# 1277. Count Square Submatrices with All Ones

Given a m * n matrix of ones and zeros, return how many square submatrices have all ones.

Example 1:

Input: matrix =
[
  [0,1,1,1],
  [1,1,1,1],
  [0,1,1,1]
]
Output: 15
Explanation: 
There are 10 squares of side 1.
There are 4 squares of side 2.
There is  1 square of side 3.
Total number of squares = 10 + 4 + 1 = 15.

Example 2:

Input: matrix = 
[
  [1,0,1],
  [1,1,0],
  [1,1,0]
]
Output: 7
Explanation: 
There are 6 squares of side 1.  
There is 1 square of side 2. 
Total number of squares = 6 + 1 = 7.

# Solution

Approach 1: DP -- same with Maximal Squares.

# Code (Python)

Approach 1:

    def countSquares(self, matrix: List[List[int]]) -> int:
        # idea: maximal square https://leetcode.com/problems/maximal-square/
        # for a square of side x we can find a square of size 1 up to x, that's x squares in total
        for r in range(1, len(matrix)):
            for c in range(1, len(matrix[0])):
                if matrix[r][c] == 0:
                    continue
                matrix[r][c] = min(matrix[r - 1][c], matrix[r][c - 1], matrix[r - 1][c - 1]) + 1
        return sum(sum(row) for row in matrix)

# Code (C++)

Approach 1:

Approach 2: