import edu.princeton.cs.introcs.In;
import edu.princeton.cs.introcs.StdOut;

/*************************************************************************
 *  Compilation:  javac TransitiveClosure.java
 *  Execution:    java TransitiveClosure filename.txt
 *  Dependencies: Digraph.java DepthFirstDirectedPaths.java In.java StdOut.java
 *  Data files:   http://algs4.cs.princeton.edu/42directed/tinyDG.txt
 *
 *  Compute transitive closure of a digraph and support
 *  reachability queries.
 *
 *  Preprocessing time: O(V(E + V)) time.
 *  Query time: O(1).
 *  Space: O(V^2).
 *
 *  % java TransitiveClosure tinyDG.txt
 *         0  1  2  3  4  5  6  7  8  9 10 11 12
 *  --------------------------------------------
 *    0:   T  T  T  T  T  T                     
 *    1:      T                                 
 *    2:   T  T  T  T  T  T                     
 *    3:   T  T  T  T  T  T                     
 *    4:   T  T  T  T  T  T                     
 *    5:   T  T  T  T  T  T                     
 *    6:   T  T  T  T  T  T  T        T  T  T  T
 *    7:   T  T  T  T  T  T  T  T  T  T  T  T  T
 *    8:   T  T  T  T  T  T  T  T  T  T  T  T  T
 *    9:   T  T  T  T  T  T           T  T  T  T
 *   10:   T  T  T  T  T  T           T  T  T  T
 *   11:   T  T  T  T  T  T           T  T  T  T
 *   12:   T  T  T  T  T  T           T  T  T  T
 *
 *************************************************************************/

/**
 *  The  TransitiveClosure  class represents a data type for 
 *  computing the transitive closure of a digraph.
 *   
 *  This implementation runs depth-first search from each vertex.
 *  The constructor takes time proportional to  V ( V  +  E )
 *  (in the worst case) and uses space proportional to  V <sup>2</sup>,
 *  where  V  is the number of vertices and  E  is the number of edges.
 *   
 *  For additional documentation, see <a href="/algs4/42digraph">Section 4.2</a> of
 *   Algorithms, 4th Edition  by Robert Sedgewick and Kevin Wayne.
 *
 *  @author Robert Sedgewick
 *  @author Kevin Wayne
 */
public class TransitiveClosure {
    private DirectedDFS[] tc;  // tc[v] = reachable from v

    /**
     * Computes the transitive closure of the digraph  G .
     * @param G the digraph
     */
    public TransitiveClosure(Digraph G) {
        tc = new DirectedDFS[G.V()];
        for (int v = 0; v < G.V(); v++)
            tc[v] = new DirectedDFS(G, v);
    }

    /**
     * Is there a directed path from vertex  v  to vertex  w  in the digraph?
     * @param v the source vertex
     * @param w the target vertex
     * @return  true  if there is a directed path from  v  to  w ,
     *     false  otherwise
     */
    public boolean reachable(int v, int w) {
        return tc[v].marked(w);
    }

    /**
     * Unit tests the  TransitiveClosure  data type.
     */
    public static void main(String[] args) {
        In in = new In(args[0]);
        Digraph G = new Digraph(in);

        TransitiveClosure tc = new TransitiveClosure(G);

        // print header
        StdOut.print("     ");
        for (int v = 0; v < G.V(); v++)
            StdOut.printf("%3d", v);
        StdOut.println();
        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.reachable(v, w)) StdOut.printf("  T");
                else                    StdOut.printf("   ");
            }
            StdOut.println();
        }
    }

}