content: /*************************************************************************
   *  Compilation:  javac AcyclicLP.java
   *  Execution:    java AcyclicP V E
   *  Dependencies: EdgeWeightedDigraph.java DirectedEdge.java Topological.java
   *  Data files:   http://algs4.cs.princeton.edu/44sp/tinyEWDAG.txt
   *  
   *  Computes longeset paths in an edge-weighted acyclic digraph.
   *
   *  Remark: should probably check that graph is a DAG before running
   *
   *  % java AcyclicLP tinyEWDAG.txt 5
   *  5 to 0 (2.44)  5->1  0.32   1->3  0.29   3->6  0.52   6->4  0.93   4->0  0.38   
   *  5 to 1 (0.32)  5->1  0.32   
   *  5 to 2 (2.77)  5->1  0.32   1->3  0.29   3->6  0.52   6->4  0.93   4->7  0.37   7->2  0.34   
   *  5 to 3 (0.61)  5->1  0.32   1->3  0.29   
   *  5 to 4 (2.06)  5->1  0.32   1->3  0.29   3->6  0.52   6->4  0.93   
   *  5 to 5 (0.00)  
   *  5 to 6 (1.13)  5->1  0.32   1->3  0.29   3->6  0.52   
   *  5 to 7 (2.43)  5->1  0.32   1->3  0.29   3->6  0.52   6->4  0.93   4->7  0.37   
   *
   *************************************************************************/
  
  public class AcyclicLP {
      private double[] distTo;          // distTo[v] = distance  of longest s->v path
      private DirectedEdge[] edgeTo;    // edgeTo[v] = last edge on longest s->v path
  
      public AcyclicLP(EdgeWeightedDigraph G, int s) {
          distTo = new double[G.V()];
          edgeTo = new DirectedEdge[G.V()];
          for (int v = 0; v < G.V(); v++) distTo[v] = Double.NEGATIVE_INFINITY;
          distTo[s] = 0.0;
  
          // relax vertices in toplogical order
          Topological topological = new Topological(G);
          for (int v : topological.order()) {
              for (DirectedEdge e : G.adj(v))
                  relax(e);
          }
      }
  
      // relax edge e, but update if you find a *longer* path
      private void relax(DirectedEdge e) {
          int v = e.from(), w = e.to();
          if (distTo[w] < distTo[v] + e.weight()) {
              distTo[w] = distTo[v] + e.weight();
              edgeTo[w] = e;
          }       
      }
  
      // return length of the longest path from s to v, -infinity if no such path
      public double distTo(int v) {
          return distTo[v];
      }
  
      //  is there a  path from s to v?
      public boolean hasPathTo(int v) {
          return distTo[v] > Double.NEGATIVE_INFINITY;
      }
  
      // return view of longest path from s to v, null if no such path
      public Iterable<DirectedEdge> pathTo(int v) {
          if (!hasPathTo(v)) return null;
          Stack<DirectedEdge> path = new Stack<DirectedEdge>();
          for (DirectedEdge e = edgeTo[v]; e != null; e = edgeTo[e.from()]) {
              path.push(e);
          }
          return path;
      }
  
  
  
      public static void main(String[] args) {
          In in = new In(args[0]);
          int s = Integer.parseInt(args[1]);
          EdgeWeightedDigraph G = new EdgeWeightedDigraph(in);
  
          AcyclicLP lp = new AcyclicLP(G, s);
  
          for (int v = 0; v < G.V(); v++) {
              if (lp.hasPathTo(v)) {
                  StdOut.printf("%d to %d (%.2f)  ", s, v, lp.distTo(v));
                  for (DirectedEdge e : lp.pathTo(v)) {
                      StdOut.print(e + "   ");
                  }
                  StdOut.println();
              }
              else {
                  StdOut.printf("%d to %d         no path\n", s, v);
              }
          }
      }
  }
  