content: /*************************************************************************
   *  Compilation:  javac BellmanFordSP.java
   *  Execution:    java BellmanFordSP filename.txt s
   *  Dependencies: EdgeWeightedDigraph.java DirectedEdge.java Queue.java
   *                EdgeWeightedDirectedCycle.java
   *  Data files:   http://algs4.cs.princeton.edu/44sp/tinyEWDn.txt
   *                http://algs4.cs.princeton.edu/44sp/mediumEWDnc.txt
   *
   *  Bellman-Ford shortest path algorithm. Computes the shortest path tree in
   *  edge-weighted digraph G from vertex s, or finds a negative cost cycle
   *  reachable from s.
   *
   *  % java BellmanFordSP tinyEWDn.txt 0
   *  0 to 0 ( 0.00)  
   *  0 to 1 ( 0.93)  0->2  0.26   2->7  0.34   7->3  0.39   3->6  0.52   6->4 -1.25   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 ( 0.26)  0->2  0.26   2->7  0.34   7->3  0.39   3->6  0.52   6->4 -1.25   
   *  0 to 5 ( 0.61)  0->2  0.26   2->7  0.34   7->3  0.39   3->6  0.52   6->4 -1.25   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 BellmanFordSP tinyEWDnc.txt 0
   *  4->5  0.35
   *  5->4 -0.66
   *
   *************************************************************************/
  
  public class BellmanFordSP {
      private double[] distTo;               // distTo[v] = distance  of shortest s->v path
      private DirectedEdge[] edgeTo;         // edgeTo[v] = last edge on shortest s->v path
      private boolean[] onQueue;             // onQueue[v] = is v currently on the queue?
      private Queue<Integer> queue;          // queue of vertices to relax
      private int cost;                      // number of calls to relax()
      private Iterable<DirectedEdge> cycle;  // negative cycle (or null if no such cycle)
  
      public BellmanFordSP(EdgeWeightedDigraph G, int s) {
          distTo  = new double[G.V()];
          edgeTo  = new DirectedEdge[G.V()];
          onQueue = new boolean[G.V()];
          for (int v = 0; v < G.V(); v++)
              distTo[v] = Double.POSITIVE_INFINITY;
          distTo[s] = 0.0;
  
          // Bellman-Ford algorithm
          queue = new Queue<Integer>();
          queue.enqueue(s);
          onQueue[s] = true;
          while (!queue.isEmpty() && !hasNegativeCycle()) {
              int v = queue.dequeue();
              onQueue[v] = false;
              relax(G, v);
          }
  
          assert check(G, s);
      }
  
      // relax vertex v and put other endpoints on queue if changed
      private void relax(EdgeWeightedDigraph G, int v) {
          for (DirectedEdge e : G.adj(v)) {
              int w = e.to();
              if (distTo[w] > distTo[v] + e.weight()) {
                  distTo[w] = distTo[v] + e.weight();
                  edgeTo[w] = e;
                  if (!onQueue[w]) {
                      queue.enqueue(w);
                      onQueue[w] = true;
                  }
              }
              if (cost++ % G.V() == 0)
                  findNegativeCycle();
          }
      }
  
  
      // is there a negative cycle reachable from s?
      public boolean hasNegativeCycle() {
          return cycle != null;
      }
  
      // return a negative cycle; null if no such cycle
      public Iterable<DirectedEdge> negativeCycle() {
          return cycle;
      }
  
      // by finding a cycle in predecessor graph
      private void findNegativeCycle() {
          int V = edgeTo.length;
          EdgeWeightedDigraph spt = new EdgeWeightedDigraph(V);
          for (int v = 0; v < V; v++)
              if (edgeTo[v] != null)
                  spt.addEdge(edgeTo[v]);
  
          EdgeWeightedDirectedCycle finder = new EdgeWeightedDirectedCycle(spt);
          cycle = finder.cycle();
      }
  
      // is there a path from s to v?
      public boolean hasPathTo(int v) {
          return distTo[v] < Double.POSITIVE_INFINITY;
      }
  
  
      // return length of shortest path from s to v
      public double distTo(int v) {
          return distTo[v];
      }
  
      // return view of shortest 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;
      }
  
      // check optimality conditions: either 
      // (i) there exists a negative cycle reacheable from s
      //     or 
      // (ii)  for all edges e = v->w:            distTo[w] <= distTo[v] + e.weight()
      // (ii') for all edges e = v->w on the SPT: distTo[w] == distTo[v] + e.weight()
      private boolean check(EdgeWeightedDigraph G, int s) {
  
          // has a negative cycle
          if (hasNegativeCycle()) {
              double weight = 0.0;
              for (DirectedEdge e : negativeCycle()) {
                  weight += e.weight();
              }
              if (weight >= 0.0) {
                  System.err.println("error: weight of negative cycle = " + weight);
                  return false;
              }
          }
  
          // no negative cycle reachable from source
          else {
  
              // check that distTo[v] and edgeTo[v] are consistent
              if (distTo[s] != 0.0 || edgeTo[s] != null) {
                  System.err.println("distanceTo[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;
                  }
              }
          }
  
          StdOut.println("Satisfies optimality conditions");
          StdOut.println();
          return true;
      }
  
  
  
      public static void main(String[] args) {
          In in = new In(args[0]);
          int s = Integer.parseInt(args[1]);
          EdgeWeightedDigraph G = new EdgeWeightedDigraph(in);
  
          BellmanFordSP sp = new BellmanFordSP(G, s);
  
          // print negative cycle
          if (sp.hasNegativeCycle()) {
              for (DirectedEdge e : sp.negativeCycle())
                  StdOut.println(e);
          }
  
          // print shortest paths
          else {
              for (int v = 0; v < G.V(); v++) {
                  if (sp.hasPathTo(v)) {
                      StdOut.printf("%d to %d (%5.2f)  ", s, v, sp.distTo(v));
                      for (DirectedEdge e : sp.pathTo(v)) {
                          StdOut.print(e + "   ");
                      }
                      StdOut.println();
                  }
                  else {
                      StdOut.printf("%d to %d           no path\n", s, v);
                  }
              }
          }
  
      }
  
  }
  