Create 1074-number-of-submatrices-that-sum-to-target.py

python/1074-number-of-submatrices-that-sum-to-target.py

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+class Solution:
+    def numSubmatrixSumTarget(self, matrix: List[List[int]], target: int) -> int:
+        ROWS, COLS = len(matrix), len(matrix[0])
+        sub_sum = [[0 for i in range(COLS)] for j in range(ROWS)]
+
+        for r in range(ROWS):
+            for c in range(COLS):
+                top = sub_sum[r - 1][c] if r > 0 else 0
+                left = sub_sum[r][c - 1] if c > 0 else 0
+                top_left = sub_sum[r - 1][c - 1] if min(r, c) > 0 else 0
+                sub_sum[r][c] = matrix[r][c] + top + left - top_left
+
+        res = 0
+        for r1 in range(ROWS):
+            for r2 in range(r1, ROWS):
+                count = defaultdict(int) # prefix_sum -> count
+                count[0] = 1
+                for c in range(COLS):
+                    cur_sum = sub_sum[r2][c] - (
+                        sub_sum[r1 - 1][c] if r1 > 0 else 0
+                    )
+                    diff = cur_sum - target
+                    res += count[diff]
+                    count[cur_sum] += 1
+
+        return res