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[7/18] 1074. Number of Submatrices That Sum to Target

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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] <= 1000
  • -10^8 <= target <= 10^8
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import collections
class Solution:
    def numSubmatrixSumTarget(self, matrix: List[List[int]], target: int) -> int:
        def subarrSumTarget(col_sum, target):
            preSum = 0
            cumulative = collections.defaultdict(int)
            total_subarr = 0
            cumulative[0] = 1
            
            for num in col_sum:
                preSum += num
                total_subarr += cumulative[preSum - target]
                cumulative[preSum] += 1
            return total_subarr
        
        ROW, COL = len(matrix), len(matrix[0])
        total_subarr = 0
        for r1 in range(ROW):
            sub_matrix = [0]*COL
            for r2 in range(r1,ROW):
                for c in range(COL):
                    sub_matrix[c] += matrix[r2][c]
                total_subarr += subarrSumTarget(sub_matrix, target)
        
        return total_subarr
                
            
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