Print all possible paths from top left to bottom right of a mXn matrix in C++

In this problem, we are given an mXn 2D matrix and we have to print all possible paths from top left to the bottom right of the matrix. For traversal, we can move only right and down in the matrix.

Let’s take an example to understand the topic better −

Input:
1 3 5
2 8 9
Output:
1 -> 3 -> 5 -> 9
1 -> 3 -> 8 -> 9
1 -> 2 -> 8 -> 9

To solve this problem, we will move from one cell to another and print the path on going down and right. We will do this recursively for each cell in the matrix.

Example

Let’s see a program that implements the recursive algorithm :

#include<iostream>
using namespace std;
void printPathTPtoBR(int *mat, int i, int j, int m, int n, int *path, int pi) {
   if (i == m - 1){
      for (int k = j; k < n; k++)
         path[pi + k - j] = *((mat + i*n) + k);
      for (int l = 0; l < pi + n - j; l++)
         cout << path[l] << " ";
         cout << endl;
      return;
   }
   if (j == n - 1){
      for (int k = i; k < m; k++)
         path[pi + k - i] = *((mat + k*n) + j);
      for (int l = 0; l < pi + m - i; l++)
         cout << path[l] << " ";
      cout << endl;
      return;
   }
   path[pi] = *((mat + i*n) + j);
   printPathTPtoBR(mat, i+1, j, m, n, path, pi + 1);
   printPathTPtoBR(mat, i, j+1, m, n, path, pi + 1);
}
void findPath(int *mat, int m, int n) {
   int *path = new int[m+n];
   printPathTPtoBR(mat, 0, 0, m, n, path, 0);
}
int main() {
   int mat[2][3] = { {1, 2, 3}, {4, 5, 6} };
   cout<<"Path from top-left to bottom-rigth of matrix are :\n";
   findPath(*mat, 2, 3);
   return 0;
}

Output

The path from top-left to bottom-right of a matrix are −

1 4 5 6
1 2 5 6
1 2 3 6