Dijkstra's algorithm (or Dijkstra's Shortest path First algorithm, SPF algorithm) is an algorithm for finding the shortest paths between nodes in a graph, which may represent, for example, road networks. A widely used application of shortest path algorithm is network routing protocols, most notably IS-IS (Intermediate System to Intermediate System) and open Shortest path As a solution, he re-observed the algorithm known as Prim's minimal spanning tree algorithm (known earlier to Jarník, and also rediscovered by Prim). He designed the shortest path algorithm and later implemented it for ARMAC for a slightly simplified transportation map of 64 city in the Netherlands (64, so that 6 bits would be sufficient to encode the city number).What is the shortest manner to travel from Rotterdam to Groningen, in general: from given city to given city.

If the destination node has been marked visited (when planning a path between two specific nodes) or if the smallest tentative distance among the nodes in the unvisited set is infinity (when planning a complete traversal; happens when there is no connection between the initial node and remaining unvisited nodes), then stop. Otherwise, choose the unvisited node that is marked with the smallest tentative distance, put it as the new" current node", and go back to step 3. When planning a path, it is actually not necessary to wait until the destination node is" visited" as above: the algorithm can stop once the destination node has the smallest tentative distance among all" unvisited" nodes (and thus could be choose as the next" current").

```
package Others;
/**
* Dijkstra's algorithm,is a graph search algorithm that solves the single-source
* shortest path problem for a graph with nonnegative edge path costs, producing
* a shortest path tree.
* <p>
* NOTE: The inputs to Dijkstra's algorithm are a directed and weighted graph consisting
* of 2 or more nodes, generally represented by an adjacency matrix or list, and a start node.
* <p>
* Original source of code: https://rosettacode.org/wiki/Dijkstra%27s_algorithm#Java
* Also most of the comments are from RosettaCode.
*/
import java.util.*;
public class Dijkstra {
private static final Graph.Edge[] GRAPH = {
// Distance from node "a" to node "b" is 7.
// In the current Graph there is no way to move the other way (e,g, from "b" to "a"),
// a new edge would be needed for that
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("b", "d", 15),
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";
/**
* main function
* Will run the code with "GRAPH" that was defined above.
*/
public static void main(String[] args) {
Graph g = new Graph(GRAPH);
g.dijkstra(START);
g.printPath(END);
//g.printAllPaths();
}
}
class Graph {
// mapping of vertex names to Vertex objects, built from a set of Edges
private final Map<String, Vertex> graph;
/**
* 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;
// MAX_VALUE assumed to be infinity
public int dist = Integer.MAX_VALUE;
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) {
if (dist == other.dist)
return name.compareTo(other.name);
return Integer.compare(dist, other.dist);
}
@Override
public boolean equals(Object object) {
if (this == object) return true;
if (object == null || getClass() != object.getClass()) return false;
if (!super.equals(object)) return false;
Vertex vertex = (Vertex) object;
if (dist != vertex.dist) return false;
if (name != null ? !name.equals(vertex.name) : vertex.name != null) return false;
if (previous != null ? !previous.equals(vertex.previous) : vertex.previous != null) return false;
if (neighbours != null ? !neighbours.equals(vertex.neighbours) : vertex.neighbours != null) return false;
return true;
}
@Override
public int hashCode() {
int result = super.hashCode();
result = 31 * result + (name != null ? name.hashCode() : 0);
result = 31 * result + dist;
result = 31 * result + (previous != null ? previous.hashCode() : 0);
result = 31 * result + (neighbours != null ? neighbours.hashCode() : 0);
return result;
}
@Override
public String toString() {
return "(" + name + ", " + 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);
NavigableSet<Vertex> q = new TreeSet<>();
// 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 binary heap.
*/
private void dijkstra(final NavigableSet<Vertex> q) {
Vertex u, v;
while (!q.isEmpty()) {
// vertex with shortest distance (first iteration will return source)
u = q.pollFirst();
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();
}
}
}
```