KruskalMST.h

#ifndef CH4_KRUSKALMST_H
#define CH4_KRUSKALMST_H

#include "../head/EdgeWeightedGraph.h"
#include "../head/UF.h"
#include <queue>

using std::queue;
using std::priority_queue;

/**
 *  The {@code KruskalMST} class represents a data type for computing a
 *  <em>minimum spanning tree</em> in an edge-weighted graph.
 *  The edge weights can be positive, zero, or negative and need not
 *  be distinct. If the graph is not connected, it computes a <em>minimum
 *  spanning forest</em>, which is the union of minimum spanning trees
 *  in each connected component. The {@code weight()} method returns the
 *  weight of a minimum spanning tree and the {@code edges()} method
 *  returns its edges.
 *  <p>
 *  This implementation uses <em>Krusal's algorithm</em> and the
 *  union-find data type.
 *  The constructor takes time proportional to <em>E</em> log <em>E</em>
 *  and extra space (not including the graph) proportional to <em>V</em>,
 *  where <em>V</em> is the number of vertices and <em>E</em> is the number of edges.
 *  Afterwards, the {@code weight()} method takes constant time
 *  and the {@code edges()} method takes time proportional to <em>V</em>.
 *  <p>
 *  For additional documentation,
 *  see <a href="https://algs4.cs.princeton.edu/43mst">Section 4.3</a> of
 *  <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
 *  For alternate implementations, see {@link LazyPrimMST}, {@link PrimMST},
 *  and {@link BoruvkaMST}.
 *
 *  @author Robert Sedgewick
 *  @author Kevin Wayne
 */
class KruskalMST {
public:
    /**
     * Compute a minimum spanning tree (or forest) of an edge-weighted graph.
     * @param G the edge-weighted graph
     */
    KruskalMST(EdgeWeightedGraph &G) {
        // more efficient to build heap by passing array of edges
        priority_queue<Edge, vector<Edge>, std::greater<Edge>> pq;
        for (Edge e : G.edges()) {
            pq.push(e);
        }

        // run greedy algorithm
        UF uf(G.V_());
        while (!pq.empty() && mst.size() < G.V_() - 1) {
            Edge e = pq.top();
            pq.pop();
            int v = e.either();
            int w = e.other(v);
            if (!uf.connected(v, w)) { // v-w does not create a cycle
                uf.union_op(v, w);  // merge v and w components
                mst.push(e);  // add edge e to mst
                weight += e.weight_();
            }
        }
    }

    /**
     * Returns the edges in a minimum spanning tree (or forest).
     * @return the edges in a minimum spanning tree (or forest) as
     *    an iterable of edges
     */
    queue<Edge> edges() {
        return mst;
    }

    /**
     * Returns the sum of the edge weights in a minimum spanning tree (or forest).
     * @return the sum of the edge weights in a minimum spanning tree (or forest)
     */
    double weight_() {
        return weight;
    }


private:
    double weight;    // weight of MST
    queue<Edge> mst;  // edges in MST
};

#endif //CH4_KRUSKALMST_H