bellman_ford.java

// A Java program for Bellman-Ford's single source shortest
// path algorithm.
 
import java.io.*;
import java.lang.*;
import java.util.*;
 
class Graph {
   
    class Edge {
        int src, dest, weight;
        Edge() { src = dest = weight = 0; }
    };
 
    int V, E;
    Edge edge[];
 
    Graph(int v, int e)
    {
        V = v;
        E = e;
        edge = new Edge[e];
        for (int i = 0; i < e; ++i)
            edge[i] = new Edge();
    }
 
    // The main function that finds shortest distances from
    // src to all other vertices using Bellman-Ford
    // algorithm. The function also detects negative weight
    // cycle
    void BellmanFord(Graph graph, int src)
    {
        int V = graph.V, E = graph.E;
        int dist[] = new int[V];
 
        // Step 1: Initialize distances from src to all
        // other vertices as INFINITE
        for (int i = 0; i < V; ++i)
            dist[i] = Integer.MAX_VALUE;
        dist[src] = 0;
 
        // Step 2: Relax all edges |V| - 1 times. A simple
        // shortest path from src to any other vertex can
        // have at-most |V| - 1 edges
        for (int i = 1; i < V; ++i) {
            for (int j = 0; j < E; ++j) {
                int u = graph.edge[j].src;
                int v = graph.edge[j].dest;
                int weight = graph.edge[j].weight;
                if (dist[u] != Integer.MAX_VALUE
                    && dist[u] + weight < dist[v])
                    dist[v] = dist[u] + weight;
            }
        }
 
        // Step 3: check for negative-weight cycles. The
        // above step guarantees shortest distances if graph
        // doesn't contain negative weight cycle. If we get
        // a shorter path, then there is a cycle.
        for (int j = 0; j < E; ++j) {
            int u = graph.edge[j].src;
            int v = graph.edge[j].dest;
            int weight = graph.edge[j].weight;
            if (dist[u] != Integer.MAX_VALUE
                && dist[u] + weight < dist[v]) {
                System.out.println(
                    "Graph contains negative weight cycle");
                return;
            }
        }
        printArr(dist, V);
    }
 
    // A utility function used to print the solution
    void printArr(int dist[], int V)
    {
        System.out.println("Vertex Distance from Source");
        for (int i = 0; i < V; ++i)
            System.out.println(i + "\t\t" + dist[i]);
    }
 
    // Driver's code
    public static void main(String[] args)
    {
        int V = 5; // Number of vertices in graph
        int E = 8; // Number of edges in graph
 
        Graph graph = new Graph(V, E);
 
        // add edge 0-1 (or A-B in above figure)
        graph.edge[0].src = 0;
        graph.edge[0].dest = 1;
        graph.edge[0].weight = -1;
 
        // add edge 0-2 (or A-C in above figure)
        graph.edge[1].src = 0;
        graph.edge[1].dest = 2;
        graph.edge[1].weight = 4;
 
        // add edge 1-2 (or B-C in above figure)
        graph.edge[2].src = 1;
        graph.edge[2].dest = 2;
        graph.edge[2].weight = 3;
 
        // add edge 1-3 (or B-D in above figure)
        graph.edge[3].src = 1;
        graph.edge[3].dest = 3;
        graph.edge[3].weight = 2;
 
        // add edge 1-4 (or B-E in above figure)
        graph.edge[4].src = 1;
        graph.edge[4].dest = 4;
        graph.edge[4].weight = 2;
 
        // add edge 3-2 (or D-C in above figure)
        graph.edge[5].src = 3;
        graph.edge[5].dest = 2;
        graph.edge[5].weight = 5;
 
        // add edge 3-1 (or D-B in above figure)
        graph.edge[6].src = 3;
        graph.edge[6].dest = 1;
        graph.edge[6].weight = 1;
 
        // add edge 4-3 (or E-D in above figure)
        graph.edge[7].src = 4;
        graph.edge[7].dest = 3;
        graph.edge[7].weight = -3;
         
          // Function call
        graph.BellmanFord(graph, 0);
    }
}