Merge pull request #537 from ushmita4/master

Bellman Ford Algorithm in C

Author: Saviour1001

Data Structures/Graphs/Bellman Ford.c

@@ -0,0 +1,54 @@
+
+/*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. Bellman Ford's Algorithm comes into the picture when there is a negative weight edge. It also detects any negative weight cycle if present.**/
+#include <stdio.h>
+#include <stdlib.h>
+/*Time Complexity:- O(VE)**/
+int Bellman_Ford(int G[20][20] , int V, int E, int edge[20][2])
+{
+    int i,u,v,k,distance[20],parent[20],S,flag=1;
+    for(i=0;i<V;i++)
+        distance[i] = 1000//assigning infinity value to all the path initially , parent[i] = -1 ;
+        printf("Enter source: ");
+        scanf("%d",&S);
+        distance[S-1]=0 ;
+    for(i=0;i<V-1;i++)
+    {
+        for(k=0;k<E;k++)
+        {
+            u = edge[k][0] , v = edge[k][1] ;
+            if(distance[u]+G[u][v] < distance[v]) //Checking for the shortest path or the minimum cost
+                distance[v] = distance[u] + G[u][v] , parent[v]=u ;
+        }
+    }
+    for(k=0;k<E;k++)
+        {
+            u = edge[k][0] , v = edge[k][1] ;
+            if(distance[u]+G[u][v] < distance[v])
+                flag = 0 ;
+        }
+        if(flag)
+            for(i=0;i<V;i++)
+                printf("Vertex %d -> cost = %d parent = %d\n",i+1,distance[i],parent[i]+1);
+
+        return flag;
+}
+int main()
+{
+    int V,edge[20][2],G[20][20],i,j,k=0;
+    printf("BELLMAN FORD\n");
+    printf("Enter no. of vertices: ");
+    scanf("%d",&V);
+    printf("Enter graph in matrix form:\n");
+    for(i=0;i<V;i++)
+        for(j=0;j<V;j++)
+        {
+            scanf("%d",&G[i][j]);
+            if(G[i][j]!=0)
+                edge[k][0]=i,edge[k++][1]=j;
+        }
+
+    if(Bellman_Ford(G,V,k,edge))
+        printf("\nNo negative weight cycle\n");
+    else printf("\nNegative weight cycle exists\n");
+    return 0;
+}