edu.princeton.cs.algs4.DijkstraUndirectedSP Maven / Gradle / Ivy
/******************************************************************************
* Compilation: javac DijkstraUndirectedSP.java
* Execution: java DijkstraUndirectedSP input.txt s
* Dependencies: EdgeWeightedGraph.java IndexMinPQ.java Stack.java Edge.java
* Data files: https://algs4.cs.princeton.edu/43mst/tinyEWG.txt
* https://algs4.cs.princeton.edu/43mst/mediumEWG.txt
* https://algs4.cs.princeton.edu/43mst/largeEWG.txt
*
* Dijkstra's algorithm. Computes the shortest path tree.
* Assumes all weights are nonnegative.
*
* % java DijkstraUndirectedSP tinyEWG.txt 6
* 6 to 0 (0.58) 6-0 0.58000
* 6 to 1 (0.76) 6-2 0.40000 1-2 0.36000
* 6 to 2 (0.40) 6-2 0.40000
* 6 to 3 (0.52) 3-6 0.52000
* 6 to 4 (0.93) 6-4 0.93000
* 6 to 5 (1.02) 6-2 0.40000 2-7 0.34000 5-7 0.28000
* 6 to 6 (0.00)
* 6 to 7 (0.74) 6-2 0.40000 2-7 0.34000
*
* % java DijkstraUndirectedSP mediumEWG.txt 0
* 0 to 0 (0.00)
* 0 to 1 (0.71) 0-44 0.06471 44-93 0.06793 ... 1-107 0.07484
* 0 to 2 (0.65) 0-44 0.06471 44-231 0.10384 ... 2-42 0.11456
* 0 to 3 (0.46) 0-97 0.07705 97-248 0.08598 ... 3-45 0.11902
* ...
*
* % java DijkstraUndirectedSP largeEWG.txt 0
* 0 to 0 (0.00)
* 0 to 1 (0.78) 0-460790 0.00190 460790-696678 0.00173 ... 1-826350 0.00191
* 0 to 2 (0.61) 0-15786 0.00130 15786-53370 0.00113 ... 2-793420 0.00040
* 0 to 3 (0.31) 0-460790 0.00190 460790-752483 0.00194 ... 3-698373 0.00172
*
******************************************************************************/
package edu.princeton.cs.algs4;
/**
* The {@code DijkstraUndirectedSP} class represents a data type for solving
* the single-source shortest paths problem in edge-weighted graphs
* 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.
* Each call to {@code distTo(int)} and {@code hasPathTo(int)} takes constant time;
* each call to {@code pathTo(int)} 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.
* See {@link DijkstraSP} for a version on edge-weighted digraphs.
*
* @author Robert Sedgewick
* @author Kevin Wayne
* @author Nate Liu
*/
public class DijkstraUndirectedSP {
private double[] distTo; // distTo[v] = distance of shortest s->v path
private Edge[] edgeTo; // edgeTo[v] = last edge on shortest s->v path
private IndexMinPQ pq; // priority queue of vertices
/**
* Computes a shortest-paths tree from the source vertex {@code s} to every
* other vertex in the edge-weighted graph {@code G}.
*
* @param G the edge-weighted digraph
* @param s the source vertex
* @throws IllegalArgumentException if an edge weight is negative
* @throws IllegalArgumentException unless {@code 0 <= s < V}
*/
public DijkstraUndirectedSP(EdgeWeightedGraph G, int s) {
for (Edge e : G.edges()) {
if (e.weight() < 0)
throw new IllegalArgumentException("edge " + e + " has negative weight");
}
distTo = new double[G.V()];
edgeTo = new Edge[G.V()];
validateVertex(s);
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(G.V());
pq.insert(s, distTo[s]);
while (!pq.isEmpty()) {
int v = pq.delMin();
for (Edge e : G.adj(v))
relax(e, v);
}
// check optimality conditions
assert check(G, s);
}
// relax edge e and update pq if changed
private void relax(Edge e, int v) {
int w = e.other(v);
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 between the source vertex {@code s} and
* vertex {@code v}.
*
* @param v the destination vertex
* @return the length of a shortest path between the source vertex {@code s} and
* the vertex {@code v}; {@code Double.POSITIVE_INFINITY} if no such path
* @throws IllegalArgumentException unless {@code 0 <= v < V}
*/
public double distTo(int v) {
validateVertex(v);
return distTo[v];
}
/**
* Returns true if there is a path between the source vertex {@code s} and
* vertex {@code v}.
*
* @param v the destination vertex
* @return {@code true} if there is a path between the source vertex
* {@code s} to vertex {@code v}; {@code false} otherwise
* @throws IllegalArgumentException unless {@code 0 <= v < V}
*/
public boolean hasPathTo(int v) {
validateVertex(v);
return distTo[v] < Double.POSITIVE_INFINITY;
}
/**
* Returns a shortest path between the source vertex {@code s} and vertex {@code v}.
*
* @param v the destination vertex
* @return a shortest path between the source vertex {@code s} and vertex {@code v};
* {@code null} if no such path
* @throws IllegalArgumentException unless {@code 0 <= v < V}
*/
public Iterable pathTo(int v) {
validateVertex(v);
if (!hasPathTo(v)) return null;
Stack path = new Stack();
int x = v;
for (Edge e = edgeTo[v]; e != null; e = edgeTo[x]) {
path.push(e);
x = e.other(x);
}
return path;
}
// check optimality conditions:
// (i) for all edges e = v-w: distTo[w] <= distTo[v] + e.weight()
// (ii) for all edge e = v-w on the SPT: distTo[w] == distTo[v] + e.weight()
private boolean check(EdgeWeightedGraph G, int s) {
// check that edge weights are nonnegative
for (Edge 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 (Edge e : G.adj(v)) {
int w = e.other(v);
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;
Edge e = edgeTo[w];
if (w != e.either() && w != e.other(e.either())) return false;
int v = e.other(w);
if (distTo[v] + e.weight() != distTo[w]) {
System.err.println("edge " + e + " on shortest path not tight");
return false;
}
}
return true;
}
// throw an IllegalArgumentException unless {@code 0 <= v < V}
private void validateVertex(int v) {
int V = distTo.length;
if (v < 0 || v >= V)
throw new IllegalArgumentException("vertex " + v + " is not between 0 and " + (V-1));
}
/**
* Unit tests the {@code DijkstraUndirectedSP} data type.
*
* @param args the command-line arguments
*/
public static void main(String[] args) {
In in = new In(args[0]);
EdgeWeightedGraph G = new EdgeWeightedGraph(in);
int s = Integer.parseInt(args[1]);
// compute shortest paths
DijkstraUndirectedSP sp = new DijkstraUndirectedSP(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));
for (Edge e : sp.pathTo(t)) {
StdOut.print(e + " ");
}
StdOut.println();
}
else {
StdOut.printf("%d to %d no path\n", s, t);
}
}
}
}
/******************************************************************************
* Copyright 2002-2018, Robert Sedgewick and Kevin Wayne.
*
* This file is part of algs4.jar, which accompanies the textbook
*
* Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne,
* Addison-Wesley Professional, 2011, ISBN 0-321-57351-X.
* http://algs4.cs.princeton.edu
*
*
* algs4.jar is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* algs4.jar is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with algs4.jar. If not, see http://www.gnu.org/licenses.
******************************************************************************/