# 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: