package algs44;
import stdlib.*;
import algs13.Stack;
import algs24.IndexMinPQ;
/* ***********************************************************************
 *  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 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 IndexMinPQ<Double> pq;    // priority queue of vertices

	public DijkstraSP(EdgeWeightedDigraph G, int s) {
		for (DirectedEdge e : G.edges()) {
			if (e.weight() < 0)
				throw new IllegalArgumentException("edge " + e + " has negative weight");
		}

		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<>(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.decreaseKey(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<>();
		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.format("%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.format("%d to %d         no path\n", s, t);
			}
		}
	}

}