/******************************************************************************
 *  Compilation:  javac DijkstraAllPairsSP.java
 *  Execution:    none
 *  Dependencies: EdgeWeightedDigraph.java Dijkstra.java
 *
 *  Dijkstra's algorithm run from each vertex.
 *  Takes time proportional to E V log V and space proportional to EV.
 *
 *  % java DijkstraAllPairsSP tinyEWD.txt
 *
 ******************************************************************************/

package edu.princeton.cs.algs4;

/**
 *  The {@code DijkstraAllPairsSP} class represents a data type for solving the
 *  all-pairs shortest paths problem in edge-weighted digraphs
 *  where the edge weights are non-negative.
 *  <p>
 *  This implementation runs Dijkstra's algorithm from each vertex.
 *  The constructor takes &Theta;(<em>V</em> (<em>E</em> log <em>V</em>)) time
 *  in the worst case, where <em>V</em> is the number of vertices and
 *  <em>E</em> is the number of edges.
 *  Each instance method takes &Theta;(1) time.
 *  It uses &Theta;(<em>V</em><sup>2</sup>) extra space (not including the
 *  edge-weighted digraph).
 *  <p>
 *  For additional documentation,
 *  see <a href="https://algs4.cs.princeton.edu/44sp">Section 4.4</a> of
 *  <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
 *
 *  @author Robert Sedgewick
 *  @author Kevin Wayne
 */
public class DijkstraAllPairsSP {
    private DijkstraSP[] all;

    /**
     * Computes a shortest paths tree from each vertex to every other vertex in
     * the edge-weighted digraph {@code G}.
     * @param G the edge-weighted digraph
     * @throws IllegalArgumentException if an edge weight is negative
     * @throws IllegalArgumentException unless {@code 0 <= s < V}
     */
    public DijkstraAllPairsSP(EdgeWeightedDigraph G) {
        all  = new DijkstraSP[G.V()];
        for (int v = 0; v < G.V(); v++)
            all[v] = new DijkstraSP(G, v);
    }

    /**
     * Returns a shortest path from vertex {@code s} to vertex {@code t}.
     * @param  s the source vertex
     * @param  t the destination vertex
     * @return a shortest path from vertex {@code s} to vertex {@code t}
     *         as an iterable of edges, and {@code null} if no such path
     * @throws IllegalArgumentException unless {@code 0 <= s < V}
     * @throws IllegalArgumentException unless {@code 0 <= t < V}
     */
    public Iterable<DirectedEdge> path(int s, int t) {
        validateVertex(s);
        validateVertex(t);
        return all[s].pathTo(t);
    }

    /**
     * Is there a path from the vertex {@code s} to vertex {@code t}?
     * @param  s the source vertex
     * @param  t the destination vertex
     * @return {@code true} if there is a path from vertex {@code s}
     *         to vertex {@code t}, and {@code false} otherwise
     * @throws IllegalArgumentException unless {@code 0 <= s < V}
     * @throws IllegalArgumentException unless {@code 0 <= t < V}
     */
    public boolean hasPath(int s, int t) {
        validateVertex(s);
        validateVertex(t);
        return dist(s, t) < Double.POSITIVE_INFINITY;
    }

    /**
     * Returns the length of a shortest path from vertex {@code s} to vertex {@code t}.
     * @param  s the source vertex
     * @param  t the destination vertex
     * @return the length of a shortest path from vertex {@code s} to vertex {@code t};
     *         {@code Double.POSITIVE_INFINITY} if no such path
     * @throws IllegalArgumentException unless {@code 0 <= s < V}
     * @throws IllegalArgumentException unless {@code 0 <= t < V}
     */
    public double dist(int s, int t) {
        validateVertex(s);
        validateVertex(t);
        return all[s].distTo(t);
    }

    // throw an IllegalArgumentException unless {@code 0 <= v < V}
    private void validateVertex(int v) {
        int V = all.length;
        if (v < 0 || v >= V)
            throw new IllegalArgumentException("vertex " + v + " is not between 0 and " + (V-1));
    }


    /**
     * Unit tests the {@code DijkstraAllPairsSP} data type.
     *
     * @param args the command-line arguments
     */
    public static void main(String[] args) {

        // read edge-weighted digraph
        In in = new In(args[0]);
        EdgeWeightedDigraph G = new EdgeWeightedDigraph(in);

        // compute shortest paths between all pairs of vertices
        DijkstraAllPairsSP spt = new DijkstraAllPairsSP(G);

        // print all-pairs shortest path distances
        StdOut.printf("  ");
        for (int v = 0; v < G.V(); v++) {
            StdOut.printf("%6d ", v);
        }
        StdOut.println();
        for (int v = 0; v < G.V(); v++) {
            StdOut.printf("%3d: ", v);
            for (int w = 0; w < G.V(); w++) {
                if (spt.hasPath(v, w)) StdOut.printf("%6.2f ", spt.dist(v, w));
                else StdOut.printf("  Inf ");
            }
            StdOut.println();
        }
        StdOut.println();

        // print all-pairs shortest paths
        for (int v = 0; v < G.V(); v++) {
            for (int w = 0; w < G.V(); w++) {
                if (spt.hasPath(v, w)) {
                    StdOut.printf("%d to %d (%5.2f)  ", v, w, spt.dist(v, w));
                    for (DirectedEdge e : spt.path(v, w))
                        StdOut.print(e + "  ");
                    StdOut.println();
                }
                else {
                    StdOut.printf("%d to %d no path\n", v, w);
                }
            }
        }
    }
}

/******************************************************************************
 *  Copyright 2002-2022, Robert Sedgewick and Kevin Wayne.
 *
 *  This file is part of algs4.jar, which accompanies the textbook
 *
 *      Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne,
 *      Addison-Wesley Professional, 2011, ISBN 0-321-57351-X.
 *      http://algs4.cs.princeton.edu
 *
 *
 *  algs4.jar is free software: you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation, either version 3 of the License, or
 *  (at your option) any later version.
 *
 *  algs4.jar is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with algs4.jar.  If not, see http://www.gnu.org/licenses.
 ******************************************************************************/