Find Area of Largest Square of 1s in a Given Matrix in Python

Suppose we have a binary matrix, we have to find largest square of 1s in that given matrix.

So, if the input is like

then the output will be 16.

To solve this, we will follow these steps −

• res := 0
• for i in range 0 to size of matrix, do
  • res := maximum of res and matrix[i, 0]
• for i in range 0 to size of matrix[0], do
  • res := maximum of res and matrix[0, i]
• for i in range 1 to row count of matrix, do
  • for j in range 1 to column count of matrix, do
    • if matrix[i, j] is same as 1, then
      • matrix[i, j] = minimum of (matrix[i - 1, j], matrix[i - 1, j - 1] and matrix[i, j - 1]) + 1
    • res = maximum of res and matrix[i, j]
• return res^2

Let us see the following implementation to get better understanding −

Example 

Live Demo

class Solution:
   def solve(self, matrix):
      res = 0
      for i in range(len(matrix)):
         res = max(res, matrix[i][0])
      for i in range(len(matrix[0])):
         res = max(res, matrix[0][i])

      for i in range(1, len(matrix)):
         for j in range(1, len(matrix[0])):
            if matrix[i][j] == 1:
               matrix[i][j] = min(matrix[i - 1][j], matrix[i - 1][j - 1], matrix[i][j - 1]) + 1

               res = max(res, matrix[i][j])

      return res * res

ob = Solution()
matrix = [
   [1, 0, 0, 0, 0, 1, 1],
   [0, 0, 0, 0, 0, 1, 1],
   [0, 1, 1, 1, 1, 0, 0],
   [0, 1, 1, 1, 1, 0, 0],
   [0, 1, 1, 1, 1, 0, 0],
   [0, 1, 1, 1, 1, 0, 0]
]
print(ob.solve(matrix))

Input

matrix = [  
[1, 0, 0, 0, 0, 1, 1],  
[0, 0, 0, 0, 0, 1, 1],  
[0, 1, 1, 1, 1, 0, 0],  
[0, 1, 1, 1, 1, 0, 0],  
[0, 1, 1, 1, 1, 0, 0],  
[0, 1, 1, 1, 1, 0, 0] ]

Output

16