Dijkstra's algorithm: Difference between revisions
→{{header|Java}}
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=={{header|Java}}==
Algorithm is derived from Wikipedia section 'Using a priority queue'.
This implementation finds the single path from a source to all reachable vertices.
Building the graph from a set of edges takes O(E log V) for each pass.
Vertices are stored in a PriorityQueue (effectively a balanced binary heap), giving O(E log V) performance for removal of the head.
Decreasing the distance of a vertex is accomplished by removing it from the heap and later re-inserting it.
The former takes linear time, resulting in a potential bottleneck.
Use of a Fibonacci heap (which doesn't exist in the standard Java library) would alleviate this issue.
<lang java>
import java.io.*;
import java.util.*;
public class
new Graph.Edge("a", "b", 7),
new Graph.Edge("a", "c", 9),
new Graph.Edge("a", "f", 14),
new Graph.Edge("b", "c", 10),
new Graph.Edge("c", "d", 11),
new Graph.Edge("c", "f", 2),
new Graph.Edge("d", "e", 6),
new Graph.Edge("e", "f", 9),
};
private static final String START = "a";
private static final String END = "e";
public static void main(String[] args) {
g.dijkstra(START);
g.printPath(END);
//g.printAllPaths();
}
}
private final Map<String, Vertex> graph; // mapping of vertex names to Vertex objects, built from a set of Edges
/** One edge of the graph (only used by Graph constructor) */
public static class Edge {
public final String v1, v2;
public final int dist;
public Edge(String v1, String v2, int dist) {
this.v1 = v1;
this.v2 = v2;
this.dist = dist;
}
}
/** One vertex of the graph, complete with mappings to neighbouring vertices */
public static class Vertex implements Comparable<Vertex> {
public final String name;
public int dist = Integer.MAX_VALUE; // MAX_VALUE assumed to be infinity
public Vertex previous = null;
public final Map<Vertex, Integer> neighbours = new HashMap<>();
public Vertex(String name) {
this.name = name;
}
private void printPath() {
if (this == this.previous) {
System.out.printf("%s", this.name);
} else if (this.previous == null) {
System.out.printf("%s(unreached)", this.name);
} else {
this.previous.printPath();
System.out.printf(" -> %s(%d)", this.name, this.dist);
}
}
public int compareTo(Vertex other) {
return Integer.compare(dist, other.dist);
}
}
/** Builds a graph from a set of edges */
public Graph(Edge[] edges) {
graph = new HashMap<>(edges.length);
//one pass to find all vertices
for (Edge e : edges) {
if (!graph.containsKey(e.v1)) graph.put(e.v1, new Vertex(e.v1));
if (!graph.containsKey(e.v2)) graph.put(e.v2, new Vertex(e.v2));
}
//another pass to set neighbouring vertices
for (Edge e : edges) {
graph.get(e.v1).neighbours.put(graph.get(e.v2), e.dist);
//graph.get(e.v2).neighbours.put(graph.get(e.v1), e.dist); // also do this for an undirected graph
}
}
/** Runs dijkstra using a specified source vertex */
public void dijkstra(String startName) {
if (!graph.containsKey(startName)) {
System.err.printf("Graph doesn't contain start vertex \"%s\"\n", startName);
return;
}
final Vertex source = graph.get(startName);
PriorityQueue<Vertex> q = new PriorityQueue<>(graph.size());
// set-up vertices
for (Vertex v : graph.values()) {
v.previous = v == source ? source : null;
v.dist = v == source ? 0 : Integer.MAX_VALUE;
q.add(v);
}
dijkstra(q);
}
/** Implementation of dijkstra's algorithm using a priority queue. */
private void dijkstra(final PriorityQueue<Vertex> q) {
Vertex u, v;
while (!q.isEmpty()) {
u = q.poll(); // vertex with shortest distance (first iteration will return source)
if (u.dist == Integer.MAX_VALUE) break; // we can ignore u (and any other remaining vertices) since they are unreachable
//look at distances to each neighbour
for (Map.Entry<Vertex, Integer> a : u.neighbours.entrySet()) {
v = a.getKey(); //the neighbour in this iteration
final int alternateDist = u.dist + a.getValue();
if (alternateDist < v.dist) { // shorter path to neighbour found
q.remove(v);
v.dist = alternateDist;
v.previous = u;
q.add(v);
}
}
}
}
/** Prints a path from the source to the specified vertex */
public void printPath(String endName) {
if (!graph.containsKey(endName)) {
System.err.printf("Graph doesn't contain end vertex \"%s\"\n", endName);
return;
}
graph.get(endName).printPath();
System.out.println();
}
/** Prints the path from the source to every vertex (output order is not guaranteed) */
public void printAllPaths() {
for (Vertex v : graph.values()) {
v.printPath();
System.out.println();
}
}
}</lang>{{out}}<pre>
a -> c(9) -> d(20) -> e(26)
</pre>
=={{header|Mathematica}}==
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