1074. Number of Submatrices That Sum to Target

Problem Link

Description

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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
Explanation: The four 1x1 submatrices that only contain 0.

Example 2:

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

Example 3:

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

 

Constraints:

• 1 <= matrix.length <= 100
• 1 <= matrix[0].length <= 100
• -1000 <= matrix[i][j] <= 1000
• -10^8 <= target <= 10^8

Solution

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Python3

class Solution:
    def numSubmatrixSumTarget(self, matrix: List[List[int]], target: int) -> int:
        rows, cols = len(matrix), len(matrix[0])
        res = 0
 
        for i in range(rows):
            for j in range(1, cols):
                matrix[i][j] += matrix[i][j - 1]
        
        for j1 in range(cols):
            for j2 in range(j1, cols):
                mp = defaultdict(int)
                curr = 0
                mp[0] += 1
 
                for i in range(rows):
                    curr += matrix[i][j2] - (matrix[i][j1 - 1] if j1 > 0 else 0)
                    res += mp[curr - target]
                    mp[curr] += 1
 
        return res