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| 1 | +''' |
| 2 | +You are given a 2D binary array grid. You need to find 3 non-overlapping rectangles having non-zero areas with horizontal and vertical sides such that all the 1's in grid lie inside these rectangles. |
| 3 | + |
| 4 | +Return the minimum possible sum of the area of these rectangles. |
| 5 | + |
| 6 | +Note that the rectangles are allowed to touch. |
| 7 | +''' |
| 8 | + |
| 9 | +class Solution: |
| 10 | + def minimumSum(self, A: List[List[int]]) -> int: |
| 11 | + res = float("inf") |
| 12 | + for _ in range(4): |
| 13 | + n, m = len(A), len(A[0]) |
| 14 | + for i in range(1, n): |
| 15 | + a1 = self.minimumArea(A[:i]) |
| 16 | + for j in range(1, m): |
| 17 | + part2 = [row[:j] for row in A[i:]] |
| 18 | + part3 = [row[j:] for row in A[i:]] |
| 19 | + a2 = self.minimumArea(part2) |
| 20 | + a3 = self.minimumArea(part3) |
| 21 | + res = min(res, a1 + a2 + a3) |
| 22 | + for i2 in range(i + 1, n): |
| 23 | + part2 = A[i:i2] |
| 24 | + part3 = A[i2:] |
| 25 | + a2 = self.minimumArea(part2) |
| 26 | + a3 = self.minimumArea(part3) |
| 27 | + res = min(res, a1 + a2 + a3) |
| 28 | + A = self.rotate(A) |
| 29 | + return res |
| 30 | + |
| 31 | + def minimumArea(self, A: List[List[int]]) -> int: |
| 32 | + if not A or not A[0]: |
| 33 | + return 0 |
| 34 | + n, m = len(A), len(A[0]) |
| 35 | + left, top, right, bottom = float("inf"), float("inf"), -1, -1 |
| 36 | + for i in range(n): |
| 37 | + for j in range(m): |
| 38 | + if A[i][j] == 1: |
| 39 | + left = min(left, j) |
| 40 | + top = min(top, i) |
| 41 | + right = max(right, j) |
| 42 | + bottom = max(bottom, i) |
| 43 | + if right == -1: |
| 44 | + return 0 |
| 45 | + return (right - left + 1) * (bottom - top + 1) |
| 46 | + |
| 47 | + def rotate(self, A: List[List[int]]) -> List[List[int]]: |
| 48 | + n, m = len(A), len(A[0]) |
| 49 | + return [[A[i][j] for i in range(n-1, -1, -1)] for j in range(m)] |
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