bellman-ford.c

// A C / C++ program for Bellman-Ford's single source shortest path algorithm.

// http://www.geeksforgeeks.org/dynamic-programming-set-23-bellman-ford-algorithm/

/* input
10 18
0 1 3
0 2 5
0 4 4
1 4 1
2 4 2
2 3 2
3 4 -1
1 7 4
4 7 -2
4 6 3
3 5 3
5 6 2
7 6 2
7 9 5
6 9 2
6 8 5
5 8 4
8 9 5

*/

#include <stdio.h>

#include <stdlib.h>

#include <string.h>

#include <limits.h>



// a structure to represent a weighted edge in graph

struct Edge

{

    int src, dest, weight;

};



// a structure to represent a connected, directed and weighted graph

struct Graph

{

    // V-> Number of vertices, E-> Number of edges

    int V, E;



    // graph is represented as an array of edges.

    struct Edge* edge;

};



// Creates a graph with V vertices and E edges

struct Graph* createGraph(int V, int E)

{

    struct Graph* graph = (struct Graph*) malloc( sizeof(struct Graph) );

    graph->V = V;

    graph->E = E;



    graph->edge = (struct Edge*) malloc( graph->E * sizeof( struct Edge ) );



    return graph;

}



// A utility function used to print the solution

void printArr(int dist[], int n)

{

    printf("Vertex   Distance from Source\n");
    int i;
    for (i = 0; i < n; ++i)

        printf("%d \t\t %d\n", i, dist[i]);

}



// 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(struct Graph* graph, int src)

{

    int V = graph->V;

    int E = graph->E;

    int dist[V];

    int i,j;

    // Step 1: Initialize distances from src to all other vertices as INFINITE

    for (i = 0; i < V; i++)

        dist[i]   = INT_MAX;

    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 (i = 1; i <= V-1; i++)

    {

        for (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] + 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 (i = 0; i < E; i++)

    {

        int u = graph->edge[i].src;

        int v = graph->edge[i].dest;

        int weight = graph->edge[i].weight;

        if (dist[u] + weight < dist[v])

            printf("Graph contains negative weight cycle");

    }



    printArr(dist, V);



    return;

}



// Driver program to test above functions

int main()

{

    /* Let us create the graph given in above example */

    int V = 10;  // Number of vertices in graph

    int E = 18;  // Number of edges in graph

    scanf("%d",&V);
    scanf("%d",&E);

    struct Graph* graph = createGraph(V, E);

    int i;
    for(i=0;i<E;i++){
        scanf("%d",&graph->edge[i].src);
        scanf("%d",&graph->edge[i].dest);
        scanf("%d",&graph->edge[i].weight);
    }

    BellmanFord(graph, 0);

    return 0;

}

thanks.

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Thanks.