Program to find area of largest square of 1s in a given matrix in python

Python Server Side Programming Programming

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

So, if the input is like

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

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

Arnab Chakraborty

Published on 02-Dec-2020 05:37:53

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