, 3);

        System.out.println( "Transitive closure matrix is ");
        g.transitiveClosure();
    }
}