content: /*************************************************************************
   *  Compilation:  javac DijkstraSP.java
   *  Execution:    java DijkstraSP input.txt s
   *  Dependencies: EdgeWeightedDigraph.java IndexMinPQ.java Stack.java DirectedEdge.java
   *  Data files:   http://algs4.cs.princeton.edu/44sp/tinyEWD.txt
   *                http://algs4.cs.princeton.edu/44sp/mediumEWD.txt
   *                http://algs4.cs.princeton.edu/44sp/largeEWD.txt
   *
   *  Dijkstra's algorithm. Computes the shortest path tree.
   *  Assumes all weights are nonnegative.
   *
   *  % java DijkstraSP tinyEWD.txt 0
   *  0 to 0 (0.00)  
   *  0 to 1 (1.05)  0->4  0.38   4->5  0.35   5->1  0.32   
   *  0 to 2 (0.26)  0->2  0.26   
   *  0 to 3 (0.99)  0->2  0.26   2->7  0.34   7->3  0.39   
   *  0 to 4 (0.38)  0->4  0.38   
   *  0 to 5 (0.73)  0->4  0.38   4->5  0.35   
   *  0 to 6 (1.51)  0->2  0.26   2->7  0.34   7->3  0.39   3->6  0.52   
   *  0 to 7 (0.60)  0->2  0.26   2->7  0.34   
   *
   *  % java DijkstraSP mediumEWD.txt 0
   *  0 to 0 (0.00)  
   *  0 to 1 (0.71)  0->44  0.06   44->93  0.07   ...  107->1  0.07   
   *  0 to 2 (0.65)  0->44  0.06   44->231  0.10  ...  42->2  0.11   
   *  0 to 3 (0.46)  0->97  0.08   97->248  0.09  ...  45->3  0.12   
   *  0 to 4 (0.42)  0->44  0.06   44->93  0.07   ...  77->4  0.11   
   *  ...
   *
   *************************************************************************/
  
  public class DijkstraSP {
      private double[] distTo;          // distTo[v] = distance  of shortest s->v path
      private DirectedEdge[] edgeTo;    // edgeTo[v] = last edge on shortest s->v path
      private IndexMinPQ<Double> pq;    // priority queue of vertices
  
      public DijkstraSP(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.POSITIVE_INFINITY;
          distTo[s] = 0.0;
  
          // relax vertices in order of distance from s
          pq = new IndexMinPQ<Double>(G.V());
          pq.insert(s, distTo[s]);
          while (!pq.isEmpty()) {
              int v = pq.delMin();
              for (DirectedEdge e : G.adj(v))
                  relax(e);
          }
  
          // check optimality conditions
          assert check(G, s);
      }
  
      // relax edge e and update pq if changed
      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;
              if (pq.contains(w)) pq.change(w, distTo[w]);
              else                pq.insert(w, distTo[w]);
          }
      }
  
      // length of shortest path from s to v
      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.POSITIVE_INFINITY;
      }
  
      // shortest path from s to v as an Iterable, 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;
      }
  
  
      // check optimality conditions:
      // (i) for all edges e:            distTo[e.to()] <= distTo[e.from()] + e.weight()
      // (ii) for all edge e on the SPT: distTo[e.to()] == distTo[e.from()] + e.weight()
      private boolean check(EdgeWeightedDigraph G, int s) {
  
          // check that edge weights are nonnegative
          for (DirectedEdge e : G.edges()) {
              if (e.weight() < 0) {
                  System.err.println("negative edge weight detected");
                  return false;
              }
          }
  
          // check that distTo[v] and edgeTo[v] are consistent
          if (distTo[s] != 0.0 || edgeTo[s] != null) {
              System.err.println("distTo[s] and edgeTo[s] inconsistent");
              return false;
          }
          for (int v = 0; v < G.V(); v++) {
              if (v == s) continue;
              if (edgeTo[v] == null && distTo[v] != Double.POSITIVE_INFINITY) {
                  System.err.println("distTo[] and edgeTo[] inconsistent");
                  return false;
              }
          }
  
          // check that all edges e = v->w satisfy distTo[w] <= distTo[v] + e.weight()
          for (int v = 0; v < G.V(); v++) {
              for (DirectedEdge e : G.adj(v)) {
                  int w = e.to();
                  if (distTo[v] + e.weight() < distTo[w]) {
                      System.err.println("edge " + e + " not relaxed");
                      return false;
                  }
              }
          }
  
          // check that all edges e = v->w on SPT satisfy distTo[w] == distTo[v] + e.weight()
          for (int w = 0; w < G.V(); w++) {
              if (edgeTo[w] == null) continue;
              DirectedEdge e = edgeTo[w];
              int v = e.from();
              if (w != e.to()) return false;
              if (distTo[v] + e.weight() != distTo[w]) {
                  System.err.println("edge " + e + " on shortest path not tight");
                  return false;
              }
          }
          return true;
      }
  
  
      public static void main(String[] args) {
          In in = new In(args[0]);
          EdgeWeightedDigraph G = new EdgeWeightedDigraph(in);
          int s = Integer.parseInt(args[1]);
  
          // compute shortest paths
          DijkstraSP sp = new DijkstraSP(G, s);
  
  
          // print shortest path
          for (int t = 0; t < G.V(); t++) {
              if (sp.hasPathTo(t)) {
                  StdOut.printf("%d to %d (%.2f)  ", s, t, sp.distTo(t));
                  if (sp.hasPathTo(t)) {
                      for (DirectedEdge e : sp.pathTo(t)) {
                          StdOut.print(e + "   ");
                      }
                  }
                  StdOut.println();
              }
              else {
                  StdOut.printf("%d to %d         no path\n", s, t);
              }
          }
      }
  
  }
  