/******************************************************************************
 *  Compilation:  javac WarshallTC.java
 *  Execution:    java  WarshallTC V E
 *  Dependencies: AdjMatrixDigraph.java StdOut.java
 *
 *  Compute transitive closure of a digraph G and support
 *  reachability queries.
 *
 *  Preprocessing time: O(V^3) time.
 *  Query time: O(1).
 *  Space: O(V^2).
 *
 *  % java WarshallTC 10 20
 *  10 20
 *  0: 9 2 7 5
 *  1: 6 7
 *  2:
 *  3: 9 9 9 7 6
 *  4: 7
 *  5: 7
 *  6: 7 1
 *  7: 2
 *  8: 7 6 0
 *  9: 2
 *
 *  Transitive closure
 *  -----------------------------------
 *         0  1  2  3  4  5  6  7  8  9
 *    0:   x     x        x     x     x
 *    1:      x  x           x  x
 *    2:         x
 *    3:      x  x  x        x  x     x
 *    4:         x     x        x
 *    5:         x        x     x
 *    6:      x  x           x  x
 *    7:         x              x
 *    8:   x  x  x        x  x  x  x  x
 *    9:         x                    x
 *
 ******************************************************************************/

public class WarshallTC {
    private boolean[][] tc;    // tc[v][w] = true iff path from v to w

    public WarshallTC(AdjMatrixDigraph G) {

        // initialize tc[][]
        int V = G.V();
        tc = new boolean[V][V];
        for (int v = 0; v < V; v++) {
            for (int w : G.adj(v)) {
                tc[v][w] = true;
            }
            tc[v][v] = true;
        }

        // Warshall's algorithm
        for (int i = 0; i < V; i++) {
            for (int v = 0; v < V; v++) {
                if (!tc[v][i]) continue;        // optimization
                for (int w = 0; w < V; w++) {
                    if (tc[v][i] && tc[i][w]) tc[v][w] = true;
                }
            }
        }

    }

    // is there a directed path from v to w?
    public boolean hasPath(int v, int w) {
        return tc[v][w];
    }


    // test client
    public static void main(String[] args) {
        int V = Integer.parseInt(args[0]);
        int E = Integer.parseInt(args[1]);
        AdjMatrixDigraph G = new AdjMatrixDigraph(V, E);
        StdOut.println(G);
        WarshallTC tc = new WarshallTC(G);

        // print header
        StdOut.println("Transitive closure");
        StdOut.println("-----------------------------------");
        StdOut.print("     ");
        for (int v = 0; v < G.V(); v++)
            StdOut.printf("%3d", v);
        StdOut.println();

        // print transitive closure
        for (int v = 0; v < G.V(); v++) {
            StdOut.printf("%3d: ", v);
            for (int w = 0; w < G.V(); w++) {
                if (tc.hasPath(v, w)) StdOut.printf("  x");
                else                  StdOut.printf("   ");
            }
            StdOut.println();
        }
    }

}