223 lines
7.9 KiB
Java
223 lines
7.9 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 DijkstraSP.java
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* Execution: java DijkstraSP input.txt s
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* Dependencies: EdgeWeightedDigraph.java IndexMinPQ.java Stack.java DirectedEdge.java
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* Data files: http://algs4.cs.princeton.edu/44sp/tinyEWD.txt
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* http://algs4.cs.princeton.edu/44sp/mediumEWD.txt
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* http://algs4.cs.princeton.edu/44sp/largeEWD.txt
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*
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* Dijkstra's algorithm. Computes the shortest path tree.
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* Assumes all weights are nonnegative.
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*
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* % java DijkstraSP tinyEWD.txt 0
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* 0 to 0 (0.00)
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* 0 to 1 (1.05) 0->4 0.38 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 (0.38) 0->4 0.38
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* 0 to 5 (0.73) 0->4 0.38 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 DijkstraSP mediumEWD.txt 0
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* 0 to 0 (0.00)
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* 0 to 1 (0.71) 0->44 0.06 44->93 0.07 ... 107->1 0.07
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* 0 to 2 (0.65) 0->44 0.06 44->231 0.10 ... 42->2 0.11
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* 0 to 3 (0.46) 0->97 0.08 97->248 0.09 ... 45->3 0.12
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* 0 to 4 (0.42) 0->44 0.06 44->93 0.07 ... 77->4 0.11
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* ...
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*
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*************************************************************************/
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/**
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* The DijkstraSP class represents a data type for solving the
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* single-source shortest paths problem in edge-weighted digraphs
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* where the edge weights are nonnegative.
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*
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* This implementation uses Dijkstra's algorithm with a binary heap.
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* The constructor takes time proportional to E log V ,
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* where V is the number of vertices and E is the number of edges.
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* Afterwards, the distTo() and hasPathTo() methods take
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* constant time and the pathTo() method takes time proportional to the
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* number of edges in the shortest path 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 DijkstraSP {
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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 IndexMinPQ<Double> pq; // priority queue of vertices
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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 edge-weighted digraph
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* @param s the source vertex
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* @throws IllegalArgumentException if an edge weight is negative
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* @throws IllegalArgumentException unless 0 ≤ s ≤ V - 1
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*/
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public DijkstraSP(EdgeWeightedDigraph G, int s) {
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for (DirectedEdge e : G.edges()) {
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if (e.weight() < 0)
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throw new IllegalArgumentException("edge " + e + " has negative weight");
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}
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distTo = new double[G.V()];
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edgeTo = new DirectedEdge[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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// relax vertices in order of distance from s
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pq = new IndexMinPQ<Double>(G.V());
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pq.insert(s, distTo[s]);
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while (!pq.isEmpty()) {
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int v = pq.delMin();
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for (DirectedEdge e : G.adj(v))
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relax(e);
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}
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// check optimality conditions
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assert check(G, s);
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}
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// relax edge e and update pq if changed
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private void relax(DirectedEdge e) {
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int v = e.from(), 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 (pq.contains(w)) pq.decreaseKey(w, distTo[w]);
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else pq.insert(w, distTo[w]);
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}
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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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*/
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public double distTo(int v) {
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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 vertex 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 vertex s to vertex v .
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* @param v the destination vertex
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* @return a shortest path from the source vertex s to vertex v
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* as an iterable of edges, and null if no such path
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*/
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public Iterable<DirectedEdge> pathTo(int v) {
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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:
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// (i) for all edges e: distTo[e.to()] <= distTo[e.from()] + e.weight()
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// (ii) for all edge e on the SPT: distTo[e.to()] == distTo[e.from()] + e.weight()
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private boolean check(EdgeWeightedDigraph G, int s) {
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// check that edge weights are nonnegative
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for (DirectedEdge e : G.edges()) {
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if (e.weight() < 0) {
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System.err.println("negative edge weight detected");
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return false;
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}
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}
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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("distTo[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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return true;
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}
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/**
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* Unit tests the DijkstraSP 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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EdgeWeightedDigraph G = new EdgeWeightedDigraph(in);
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int s = Integer.parseInt(args[1]);
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// compute shortest paths
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DijkstraSP sp = new DijkstraSP(G, s);
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// print shortest path
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for (int t = 0; t < G.V(); t++) {
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if (sp.hasPathTo(t)) {
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StdOut.printf("%d to %d (%.2f) ", s, t, sp.distTo(t));
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if (sp.hasPathTo(t)) {
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for (DirectedEdge e : sp.pathTo(t)) {
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StdOut.print(e + " ");
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}
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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, t);
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}
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}
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}
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}
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