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: http://algs4.cs.princeton.edu/44sp/tinyEWDn.txt * http://algs4.cs.princeton.edu/44sp/mediumEWDnc.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 * *************************************************************************/ public class BellmanFordSP { 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) 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()) { distTo[w] = distTo[v] + e.weight(); edgeTo[w] = e; if (!onQueue[w]) { queue.enqueue(w); onQueue[w] = true; } } if (cost++ % G.V() == 0) findNegativeCycle(); } } // is there a negative cycle reachable from s? public boolean hasNegativeCycle() { return cycle != null; } // return a negative cycle; null if 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(); } // is there a path from s to v? public boolean hasPathTo(int v) { return distTo[v] < Double.POSITIVE_INFINITY; } // return length of shortest path from s to v public double distTo(int v) { return distTo[v]; } // return view of shortest path from s to v, null if no such path public Iterable<DirectedEdge> pathTo(int v) { 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 reacheable 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; } 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); } } } } }