Surface Area of 3D Shapes

lc892.py

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+'''
+之前有道题求投影，这个是求表面积，因此需要考虑凹的情况。
+上下（也就是平行于xy平面）容易，依然是投影。
+
+平行于yz、xz平面的分成两部分：
+1. 先求周围一圈
+2. 再求被挡住的
+'''
+
+
+class Solution:
+    def surfaceArea(self, grid):
+        """
+        :type grid: List[List[int]]
+        :rtype: int
+        """
+        n = len(grid[0])
+        xy = sum(v > 0 for row in grid for v in row) * 2
+        front = sum(x for x in grid[n - 1])
+        back = sum(x for x in grid[0])
+        left = sum(grid[i][0] for i in range(n))
+        right = sum(grid[i][n - 1] for i in range(n))
+
+        for i in range(n - 1):
+            # front to back
+            front += sum(max(grid[i][j] - grid[i + 1][j], 0) for j in range(n))
+            # back to front
+            back += sum(max(grid[i + 1][j] - grid[i][j], 0) for j in range(n))
+            left += sum(max(grid[j][i + 1] - grid[j][i], 0) for j in range(n))
+            right += sum(max(grid[j][i] - grid[j][i + 1], 0) for j in range(n))
+
+        return xy + front + back + left + right
+
+
+s = Solution()
+grid = [[1, 1, 1], [1, 0, 1], [1, 1, 1]]
+print(s.surfaceArea(grid))