Count all possible walks from a source to a destination with exactly k edges in C++

In this tutorial, we will be discussing a program to find the number of walks from a source to a destination with exactly k edges.

For this we will be provided with a graph and the values of source and destination. Our task is to find all the possible paths starting from the source to the destination having exactly k edges.

Example

 Live Demo

#include <iostream>
using namespace std;
#define V 4
//counting walks using recursion
int countwalks(int graph[][V], int u, int v, int k){
   if (k == 0 && u == v)
      return 1;
   if (k == 1 && graph[u][v])
      return 1;
   if (k <= 0)
      return 0;
   int count = 0;
      //moving to the adjacent nodes
      for (int i = 0; i < V; i++)
      if (graph[u][i] == 1)
      count += countwalks(graph, i, v, k-1);
   return count;
}
int main(){
int graph[V][V] = {
      {0, 1, 1, 1},
      {0, 0, 0, 1},
      {0, 0, 0, 1},
      {0, 0, 0, 0}
   };
   int u = 0, v = 3, k = 2;
   cout << countwalks(graph, u, v, k);
   return 0;
}

Output

2