Number of Submatrices That Sum to Target
Given a matrix and a target, return the number of non-empty submatrices that sum to target.
A submatrix x1, y1, x2, y2 is the set of all cells matrix[x][y] with x1 <= x <= x2 and y1 <= y <= y2.
Two submatrices (x1, y1, x2, y2) and (x1', y1', x2', y2') are different if they have some coordinate that is different; for example, if x1 != x1'.
Example 1
0 1 0 1 1 1 0 1 0
Input
matrix = [[0,1,0],[1,1,1],[0,1,0]], target = 0Output
4The four 1x1 submatrices that only contain 0.
Example 2
1 -1 -1 1
Input
matrix = [[1,-1],[-1,1]], target = 0Output
5The two 1x2 submatrices, plus the two 2x1 submatrices, plus the 2x2 submatrix.
Constraints
- 1 <= matrix.length <= 100
- 1 <= matrix[0].length <= 100
- -1000 <= matrix[i][j] <= 1000
- -10^8 <= target <= 10^8