package algs44;
import stdlib.*;
import algs13.Queue;
import algs13.Stack;
/* ***********************************************************************
 *  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 final double[] distTo;               // distTo[v] = distance  of shortest s->v path
  private final DirectedEdge[] edgeTo;         // edgeTo[v] = last edge on shortest s->v path
  private final boolean[] onQueue;             // onQueue[v] = is v currently on the queue?
  private final 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<>();
    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<>();
    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.format("%d to %d (%5.2f)  ", s, v, sp.distTo(v));
          for (DirectedEdge e : sp.pathTo(v)) {
            StdOut.print(e + "   ");
          }
          StdOut.println();
        }
        else {
          StdOut.format("%d to %d           no path\n", s, v);
        }
      }
    }

  }

}