Program to count number of square submatrices with all ones using Python

Suppose we have m x n binary matrix, we have to find how many square submatrices have all ones.

So, if the input is like.

then the output will be 15, as there are 10 squares of side 1. 4 squares of side 2 and 1 square of side 3. Then total number of squares = 10 + 4 + 1 = 15.

To solve this, we will follow these steps −

• if matrix has single one, then

  • return 1

• rows := row count of matrix

• cols := column count of matrix[0]

• result := 0

• for row in range 0 to rows - 1, do

  • for col in range 0 to cols - 1, do

    • if row is same as 0 or col is same as 0, then

      • if matrix[row, col] is same as 1, then

        • result := result + 1

      • otherwise when matrix[row, col] is same as 1, then

        • square := 1 + (minimum of matrix[row-1,col], matrix[row,col-1] and matrix[row-1,col-1])

        • matrix[row, col] := square

        • result := result + square

• return result

Let us see the following implementation to get better understanding −

Example

def solve(matrix):
   if matrix == [[1]]:
      return 1
   rows = len(matrix)
   cols = len(matrix[0])
   result = 0
   for row in range(rows):
      for col in range(cols):
         if (row == 0 or col == 0):
            if matrix[row][col] == 1:
               result += 1
         elif matrix[row][col] == 1:
            square = min(matrix[row-1][col], min(matrix[row][col-1], matrix[row-1][col-1])) + 1
            matrix[row][col] = square
            result += square
   return result
matrix = [[0,1,1,1],[1,1,1,1],[0,1,1,1]]
print(solve(matrix))

Input

{{0,1,1,1},{1,1,1,1},{0,1,1,1}}

Output

15