Find Number of Elements in Matrix Following Row Column Criteria in Python

Suppose we have a binary matrix; we have to find the number of elements in matrix that follows the following rules −

• matrix[r, c] = 1

• matrix[r, j] = 0 for every j when j is not equal to c and matrix[i, c] = 0 for every i when i is not equal to r.

So, if the input is like

then the output will be 3, because we have cells (0,2), (1,0) and (2,1) those meet the criteria.

To solve this, we will follow these steps −

• if matrix is empty, then

  • return 0

• row := a list of sum of all row entries in matrix

• col := a list of sum of all column entries in matrix

• m := row count of matrix

• n := column count of matrix

• res := 0

• for r in range 0 to m - 1, do

  • for c in range 0 to n - 1, do

    • if matrix[r, c] is 1 and row[r] is 1 and col[c] is also 1, then

      • res := res + 1

• return res

Example

Let us see the following implementation to get better understanding

def solve(matrix):
   if not matrix:
      return 0

   row = [sum(r) for r in matrix]
   col = [sum(c) for c in zip(*matrix)]

   m, n = len(matrix), len(matrix[0])
   res = 0
   for r in range(m):
      for c in range(n):
         if matrix[r][c] == 1 and row[r] == 1 and col[c] == 1:
            res += 1
   return res

matrix = [
   [0, 0, 1],
   [1, 0, 0],
   [0, 1, 0]
]
print(solve(matrix))

Input

[[0, 0, 1],[1, 0, 0],[0, 1, 0]]

Output

3