Number of Submatrices That Sum to Target

arrayhash tablematrix

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

Input: matrix = [[0,1,0],[1,1,1],[0,1,0]], target = 0
Output: 4
The four 1x1 submatrices that only contain 0.

Example 2

Input: matrix = [[1,-1],[-1,1]], target = 0
Output: 5
The two 1x2 submatrices, plus the two 2x1 submatrices, plus the 2x2 submatrix.

Example 3

Input: matrix = [[904]], target = 0
Output: 0

1 <= matrix.length <= 100

1 <= matrix[0].length <= 100

-1000 <= matrix[i][j] <= 1000

-10^8 <= target <= 10^8

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Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicHash Table