DijkstraSP.h

#ifndef CH4_DIJKSTRASP_H
#define CH4_DIJKSTRASP_H

#include "../head/EdgeWeightedDigraph.h"
#include "IndexMinPQ.h"
#include <numeric>

using std::numeric_limits;

/**
 *  The {@code DijkstraSP} class represents a data type for solving the
 *  single-source shortest paths problem in edge-weighted digraphs
 *  where the edge weights are nonnegative.
 *  <p>
 *  This implementation uses Dijkstra's algorithm with a binary heap.
 *  The constructor takes time proportional to <em>E</em> log <em>V</em>,
 *  where <em>V</em> is the number of vertices and <em>E</em> is the number of edges.
 *  Each call to {@code distTo(int)} and {@code hasPathTo(int)} takes constant time;
 *  each call to {@code pathTo(int)} takes time proportional to the number of
 *  edges in the shortest path returned.
 *  <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
 */
class DijkstraSP {
public:
    /**
     * Computes a shortest-paths tree from the source vertex {@code s} to every other
     * vertex in the edge-weighted digraph {@code G}.
     *
     * @param  G the edge-weighted digraph
     * @param  s the source vertex
     * @throws IllegalArgumentException if an edge weight is negative
     * @throws IllegalArgumentException unless {@code 0 <= s < V}
     */
    DijkstraSP(EdgeWeightedDigraph &G, int s) : distTo(G.V_(), numeric_limits<double>::max()), edgeTo(G.V_()),
                                                pq(G.V_()) {
        for (DirectedEdge e : G.edges()) {
            if (e.weight_() < 0)
                throw runtime_error("edge has negative weight");
        }

        validateVertex(s);

        distTo[s] = 0.0;

        // relax vertices in order of distance from s
        pq.insert(s, distTo[s]);
        while (!pq.isEmpty()) {
            int v = pq.delMin();
            for (DirectedEdge e : G.adj_(v))
                relax(e);
        }
    }

    // default for vector
    DijkstraSP() : pq(0) {}

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

    /**
     * Returns true if there is a path from the source vertex {@code s} to vertex {@code v}.
     *
     * @param  v the destination vertex
     * @return {@code true} if there is a path from the source vertex
     *         {@code s} to vertex {@code v}; {@code false} otherwise
     * @throws IllegalArgumentException unless {@code 0 <= v < V}
     */
    bool hasPathTo(int v) {
        validateVertex(v);
        return distTo[v] < numeric_limits<double>::max();
    }

    /**
     * Returns a shortest path from the source vertex {@code s} to vertex {@code v}.
     *
     * @param  v the destination vertex
     * @return a shortest path from the source vertex {@code s} to vertex {@code v}
     *         as an iterable of edges, and {@code null} if no such path
     * @throws IllegalArgumentException unless {@code 0 <= v < V}
     */
    forward_list<DirectedEdge> pathTo(int v) {
        validateVertex(v);
//        if (!hasPathTo(v)) return forward_list<DirectedEdge>();
        if (!hasPathTo(v)) throw runtime_error("not have path to this vertex");
        forward_list<DirectedEdge> path;
        for (DirectedEdge e = edgeTo[v]; e.from() != -1; e = edgeTo[e.from()]) {
            path.push_front(e);
        }
        return path;
    }

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

    // relax edge e and update pq if changed
    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]);
        }
    }


private:
    vector<double> distTo;        // distTo[v] = distance  of shortest s->v path
    vector<DirectedEdge> edgeTo;  // edgeTo[v] = last edge on shortest s->v path
    IndexMinPQ<double> pq;        // priority queue of vertices
};

#endif //CH4_DIJKSTRASP_H