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);
				}
			}
		}

	}

}