You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
223 lines
7.9 KiB
Java
223 lines
7.9 KiB
Java
|
|
|
|
import edu.princeton.cs.introcs.In;
|
|
import edu.princeton.cs.introcs.StdOut;
|
|
|
|
/*************************************************************************
|
|
* Compilation: javac DijkstraSP.java
|
|
* Execution: java DijkstraSP input.txt s
|
|
* Dependencies: EdgeWeightedDigraph.java IndexMinPQ.java Stack.java DirectedEdge.java
|
|
* Data files: http://algs4.cs.princeton.edu/44sp/tinyEWD.txt
|
|
* http://algs4.cs.princeton.edu/44sp/mediumEWD.txt
|
|
* http://algs4.cs.princeton.edu/44sp/largeEWD.txt
|
|
*
|
|
* Dijkstra's algorithm. Computes the shortest path tree.
|
|
* Assumes all weights are nonnegative.
|
|
*
|
|
* % java DijkstraSP tinyEWD.txt 0
|
|
* 0 to 0 (0.00)
|
|
* 0 to 1 (1.05) 0->4 0.38 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 (0.38) 0->4 0.38
|
|
* 0 to 5 (0.73) 0->4 0.38 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 DijkstraSP mediumEWD.txt 0
|
|
* 0 to 0 (0.00)
|
|
* 0 to 1 (0.71) 0->44 0.06 44->93 0.07 ... 107->1 0.07
|
|
* 0 to 2 (0.65) 0->44 0.06 44->231 0.10 ... 42->2 0.11
|
|
* 0 to 3 (0.46) 0->97 0.08 97->248 0.09 ... 45->3 0.12
|
|
* 0 to 4 (0.42) 0->44 0.06 44->93 0.07 ... 77->4 0.11
|
|
* ...
|
|
*
|
|
*************************************************************************/
|
|
|
|
|
|
/**
|
|
* The DijkstraSP class represents a data type for solving the
|
|
* single-source shortest paths problem in edge-weighted digraphs
|
|
* where the edge weights are nonnegative.
|
|
*
|
|
* This implementation uses Dijkstra's algorithm with a binary heap.
|
|
* The constructor takes time proportional to E log V ,
|
|
* 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 <a href="/algs4/44sp">Section 4.4</a> of
|
|
* Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.
|
|
*
|
|
* @author Robert Sedgewick
|
|
* @author Kevin Wayne
|
|
*/
|
|
public class DijkstraSP {
|
|
private double[] distTo; // distTo[v] = distance of shortest s->v path
|
|
private DirectedEdge[] edgeTo; // edgeTo[v] = last edge on shortest s->v path
|
|
private IndexMinPQ<Double> pq; // priority queue of vertices
|
|
|
|
/**
|
|
* Computes a shortest paths tree from s to every other vertex in
|
|
* the edge-weighted digraph G .
|
|
* @param G the edge-weighted digraph
|
|
* @param s the source vertex
|
|
* @throws IllegalArgumentException if an edge weight is negative
|
|
* @throws IllegalArgumentException unless 0 ≤ s ≤ V - 1
|
|
*/
|
|
public DijkstraSP(EdgeWeightedDigraph G, int s) {
|
|
for (DirectedEdge e : G.edges()) {
|
|
if (e.weight() < 0)
|
|
throw new IllegalArgumentException("edge " + e + " has negative weight");
|
|
}
|
|
|
|
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;
|
|
|
|
// relax vertices in order of distance from s
|
|
pq = new IndexMinPQ<Double>(G.V());
|
|
pq.insert(s, distTo[s]);
|
|
while (!pq.isEmpty()) {
|
|
int v = pq.delMin();
|
|
for (DirectedEdge e : G.adj(v))
|
|
relax(e);
|
|
}
|
|
|
|
// check optimality conditions
|
|
assert check(G, s);
|
|
}
|
|
|
|
// relax edge e and update pq if changed
|
|
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;
|
|
if (pq.contains(w)) pq.decreaseKey(w, distTo[w]);
|
|
else pq.insert(w, distTo[w]);
|
|
}
|
|
}
|
|
|
|
/**
|
|
* 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<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:
|
|
// (i) for all edges e: distTo[e.to()] <= distTo[e.from()] + e.weight()
|
|
// (ii) for all edge e on the SPT: distTo[e.to()] == distTo[e.from()] + e.weight()
|
|
private boolean check(EdgeWeightedDigraph G, int s) {
|
|
|
|
// check that edge weights are nonnegative
|
|
for (DirectedEdge e : G.edges()) {
|
|
if (e.weight() < 0) {
|
|
System.err.println("negative edge weight detected");
|
|
return false;
|
|
}
|
|
}
|
|
|
|
// check that distTo[v] and edgeTo[v] are consistent
|
|
if (distTo[s] != 0.0 || edgeTo[s] != null) {
|
|
System.err.println("distTo[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;
|
|
}
|
|
}
|
|
return true;
|
|
}
|
|
|
|
|
|
/**
|
|
* Unit tests the DijkstraSP data type.
|
|
*/
|
|
public static void main(String[] args) {
|
|
In in = new In(args[0]);
|
|
EdgeWeightedDigraph G = new EdgeWeightedDigraph(in);
|
|
int s = Integer.parseInt(args[1]);
|
|
|
|
// compute shortest paths
|
|
DijkstraSP sp = new DijkstraSP(G, s);
|
|
|
|
|
|
// print shortest path
|
|
for (int t = 0; t < G.V(); t++) {
|
|
if (sp.hasPathTo(t)) {
|
|
StdOut.printf("%d to %d (%.2f) ", s, t, sp.distTo(t));
|
|
if (sp.hasPathTo(t)) {
|
|
for (DirectedEdge e : sp.pathTo(t)) {
|
|
StdOut.print(e + " ");
|
|
}
|
|
}
|
|
StdOut.println();
|
|
}
|
|
else {
|
|
StdOut.printf("%d to %d no path\n", s, t);
|
|
}
|
|
}
|
|
}
|
|
|
|
}
|