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// Exercise 4.4.28 (Solution published at http://algs4.cs.princeton.edu/)
package algs44;
import stdlib.*;
import algs13.Stack;
import algs42.Topological;
/* ***********************************************************************
 *  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 longest 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 final double[] distTo;          // distTo[v] = distance  of longest s->v path
  private final 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<>();
    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.format("%d to %d (%.2f)  ", s, v, lp.distTo(v));
        for (DirectedEdge e : lp.pathTo(v)) {
          StdOut.print(e + "   ");
        }
        StdOut.println();
      }
      else {
        StdOut.format("%d to %d         no path\n", s, v);
      }
    }
  }
}