Question

1. Given a graph G = (V, E).

a) Design an algorithm to print all the shortest path from a starting node s to all other nodes

b) Implement your proposed algorithm above in your preferred programming languages.

You can choose to represent the edges in such graph by either adjacency matrix or adjacency list.

Answer 1

Given below is the code of Dijkstra's algorithm in C language:

#include<stdio.h>
#include<conio.h>

main()
{
        int a[20][20],s,dist[20],vis[20];
        int n,i,j,min,u,v;
        
        printf("Enter number of elements: ");
        scanf("%d",&n);
        printf("\n");
        
        for(i=1;i<=n;i++)
        {
                for(j=1;j<=n;j++)
                {
                        printf("Enter distance between %d element %d: ",i,j);
                        scanf("%d",&a[i][j]);
                }
        }
        
        printf("\n");
        
        for(i=1;i<=n;i++)
        {
                for(j=1;j<=n;j++)
                {
                        printf("\t%d",a[i][j]);
                }
                printf("\n");
        }
        
        printf("\nEnter source: ");
        scanf("%d",&s);
        
        for(i=1;i<=n;i++)
        {
                vis[i]=0;
                dist[i]=a[s][i];                
        }
        
        for(i=2;i<=n;i++)
        {
                min=999;
                
                for(j=2;j<=n;j++)
                {
                        if(dist[j]<min && vis[j]==0)
                        {
                                min=dist[j];
                                u=j;
                        }
                }
                vis[u]=i;
                
                for(v=2;v<=n;v++)
                {
                        if(dist[v]>a[u][v] + dist[u])
                        {
                                dist[v]=a[u][v] + dist[u];
                        }
                }
        }
        
        printf("\n");
        
        for(i=1;i<=n;i++)
        {
                printf("\nDistance of %d from %d: %d",i,s,dist[i]);
        }
        
getch();        
}