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/*This is a java program to find shortest path from a single vertex. The Bellman–Ford algorithm is an algorithm that computes shortest paths from a single source vertex to all of the other vertices in a weighted digraph.[1] It is slower than Dijkstra’s algorithm for the same problem, but more versatile, as it is capable of handling graphs in which some of the edge weights are negative numbers.*/
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import java.util.Scanner;
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public class BellmanFord
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{
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private int distances[];
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private int numberofvertices;
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public static final int MAX_VALUE = 999;
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public BellmanFord(int numberofvertices)
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{
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this.numberofvertices = numberofvertices;
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distances = new int[numberofvertices + 1];
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}
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public void BellmanFordEvaluation(int source, int destination,
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int adjacencymatrix[][])
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{
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for (int node = 1; node <= numberofvertices; node++)
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{
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distances[node] = MAX_VALUE;
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}
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distances[source] = 0;
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for (int node = 1; node <= numberofvertices - 1; node++)
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{
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for (int sourcenode = 1; sourcenode <= numberofvertices; sourcenode++)
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{
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for (int destinationnode = 1; destinationnode <= numberofvertices; destinationnode++)
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{
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if (adjacencymatrix[sourcenode][destinationnode] != MAX_VALUE)
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{
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if (distances[destinationnode] > distances[sourcenode]
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+ adjacencymatrix[sourcenode][destinationnode])
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distances[destinationnode] = distances[sourcenode]
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+ adjacencymatrix[sourcenode][destinationnode];
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}
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}
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}
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}
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for (int sourcenode = 1; sourcenode <= numberofvertices; sourcenode++)
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{
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for (int destinationnode = 1; destinationnode <= numberofvertices; destinationnode++)
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{
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if (adjacencymatrix[sourcenode][destinationnode] != MAX_VALUE)
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{
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if (distances[destinationnode] > distances[sourcenode]
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+ adjacencymatrix[sourcenode][destinationnode])
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System.out
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.println("The Graph contains negative egde cycle");
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}
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}
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}
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for (int vertex = 1; vertex <= numberofvertices; vertex++)
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{
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if (vertex == destination)
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System.out.println("distance of source " + source + " to "
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+ vertex + " is " + distances[vertex]);
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}
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}
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public static void main(String... arg)
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{
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int numberofvertices = 0;
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int source, destination;
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Scanner scanner = new Scanner(System.in);
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System.out.println("Enter the number of vertices");
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numberofvertices = scanner.nextInt();
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int adjacencymatrix[][] = new int[numberofvertices + 1][numberofvertices + 1];
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System.out.println("Enter the adjacency matrix");
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for (int sourcenode = 1; sourcenode <= numberofvertices; sourcenode++)
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{
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for (int destinationnode = 1; destinationnode <= numberofvertices; destinationnode++)
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{
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adjacencymatrix[sourcenode][destinationnode] = scanner
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.nextInt();
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if (sourcenode == destinationnode)
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{
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adjacencymatrix[sourcenode][destinationnode] = 0;
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continue;
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}
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if (adjacencymatrix[sourcenode][destinationnode] == 0)
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{
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adjacencymatrix[sourcenode][destinationnode] = MAX_VALUE;
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}
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}
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}
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System.out.println("Enter the source vertex");
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source = scanner.nextInt();
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System.out.println("Enter the destination vertex: ");
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destination = scanner.nextInt();
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BellmanFord bellmanford = new BellmanFord(numberofvertices);
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bellmanford.BellmanFordEvaluation(source, destination, adjacencymatrix);
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scanner.close();
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}
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}
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/*
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Output:
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Enter the number of vertices
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6
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Enter the adjacency matrix
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0 4 0 0 -1 0
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0 0 -1 0 -2 0
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0 0 0 0 0 0
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0 0 0 0 0 0
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0 0 0 -5 0 3
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0 0 0 0 0 0
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Enter the source vertex
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1
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Enter the destination vertex:
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4
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distance of source 1 to 4 is -6
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