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[7/18] 1074. Number of Submatrices That Sum to Target
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Hard
255857Add to ListShareGiven 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 <= 1001 <= matrix[0].length <= 100-1000 <= matrix[i] <= 1000-10^8 <= target <= 10^8
Accepted
78,443
Submissions
112,470
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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
