Below is the syntax highlighted version of BellmanFordSP.java
from §4.4 Shortest Paths.
/****************************************************************************** * Compilation: javac BellmanFordSP.java * Execution: java BellmanFordSP filename.txt s * Dependencies: EdgeWeightedDigraph.java DirectedEdge.java Queue.java * EdgeWeightedDirectedCycle.java * Data files: https://algs4.cs.princeton.edu/44sp/tinyEWDn.txt * https://algs4.cs.princeton.edu/44sp/tinyEWDnc.txt * https://algs4.cs.princeton.edu/44sp/mediumEWD.txt * https://algs4.cs.princeton.edu/44sp/largeEWD.txt * * Bellman-Ford shortest path algorithm. Computes the shortest path tree in * edge-weighted digraph G from vertex s, or finds a negative cost cycle * reachable from s. * * % java BellmanFordSP tinyEWDn.txt 0 * 0 to 0 ( 0.00) * 0 to 1 ( 0.93) 0->2 0.26 2->7 0.34 7->3 0.39 3->6 0.52 6->4 -1.25 4->5 0.35 5->1 0.32 * 0 to 2 ( 0.26) 0->2 0.26 * 0 to 3 ( 0.99) 0->2 0.26 2->7 0.34 7->3 0.39 * 0 to 4 ( 0.26) 0->2 0.26 2->7 0.34 7->3 0.39 3->6 0.52 6->4 -1.25 * 0 to 5 ( 0.61) 0->2 0.26 2->7 0.34 7->3 0.39 3->6 0.52 6->4 -1.25 4->5 0.35 * 0 to 6 ( 1.51) 0->2 0.26 2->7 0.34 7->3 0.39 3->6 0.52 * 0 to 7 ( 0.60) 0->2 0.26 2->7 0.34 * * % java BellmanFordSP tinyEWDnc.txt 0 * 4->5 0.35 * 5->4 -0.66 * * ******************************************************************************/ /** * The {@code BellmanFordSP} class represents a data type for solving the * single-source 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 from the source vertex <em>s</em> * to every other vertex or a negative cycle reachable from the source vertex. * <p> * This implementation uses a queue-based implementation of * the Bellman-Ford-Moore algorithm. * The constructor takes Θ(<em>E</em> <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. In practice, it performs much better. * Each instance method takes Θ(1) time. * It uses Θ(<em>V</em>) 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 BellmanFordSP { // for floating-point precision issues private static final double EPSILON = 1E-14; private double[] distTo; // distTo[v] = distance of shortest s->v path private DirectedEdge[] edgeTo; // edgeTo[v] = last edge on shortest s->v path private boolean[] onQueue; // onQueue[v] = is v currently on the queue? private Queue<Integer> queue; // queue of vertices to relax private int cost; // number of calls to relax() private Iterable<DirectedEdge> cycle; // negative cycle (or null if no such cycle) /** * Computes a shortest paths tree from {@code s} to every other vertex in * the edge-weighted digraph {@code G}. * @param G the acyclic digraph * @param s the source vertex * @throws IllegalArgumentException unless {@code 0 <= s < V} */ public BellmanFordSP(EdgeWeightedDigraph G, int s) { distTo = new double[G.V()]; edgeTo = new DirectedEdge[G.V()]; onQueue = new boolean[G.V()]; for (int v = 0; v < G.V(); v++) distTo[v] = Double.POSITIVE_INFINITY; distTo[s] = 0.0; // Bellman-Ford algorithm queue = new Queue<Integer>(); queue.enqueue(s); onQueue[s] = true; while (!queue.isEmpty() && !hasNegativeCycle()) { int v = queue.dequeue(); onQueue[v] = false; relax(G, v); } assert check(G, s); } // relax vertex v and put other endpoints on queue if changed private void relax(EdgeWeightedDigraph G, int v) { for (DirectedEdge e : G.adj(v)) { int w = e.to(); if (distTo[w] > distTo[v] + e.weight() + EPSILON) { distTo[w] = distTo[v] + e.weight(); edgeTo[w] = e; if (!onQueue[w]) { queue.enqueue(w); onQueue[w] = true; } } if (++cost % G.V() == 0) { findNegativeCycle(); if (hasNegativeCycle()) return; // found a negative cycle } } } /** * Is there a negative cycle reachable from the source vertex {@code s}? * @return {@code true} if there is a negative cycle reachable from the * source vertex {@code s}, and {@code false} otherwise */ public boolean hasNegativeCycle() { return cycle != null; } /** * Returns a negative cycle reachable from the source vertex {@code s}, or {@code null} * if there is no such cycle. * @return a negative cycle reachable from the source vertex {@code s} * as an iterable of edges, and {@code null} if there is no such cycle */ public Iterable<DirectedEdge> negativeCycle() { return cycle; } // by finding a cycle in predecessor graph private void findNegativeCycle() { int V = edgeTo.length; EdgeWeightedDigraph spt = new EdgeWeightedDigraph(V); for (int v = 0; v < V; v++) if (edgeTo[v] != null) spt.addEdge(edgeTo[v]); EdgeWeightedDirectedCycle finder = new EdgeWeightedDirectedCycle(spt); cycle = finder.cycle(); } /** * 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 UnsupportedOperationException if there is a negative cost cycle reachable * from the source vertex {@code s} * @throws IllegalArgumentException unless {@code 0 <= v < V} */ public double distTo(int v) { validateVertex(v); if (hasNegativeCycle()) throw new UnsupportedOperationException("Negative cost cycle exists"); return distTo[v]; } /** * Is there a path from the source {@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}, and {@code false} otherwise * @throws IllegalArgumentException unless {@code 0 <= v < V} */ public boolean hasPathTo(int v) { validateVertex(v); return distTo[v] < Double.POSITIVE_INFINITY; } /** * Returns a shortest path from the source {@code s} to vertex {@code v}. * @param v the destination vertex * @return a shortest path from the source {@code s} to vertex {@code v} * as an iterable of edges, and {@code null} if no such path * @throws UnsupportedOperationException if there is a negative cost cycle reachable * from the source vertex {@code s} * @throws IllegalArgumentException unless {@code 0 <= v < V} */ public Iterable<DirectedEdge> pathTo(int v) { validateVertex(v); if (hasNegativeCycle()) throw new UnsupportedOperationException("Negative cost cycle exists"); if (!hasPathTo(v)) return null; Stack<DirectedEdge> path = new Stack<DirectedEdge>(); for (DirectedEdge e = edgeTo[v]; e != null; e = edgeTo[e.from()]) { path.push(e); } return path; } // check optimality conditions: either // (i) there exists a negative cycle reachable from s // or // (ii) for all edges e = v->w: distTo[w] <= distTo[v] + e.weight() // (ii') for all edges e = v->w on the SPT: distTo[w] == distTo[v] + e.weight() private boolean check(EdgeWeightedDigraph G, int s) { // has a negative cycle if (hasNegativeCycle()) { double weight = 0.0; for (DirectedEdge e : negativeCycle()) { weight += e.weight(); } if (weight >= 0.0) { System.err.println("error: weight of negative cycle = " + weight); return false; } } // no negative cycle reachable from source else { // check that distTo[v] and edgeTo[v] are consistent if (distTo[s] != 0.0 || edgeTo[s] != null) { System.err.println("distanceTo[s] and edgeTo[s] inconsistent"); return false; } for (int v = 0; v < G.V(); v++) { if (v == s) continue; if (edgeTo[v] == null && distTo[v] != Double.POSITIVE_INFINITY) { System.err.println("distTo[] and edgeTo[] inconsistent"); return false; } } // check that all edges e = v->w satisfy distTo[w] <= distTo[v] + e.weight() for (int v = 0; v < G.V(); v++) { for (DirectedEdge e : G.adj(v)) { int w = e.to(); if (distTo[v] + e.weight() < distTo[w]) { System.err.println("edge " + e + " not relaxed"); return false; } } } // check that all edges e = v->w on SPT satisfy distTo[w] == distTo[v] + e.weight() for (int w = 0; w < G.V(); w++) { if (edgeTo[w] == null) continue; DirectedEdge e = edgeTo[w]; int v = e.from(); if (w != e.to()) return false; if (distTo[v] + e.weight() != distTo[w]) { System.err.println("edge " + e + " on shortest path not tight"); return false; } } } StdOut.println("Satisfies optimality conditions"); StdOut.println(); 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 BellmanFordSP} data type. * * @param args the command-line arguments */ public static void main(String[] args) { In in = new In(args[0]); int s = Integer.parseInt(args[1]); EdgeWeightedDigraph G = new EdgeWeightedDigraph(in); BellmanFordSP sp = new BellmanFordSP(G, s); // print negative cycle if (sp.hasNegativeCycle()) { for (DirectedEdge e : sp.negativeCycle()) StdOut.println(e); } // print shortest paths else { for (int v = 0; v < G.V(); v++) { if (sp.hasPathTo(v)) { StdOut.printf("%d to %d (%5.2f) ", s, v, sp.distTo(v)); for (DirectedEdge e : sp.pathTo(v)) { StdOut.print(e + " "); } StdOut.println(); } else { StdOut.printf("%d to %d no path\n", s, v); } } } } }