Below is the syntax highlighted version of LazyPrimMST.java.
/****************************************************************************** * Compilation: javac LazyPrimMST.java * Execution: java LazyPrimMST filename.txt * Dependencies: EdgeWeightedGraph.java Edge.java Queue.java * MinPQ.java UF.java In.java StdOut.java * Data files: https://algs4.cs.princeton.edu/43mst/tinyEWG.txt * https://algs4.cs.princeton.edu/43mst/mediumEWG.txt * https://algs4.cs.princeton.edu/43mst/largeEWG.txt * * Compute a minimum spanning forest using a lazy version of Prim's * algorithm. * * % java LazyPrimMST tinyEWG.txt * 0-7 0.16000 * 1-7 0.19000 * 0-2 0.26000 * 2-3 0.17000 * 5-7 0.28000 * 4-5 0.35000 * 6-2 0.40000 * 1.81000 * * % java LazyPrimMST mediumEWG.txt * 0-225 0.02383 * 49-225 0.03314 * 44-49 0.02107 * 44-204 0.01774 * 49-97 0.03121 * 202-204 0.04207 * 176-202 0.04299 * 176-191 0.02089 * 68-176 0.04396 * 58-68 0.04795 * 10.46351 * * % java LazyPrimMST largeEWG.txt * ... * 647.66307 * ******************************************************************************/ package edu.princeton.cs.algs4; /** * The {@code LazyPrimMST} 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 a lazy version of <em>Prim's algorithm</em> * with a binary heap of edges. * The constructor takes Θ(<em>E</em> log <em>E</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 Θ(1) time. * It uses Θ(<em>E</em>) extra space in the worst case * (not including the edge-weighted graph). * <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 PrimMST}, {@link KruskalMST}, * and {@link BoruvkaMST}. * * @author Robert Sedgewick * @author Kevin Wayne */ public class LazyPrimMST { private static final double FLOATING_POINT_EPSILON = 1.0E-12; private double weight; // total weight of MST private Queue<Edge> mst; // edges in the MST private boolean[] marked; // marked[v] = true iff v on tree private MinPQ<Edge> pq; // edges with one endpoint in tree /** * Compute a minimum spanning tree (or forest) of an edge-weighted graph. * @param G the edge-weighted graph */ public LazyPrimMST(EdgeWeightedGraph G) { mst = new Queue<Edge>(); pq = new MinPQ<Edge>(); marked = new boolean[G.V()]; for (int v = 0; v < G.V(); v++) // run Prim from all vertices to if (!marked[v]) prim(G, v); // get a minimum spanning forest // check optimality conditions assert check(G); } // run Prim's algorithm private void prim(EdgeWeightedGraph G, int s) { scan(G, s); while (!pq.isEmpty()) { // better to stop when mst has V-1 edges Edge e = pq.delMin(); // smallest edge on pq int v = e.either(), w = e.other(v); // two endpoints assert marked[v] || marked[w]; if (marked[v] && marked[w]) continue; // lazy, both v and w already scanned mst.enqueue(e); // add e to MST weight += e.weight(); if (!marked[v]) scan(G, v); // v becomes part of tree if (!marked[w]) scan(G, w); // w becomes part of tree } } // add all edges e incident to v onto pq if the other endpoint has not yet been scanned private void scan(EdgeWeightedGraph G, int v) { assert !marked[v]; marked[v] = true; for (Edge e : G.adj(v)) if (!marked[e.other(v)]) pq.insert(e); } /** * 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 */ public Iterable<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) */ public double weight() { return weight; } // check optimality conditions (takes time proportional to E V lg* V) private boolean check(EdgeWeightedGraph G) { // check weight double totalWeight = 0.0; for (Edge e : edges()) { totalWeight += e.weight(); } if (Math.abs(totalWeight - weight()) > FLOATING_POINT_EPSILON) { System.err.printf("Weight of edges does not equal weight(): %f vs. %f\n", totalWeight, weight()); return false; } // check that it is acyclic UF uf = new UF(G.V()); for (Edge e : edges()) { int v = e.either(), w = e.other(v); if (uf.find(v) == uf.find(w)) { System.err.println("Not a forest"); return false; } uf.union(v, w); } // check that it is a spanning forest for (Edge e : G.edges()) { int v = e.either(), w = e.other(v); if (uf.find(v) != uf.find(w)) { System.err.println("Not a spanning forest"); return false; } } // check that it is a minimal spanning forest (cut optimality conditions) for (Edge e : edges()) { // all edges in MST except e uf = new UF(G.V()); for (Edge f : mst) { int x = f.either(), y = f.other(x); if (f != e) uf.union(x, y); } // check that e is min weight edge in crossing cut for (Edge f : G.edges()) { int x = f.either(), y = f.other(x); if (uf.find(x) != uf.find(y)) { if (f.weight() < e.weight()) { System.err.println("Edge " + f + " violates cut optimality conditions"); return false; } } } } return true; } /** * Unit tests the {@code LazyPrimMST} data type. * * @param args the command-line arguments */ public static void main(String[] args) { In in = new In(args[0]); EdgeWeightedGraph G = new EdgeWeightedGraph(in); LazyPrimMST mst = new LazyPrimMST(G); for (Edge e : mst.edges()) { StdOut.println(e); } StdOut.printf("%.5f\n", mst.weight()); } } /****************************************************************************** * 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. ******************************************************************************/