Soyo

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.
``````

Constraints:

• `1 <= arr.length <= 300`
• `1 <= arr.length <= 300`
• `0 <= arr[i][j] <= 1`

## Solution

DP with formula f(i,j) = min(f(i-1,j), f(i,j-1), f(i-1,j-1))

``````class Solution {
func countSquares(_ matrix: [[Int]]) -> Int {
var copy = matrix
var count: Int = 0
for i in 0..<copy.count {
for j in 0..<copy.count {
if (i != 0 && j != 0 && matrix[i][j] != 0) {
copy[i][j] = min(copy[i-1][j], min(copy[i][j-1], copy[i-1][j-1])) + 1
}
count += copy[i][j]
}
}

return count
}
}
``````