Find the original matrix when largest element in a row and a column are given in Python

Suppose we have two arrays A and B of size N and M respectively and we also have one N X M binary matrix where 1 denotes that there was a positive integer in the original matrix and 0 means that position is holding 0 into the original matrix also. We have to generate the original matrix so that A[i] denotes the largest element in the ith row and B[j] denotes the largest element in the jth column.

So, if the input is like A = [4, 2, 3], B = [3, 1, 0, 0, 4, 0, 5] matrix, then the output will be matrix

To solve this, we will follow these steps −

• N := size of A

• M := size of B

• for i in range 0 to N, do

  • for j in range 0 to M, do

    • if mat[i, j] is same as 1, then

      • display minimum of A[i] and B[j]

    • otherwise,

      • print a new line

Example

Let us see the following implementation to get better understanding −

 Live Demo

def print_original_mat(A, B, mat) :
   N = len(A)
   M = len(B)
   for i in range(N) :
      for j in range(M) :
         if (mat[i][j] == 1) :
            print(min(A[i], B[j]), end = " ")
         else :
            print(0, end = " ")
      print()
A = [4, 2, 3]
B = [3, 1, 0, 0, 4, 0, 5]
mat = [
   [1, 0, 0, 0, 1, 0, 1],
   [0, 0, 1, 0, 0, 1, 1],
   [1, 1, 0, 1, 1, 0, 0]]
print_original_mat(A, B, mat);

Input

[4, 2, 3],
[3, 1, 0, 0, 4, 0, 5],
[[1, 0, 0, 0, 1, 0, 1],
[0, 0, 1, 0, 0, 1, 1],
[1, 1, 0, 1, 1, 0, 0]]

Output

3 0 0 0 4 0 4
0 0 0 0 0 0 2
3 1 0 0 3 0 0