content: /*************************************************************************
   *  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
   *
   *************************************************************************/
  
  public class TransitiveClosure {
      private DirectedDFS[] tc;  // tc[v] = reachable from v
  
      public TransitiveClosure(Digraph G) {
          tc = new DirectedDFS[G.V()];
          for (int v = 0; v < G.V(); v++)
              tc[v] = new DirectedDFS(G, v);
      }
  
      public boolean reachable(int v, int w) {
          return tc[v].marked(w);
      }
  
      // test client
      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();
          }
      }
  
  }
  