import edu.princeton.cs.introcs.In; import edu.princeton.cs.introcs.StdOut; /************************************************************************* * Compilation: javac AcyclicSP.java * Execution: java AcyclicSP V E * Dependencies: EdgeWeightedDigraph.java DirectedEdge.java Topological.java * Data files: http://algs4.cs.princeton.edu/44sp/tinyEWDAG.txt * * Computes shortest paths in an edge-weighted acyclic digraph. * * % java AcyclicSP tinyEWDAG.txt 5 * 5 to 0 (0.73) 5->4 0.35 4->0 0.38 * 5 to 1 (0.32) 5->1 0.32 * 5 to 2 (0.62) 5->7 0.28 7->2 0.34 * 5 to 3 (0.61) 5->1 0.32 1->3 0.29 * 5 to 4 (0.35) 5->4 0.35 * 5 to 5 (0.00) * 5 to 6 (1.13) 5->1 0.32 1->3 0.29 3->6 0.52 * 5 to 7 (0.28) 5->7 0.28 * *************************************************************************/ /** * The AcyclicSP class represents a data type for solving the * single-source shortest paths problem in edge-weighted directed acyclic * graphs (DAGs). The edge weights can be positive, negative, or zero. * * This implementation uses a topological-sort based algorithm. * The constructor takes time proportional to V + E , * where V is the number of vertices and E is the number of edges. * Afterwards, the distTo() and hasPathTo() methods take * constant time and the pathTo() method takes time proportional to the * number of edges in the shortest path returned. * * For additional documentation, see Section 4.4 of * Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne. * * @author Robert Sedgewick * @author Kevin Wayne */ public class AcyclicSP { private double[] distTo; // distTo[v] = distance of shortest s->v path private DirectedEdge[] edgeTo; // edgeTo[v] = last edge on shortest s->v path /** * Computes a shortest paths tree from s to every other vertex in * the directed acyclic graph G . * @param G the acyclic digraph * @param s the source vertex * @throws IllegalArgumentException if the digraph is not acyclic * @throws IllegalArgumentException unless 0 ≤ s ≤ V - 1 */ public AcyclicSP(EdgeWeightedDigraph G, int s) { distTo = new double[G.V()]; edgeTo = new DirectedEdge[G.V()]; for (int v = 0; v < G.V(); v++) distTo[v] = Double.POSITIVE_INFINITY; distTo[s] = 0.0; // visit vertices in toplogical order Topological topological = new Topological(G); if (!topological.hasOrder()) throw new IllegalArgumentException("Digraph is not acyclic."); for (int v : topological.order()) { for (DirectedEdge e : G.adj(v)) relax(e); } } // relax edge e private void relax(DirectedEdge e) { int v = e.from(), w = e.to(); if (distTo[w] > distTo[v] + e.weight()) { distTo[w] = distTo[v] + e.weight(); edgeTo[w] = e; } } /** * Returns the length of a shortest path from the source vertex s to vertex v . * @param v the destination vertex * @return the length of a shortest path from the source vertex s to vertex v ; * Double.POSITIVE_INFINITY if no such path */ public double distTo(int v) { return distTo[v]; } /** * Is there a path from the source vertex s to vertex v ? * @param v the destination vertex * @return true if there is a path from the source vertex * s to vertex v , and false otherwise */ public boolean hasPathTo(int v) { return distTo[v] < Double.POSITIVE_INFINITY; } /** * Returns a shortest path from the source vertex s to vertex v . * @param v the destination vertex * @return a shortest path from the source vertex s to vertex v * as an iterable of edges, and null if no such path */ public Iterable pathTo(int v) { if (!hasPathTo(v)) return null; Stack path = new Stack(); for (DirectedEdge e = edgeTo[v]; e != null; e = edgeTo[e.from()]) { path.push(e); } return path; } /** * Unit tests the AcyclicSP data type. */ public static void main(String[] args) { In in = new In(args[0]); int s = Integer.parseInt(args[1]); EdgeWeightedDigraph G = new EdgeWeightedDigraph(in); // find shortest path from s to each other vertex in DAG AcyclicSP sp = new AcyclicSP(G, s); for (int v = 0; v < G.V(); v++) { if (sp.hasPathTo(v)) { StdOut.printf("%d to %d (%.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); } } } }