Below is the syntax highlighted version of FloydWarshall.java.
/****************************************************************************** * Compilation: javac FloydWarshall.java * Execution: java FloydWarshall V E * Dependencies: AdjMatrixEdgeWeightedDigraph.java * * Floyd-Warshall all-pairs shortest path algorithm. * * % java FloydWarshall 100 500 * * Should check for negative cycles during triple loop; otherwise * intermediate numbers can get exponentially large. * Reference: "The Floyd-Warshall algorithm on graphs with negative cycles" * by Stefan Hougardy * ******************************************************************************/ package edu.princeton.cs.algs4; /** * The {@code FloydWarshall} class represents a data type for solving the * all-pairs shortest paths problem in edge-weighted digraphs with * no negative cycles. * The edge weights can be positive, negative, or zero. * This class finds either a shortest path between every pair of vertices * or a negative cycle. * <p> * This implementation uses the Floyd-Warshall algorithm. * The constructor takes Θ(<em>V</em><sup>3</sup>) time, * where <em>V</em> is the number of vertices. * Each instance method takes Θ(1) time. * It uses Θ(<em>V</em><sup>2</sup>) extra space * (not including the edge-weighted digraph). * <p> * This correctly computes shortest paths if all arithmetic performed is * without floating-point rounding error or arithmetic overflow. * This is the case if all edge weights are integers and if none of the * intermediate results exceeds 2<sup>52</sup>. Since all intermediate * results are sums of edge weights, they are bounded by <em>V C</em>, * where <em>V</em> is the number of vertices and <em>C</em> is the maximum * absolute value of any edge weight. * <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 FloydWarshall { private boolean hasNegativeCycle; // is there a negative cycle? private double[][] distTo; // distTo[v][w] = length of shortest v->w path private DirectedEdge[][] edgeTo; // edgeTo[v][w] = last edge on shortest v->w path /** * Computes a shortest paths tree from each vertex to every other vertex in * the edge-weighted digraph {@code G}. If no such shortest path exists for * some pair of vertices, it computes a negative cycle. * @param G the edge-weighted digraph */ public FloydWarshall(AdjMatrixEdgeWeightedDigraph G) { int V = G.V(); distTo = new double[V][V]; edgeTo = new DirectedEdge[V][V]; // initialize distances to infinity for (int v = 0; v < V; v++) { for (int w = 0; w < V; w++) { distTo[v][w] = Double.POSITIVE_INFINITY; } } // initialize distances using edge-weighted digraph's for (int v = 0; v < G.V(); v++) { for (DirectedEdge e : G.adj(v)) { distTo[e.from()][e.to()] = e.weight(); edgeTo[e.from()][e.to()] = e; } // in case of self-loops if (distTo[v][v] >= 0.0) { distTo[v][v] = 0.0; edgeTo[v][v] = null; } } // Floyd-Warshall updates for (int i = 0; i < V; i++) { // compute shortest paths using only 0, 1, ..., i as intermediate vertices for (int v = 0; v < V; v++) { if (edgeTo[v][i] == null) continue; // optimization for (int w = 0; w < V; w++) { if (distTo[v][w] > distTo[v][i] + distTo[i][w]) { distTo[v][w] = distTo[v][i] + distTo[i][w]; edgeTo[v][w] = edgeTo[i][w]; } } // check for negative cycle if (distTo[v][v] < 0.0) { hasNegativeCycle = true; return; } } } assert check(G); } /** * Is there a negative cycle? * @return {@code true} if there is a negative cycle, and {@code false} otherwise */ public boolean hasNegativeCycle() { return hasNegativeCycle; } /** * Returns a negative cycle, or {@code null} if there is no such cycle. * @return a negative cycle as an iterable of edges, * or {@code null} if there is no such cycle */ public Iterable<DirectedEdge> negativeCycle() { for (int v = 0; v < distTo.length; v++) { // negative cycle in v's predecessor graph if (distTo[v][v] < 0.0) { int V = edgeTo.length; EdgeWeightedDigraph spt = new EdgeWeightedDigraph(V); for (int w = 0; w < V; w++) if (edgeTo[v][w] != null) spt.addEdge(edgeTo[v][w]); EdgeWeightedDirectedCycle finder = new EdgeWeightedDirectedCycle(spt); assert finder.hasCycle(); return finder.cycle(); } } return null; } /** * 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 distTo[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 UnsupportedOperationException if there is a negative cost cycle * @throws IllegalArgumentException unless {@code 0 <= v < V} */ public double dist(int s, int t) { validateVertex(s); validateVertex(t); if (hasNegativeCycle()) throw new UnsupportedOperationException("Negative cost cycle exists"); return distTo[s][t]; } /** * 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 UnsupportedOperationException if there is a negative cost cycle * @throws IllegalArgumentException unless {@code 0 <= v < V} */ public Iterable<DirectedEdge> path(int s, int t) { validateVertex(s); validateVertex(t); if (hasNegativeCycle()) throw new UnsupportedOperationException("Negative cost cycle exists"); if (!hasPath(s, t)) return null; Stack<DirectedEdge> path = new Stack<DirectedEdge>(); for (DirectedEdge e = edgeTo[s][t]; e != null; e = edgeTo[s][e.from()]) { path.push(e); } return path; } // check optimality conditions private boolean check(AdjMatrixEdgeWeightedDigraph G) { // no negative cycle if (!hasNegativeCycle()) { for (int v = 0; v < G.V(); v++) { for (DirectedEdge e : G.adj(v)) { int w = e.to(); for (int i = 0; i < G.V(); i++) { if (distTo[i][w] > distTo[i][v] + e.weight()) { System.err.println("edge " + e + " is eligible"); return false; } } } } } return true; } // throw an IllegalArgumentException unless {@code 0 <= v < V} private void validateVertex(int v) { int V = distTo.length; if (v < 0 || v >= V) throw new IllegalArgumentException("vertex " + v + " is not between 0 and " + (V-1)); } /** * Unit tests the {@code FloydWarshall} data type. * * @param args the command-line arguments */ public static void main(String[] args) { // random graph with V vertices and E edges, parallel edges allowed int V = Integer.parseInt(args[0]); int E = Integer.parseInt(args[1]); AdjMatrixEdgeWeightedDigraph G = new AdjMatrixEdgeWeightedDigraph(V); for (int i = 0; i < E; i++) { int v = StdRandom.uniformInt(V); int w = StdRandom.uniformInt(V); double weight = 0.01 * StdRandom.uniformInt(-15, 100); if (v == w) G.addEdge(new DirectedEdge(v, w, Math.abs(weight))); else G.addEdge(new DirectedEdge(v, w, weight)); } StdOut.println(G); // run Floyd-Warshall algorithm FloydWarshall spt = new FloydWarshall(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(); } // print negative cycle if (spt.hasNegativeCycle()) { StdOut.println("Negative cost cycle:"); for (DirectedEdge e : spt.negativeCycle()) StdOut.println(e); StdOut.println(); } // print all-pairs shortest paths else { 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. ******************************************************************************/