Floyd Warshall Algorithm / All pair shortest path without recursion and functions

Floyd Warshall Algorithm / All pair shortest path

The Floyd Warshall Algorithm is for solving the All Pairs Shortest Path problem. The problem is to find shortest distances between every pair of vertices in a given edge weighted directed Graph.

formulas used in algorithm:

d[i][j]=d[i][k]+d[k][j];

where i , j are the source and destination

k is the vextex which should be included while going from i to j.
click to download the code

Example:

Input:
       graph[][] = { {0,   5,  INF, 10},
                    {INF,  0,  3,  INF},
                    {INF, INF, 0,   1},
                    {INF, INF, INF, 0} }
which represents the following graph
             10
       (0)------->(3)
        |         /|\
      5 |          |
        |          | 1
       \|/         |
       (1)------->(2)
            3       
Note that the value of graph[i][j] is 0 if i is equal to j 
And graph[i][j] is INF (infinite) if there is no edge from vertex i to j.

Output:
Shortest distance matrix
      0      5      8      9
    INF      0      3      4
    INF    INF      0      1
    INF    INF    INF      0 

code :

#include<iostream>
using namespace std;
int main() //main function
{
 int V;
 cout<<"enter the number of the vertex";
 cin>>V;
 int graph[V][V],d[V][V];  //graph is a 2-d matrix which stores the adjacency matrix of the graph g.
 cout<<"enter  nine's in case of non infinity\n";
 cout<<"enter matrix\n";
 for(int i=0;i<V;i++)
 {
  for(int j=0;j<V;j++)
  {
   cin>>graph[i][j];
  }
 }
       for(int i=0;i<V;i++)  //copying the graph into another matrix d;
 {
  for(int j=0;j<V;j++)
  {
   d[i][j]=graph[i][j];
  }
 }
 for(int k=0;k<V;k++)
 {
  for(int i=0;i<V;i++)
 {
  for(int j=0;j<V;j++)
  {
   if(d[i][j]>d[i][k]+d[k][j]) //comparing if the prior d[i][j] is greater than than the value that includes vertex k.
   {
    d[i][j]=d[i][k]+d[k][j];
   }
  }
 }
 }
 cout<<"\ngraph is\n"; //printing the matrix.
  for(int i=0;i<V;i++)
 {
  for(int j=0;j<V;j++)
  {
   if(d[i][j]>=9999)  //9999 indicates the infinity.
     {
        cout<<"INF"<<"     ";
     }
     else
     {
      cout<<d[i][j]<<"     ";
     }
  }
  cout<<"\n";
 }
    
}