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283 lines
10 KiB
Java
283 lines
10 KiB
Java
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import edu.princeton.cs.introcs.In;
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import edu.princeton.cs.introcs.StdOut;
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/*************************************************************************
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* Compilation: javac BellmanFordSP.java
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* Execution: java BellmanFordSP filename.txt s
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* Dependencies: EdgeWeightedDigraph.java DirectedEdge.java Queue.java
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* EdgeWeightedDirectedCycle.java
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* Data files: http://algs4.cs.princeton.edu/44sp/tinyEWDn.txt
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* http://algs4.cs.princeton.edu/44sp/mediumEWDnc.txt
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*
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* Bellman-Ford shortest path algorithm. Computes the shortest path tree in
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* edge-weighted digraph G from vertex s, or finds a negative cost cycle
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* reachable from s.
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*
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* % java BellmanFordSP tinyEWDn.txt 0
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* 0 to 0 ( 0.00)
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* 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
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* 0 to 2 ( 0.26) 0->2 0.26
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* 0 to 3 ( 0.99) 0->2 0.26 2->7 0.34 7->3 0.39
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* 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
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* 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
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* 0 to 6 ( 1.51) 0->2 0.26 2->7 0.34 7->3 0.39 3->6 0.52
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* 0 to 7 ( 0.60) 0->2 0.26 2->7 0.34
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*
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* % java BellmanFordSP tinyEWDnc.txt 0
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* 4->5 0.35
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* 5->4 -0.66
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*
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*
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*************************************************************************/
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/**
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* The BellmanFordSP class represents a data type for solving the
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* single-source shortest paths problem in edge-weighted digraphs with
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* no negative cycles.
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* The edge weights can be positive, negative, or zero.
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* This class finds either a shortest path from the source vertex s
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* to every other vertex or a negative cycle reachable from the source vertex.
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*
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* This implementation uses the Bellman-Ford-Moore algorithm.
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* The constructor takes time proportional to V ( V + E )
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* in the worst case, where V is the number of vertices and E
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* is the number of edges.
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* Afterwards, the distTo() , hasPathTo() , and hasNegativeCycle()
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* methods take constant time; the pathTo() and negativeCycle()
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* method takes time proportional to the number of edges returned.
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*
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* For additional documentation, see <a href="/algs4/44sp">Section 4.4</a> of
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* Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.
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*
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* @author Robert Sedgewick
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* @author Kevin Wayne
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*/
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public class BellmanFordSP {
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private double[] distTo; // distTo[v] = distance of shortest s->v path
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private DirectedEdge[] edgeTo; // edgeTo[v] = last edge on shortest s->v path
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private boolean[] onQueue; // onQueue[v] = is v currently on the queue?
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private Queue<Integer> queue; // queue of vertices to relax
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private int cost; // number of calls to relax()
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private Iterable<DirectedEdge> cycle; // negative cycle (or null if no such cycle)
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/**
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* Computes a shortest paths tree from s to every other vertex in
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* the edge-weighted digraph G .
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* @param G the acyclic digraph
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* @param s the source vertex
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* @throws IllegalArgumentException unless 0 ≤ s ≤ V - 1
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*/
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public BellmanFordSP(EdgeWeightedDigraph G, int s) {
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distTo = new double[G.V()];
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edgeTo = new DirectedEdge[G.V()];
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onQueue = new boolean[G.V()];
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for (int v = 0; v < G.V(); v++)
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distTo[v] = Double.POSITIVE_INFINITY;
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distTo[s] = 0.0;
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// Bellman-Ford algorithm
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queue = new Queue<Integer>();
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queue.enqueue(s);
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onQueue[s] = true;
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while (!queue.isEmpty() && !hasNegativeCycle()) {
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int v = queue.dequeue();
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onQueue[v] = false;
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relax(G, v);
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}
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assert check(G, s);
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}
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// relax vertex v and put other endpoints on queue if changed
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private void relax(EdgeWeightedDigraph G, int v) {
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for (DirectedEdge e : G.adj(v)) {
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int w = e.to();
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if (distTo[w] > distTo[v] + e.weight()) {
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distTo[w] = distTo[v] + e.weight();
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edgeTo[w] = e;
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if (!onQueue[w]) {
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queue.enqueue(w);
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onQueue[w] = true;
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}
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}
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if (cost++ % G.V() == 0)
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findNegativeCycle();
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}
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}
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/**
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* Is there a negative cycle reachable from the source vertex s ?
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* @return true if there is a negative cycle reachable from the
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* source vertex s , and false otherwise
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*/
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public boolean hasNegativeCycle() {
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return cycle != null;
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}
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/**
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* Returns a negative cycle reachable from the source vertex s , or null
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* if there is no such cycle.
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* @return a negative cycle reachable from the soruce vertex s
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* as an iterable of edges, and null if there is no such cycle
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*/
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public Iterable<DirectedEdge> negativeCycle() {
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return cycle;
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}
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// by finding a cycle in predecessor graph
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private void findNegativeCycle() {
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int V = edgeTo.length;
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EdgeWeightedDigraph spt = new EdgeWeightedDigraph(V);
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for (int v = 0; v < V; v++)
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if (edgeTo[v] != null)
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spt.addEdge(edgeTo[v]);
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EdgeWeightedDirectedCycle finder = new EdgeWeightedDirectedCycle(spt);
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cycle = finder.cycle();
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}
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/**
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* Returns the length of a shortest path from the source vertex s to vertex v .
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* @param v the destination vertex
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* @return the length of a shortest path from the source vertex s to vertex v ;
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* Double.POSITIVE_INFINITY if no such path
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* @throws UnsupportedOperationException if there is a negative cost cycle reachable
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* from the source vertex s
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*/
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public double distTo(int v) {
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if (hasNegativeCycle())
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throw new UnsupportedOperationException("Negative cost cycle exists");
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return distTo[v];
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}
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/**
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* Is there a path from the source s to vertex v ?
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* @param v the destination vertex
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* @return true if there is a path from the source vertex
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* s to vertex v , and false otherwise
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*/
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public boolean hasPathTo(int v) {
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return distTo[v] < Double.POSITIVE_INFINITY;
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}
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/**
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* Returns a shortest path from the source s to vertex v .
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* @param v the destination vertex
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* @return a shortest path from the source s to vertex v
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* as an iterable of edges, and null if no such path
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* @throws UnsupportedOperationException if there is a negative cost cycle reachable
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* from the source vertex s
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*/
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public Iterable<DirectedEdge> pathTo(int v) {
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if (hasNegativeCycle())
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throw new UnsupportedOperationException("Negative cost cycle exists");
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if (!hasPathTo(v)) return null;
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Stack<DirectedEdge> path = new Stack<DirectedEdge>();
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for (DirectedEdge e = edgeTo[v]; e != null; e = edgeTo[e.from()]) {
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path.push(e);
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}
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return path;
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}
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// check optimality conditions: either
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// (i) there exists a negative cycle reacheable from s
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// or
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// (ii) for all edges e = v->w: distTo[w] <= distTo[v] + e.weight()
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// (ii') for all edges e = v->w on the SPT: distTo[w] == distTo[v] + e.weight()
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private boolean check(EdgeWeightedDigraph G, int s) {
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// has a negative cycle
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if (hasNegativeCycle()) {
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double weight = 0.0;
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for (DirectedEdge e : negativeCycle()) {
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weight += e.weight();
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}
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if (weight >= 0.0) {
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System.err.println("error: weight of negative cycle = " + weight);
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return false;
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}
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}
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// no negative cycle reachable from source
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else {
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// check that distTo[v] and edgeTo[v] are consistent
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if (distTo[s] != 0.0 || edgeTo[s] != null) {
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System.err.println("distanceTo[s] and edgeTo[s] inconsistent");
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return false;
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}
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for (int v = 0; v < G.V(); v++) {
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if (v == s) continue;
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if (edgeTo[v] == null && distTo[v] != Double.POSITIVE_INFINITY) {
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System.err.println("distTo[] and edgeTo[] inconsistent");
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return false;
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}
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}
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// check that all edges e = v->w satisfy distTo[w] <= distTo[v] + e.weight()
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for (int v = 0; v < G.V(); v++) {
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for (DirectedEdge e : G.adj(v)) {
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int w = e.to();
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if (distTo[v] + e.weight() < distTo[w]) {
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System.err.println("edge " + e + " not relaxed");
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return false;
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}
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}
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}
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// check that all edges e = v->w on SPT satisfy distTo[w] == distTo[v] + e.weight()
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for (int w = 0; w < G.V(); w++) {
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if (edgeTo[w] == null) continue;
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DirectedEdge e = edgeTo[w];
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int v = e.from();
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if (w != e.to()) return false;
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if (distTo[v] + e.weight() != distTo[w]) {
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System.err.println("edge " + e + " on shortest path not tight");
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return false;
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}
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}
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}
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StdOut.println("Satisfies optimality conditions");
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StdOut.println();
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return true;
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}
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/**
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* Unit tests the BellmanFordSP data type.
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*/
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public static void main(String[] args) {
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In in = new In(args[0]);
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int s = Integer.parseInt(args[1]);
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EdgeWeightedDigraph G = new EdgeWeightedDigraph(in);
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BellmanFordSP sp = new BellmanFordSP(G, s);
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// print negative cycle
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if (sp.hasNegativeCycle()) {
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for (DirectedEdge e : sp.negativeCycle())
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StdOut.println(e);
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}
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// print shortest paths
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else {
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for (int v = 0; v < G.V(); v++) {
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if (sp.hasPathTo(v)) {
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StdOut.printf("%d to %d (%5.2f) ", s, v, sp.distTo(v));
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for (DirectedEdge e : sp.pathTo(v)) {
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StdOut.print(e + " ");
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}
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StdOut.println();
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}
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else {
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StdOut.printf("%d to %d no path\n", s, v);
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}
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}
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}
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}
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}
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