Below is the syntax highlighted version of PrimMST.java
from §4.3 Minimum Spanning Trees.
/****************************************************************************** * Compilation: javac PrimMST.java * Execution: java PrimMST filename.txt * Dependencies: EdgeWeightedGraph.java Edge.java Queue.java * IndexMinPQ.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 Prim's algorithm. * * % java PrimMST tinyEWG.txt * 1-7 0.19000 * 0-2 0.26000 * 2-3 0.17000 * 4-5 0.35000 * 5-7 0.28000 * 6-2 0.40000 * 0-7 0.16000 * 1.81000 * * % java PrimMST mediumEWG.txt * 1-72 0.06506 * 2-86 0.05980 * 3-67 0.09725 * 4-55 0.06425 * 5-102 0.03834 * 6-129 0.05363 * 7-157 0.00516 * ... * 10.46351 * * % java PrimMST largeEWG.txt * ... * 647.66307 * ******************************************************************************/ /** * The {@code PrimMST} 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>Prim's algorithm</em> with an indexed * binary heap. * The constructor takes Θ(<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 Θ(1) time. * It uses Θ(<em>V</em>) extra space (not including the * edge-weighted graph). * <p> * This {@code weight()} method correctly computes the weight of the MST * if all arithmetic performed is without floating-point rounding error * or arithmetic overflow. * This is the case if all edge weights are non-negative integers * and the weight of the MST does not exceed 2<sup>52</sup>. * <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 KruskalMST}, * and {@link BoruvkaMST}. * * @author Robert Sedgewick * @author Kevin Wayne */ public class PrimMST { private static final double FLOATING_POINT_EPSILON = 1.0E-12; private Edge[] edgeTo; // edgeTo[v] = shortest edge from tree vertex to non-tree vertex private double[] distTo; // distTo[v] = weight of shortest such edge private boolean[] marked; // marked[v] = true if v on tree, false otherwise private IndexMinPQ<Double> pq; /** * Compute a minimum spanning tree (or forest) of an edge-weighted graph. * @param G the edge-weighted graph */ public PrimMST(EdgeWeightedGraph G) { edgeTo = new Edge[G.V()]; distTo = new double[G.V()]; marked = new boolean[G.V()]; pq = new IndexMinPQ<Double>(G.V()); for (int v = 0; v < G.V(); v++) distTo[v] = Double.POSITIVE_INFINITY; for (int v = 0; v < G.V(); v++) // run from each vertex to find if (!marked[v]) prim(G, v); // minimum spanning forest // check optimality conditions assert check(G); } // run Prim's algorithm in graph G, starting from vertex s private void prim(EdgeWeightedGraph G, int s) { distTo[s] = 0.0; pq.insert(s, distTo[s]); while (!pq.isEmpty()) { int v = pq.delMin(); scan(G, v); } } // scan vertex v private void scan(EdgeWeightedGraph G, int v) { marked[v] = true; for (Edge e : G.adj(v)) { int w = e.other(v); if (marked[w]) continue; // v-w is obsolete edge if (e.weight() < distTo[w]) { distTo[w] = e.weight(); edgeTo[w] = e; if (pq.contains(w)) pq.decreaseKey(w, distTo[w]); else pq.insert(w, distTo[w]); } } } /** * 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() { Queue<Edge> mst = new Queue<Edge>(); for (int v = 0; v < edgeTo.length; v++) { Edge e = edgeTo[v]; if (e != null) { mst.enqueue(e); } } 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() { double weight = 0.0; for (Edge e : edges()) weight += e.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 : edges()) { 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 PrimMST} 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); PrimMST mst = new PrimMST(G); for (Edge e : mst.edges()) { StdOut.println(e); } StdOut.printf("%.5f\n", mst.weight()); } }