Leetcode 887 Projection Area of 3D Shapes

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On a N * N grid, we place some 1 * 1 * 1 cubes that are axis-aligned with the x, y, and z axes.

Each value v = grid[i][j] represents a tower of v cubes placed on top of grid cell (i, j).

Now we view the projection of these cubes onto the xy, yz, and zx planes.

A projection is like a shadow, that maps our 3 dimensional figure to a 2 dimensional plane.

Here, we are viewing the “shadow” when looking at the cubes from the top, the front, and the side.

Return the total area of all three projections.


Note:

  1. 1 <= grid.length = grid[0].length <= 50
  2. 0 <= grid[i][j] <= 50

分析：

  1. 这道题就是高中所学的正视图、侧视图、俯视图
  2. 对于正视图，也就是从x轴方向看，我们看到的就是沿y轴方向的一系列最高的柱子
  3. 对于侧视图，也就是从y轴方向看，我们看到的就是沿x轴方向的一系列最高的柱子
  4. 对于俯视图，所有的柱子都是1，因为底面积是1
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class Solution(object):
    def projectionArea(self, grid):
        """
        :type grid: List[List[int]]
        :rtype: int
        """
        if not grid or not grid[0]: return 0
        res = 0
        m,n = len(grid),len(grid[0])
        # 俯视图的所有柱子，包括了0，等下需要减去
        res += m*n
        # 侧视图的最高
        for row in grid: 
            res += max(row)
            # 减去俯视图里多计算的0的数量
            res -= row.count(0)
        # 正视图的最高
        for row in zip(*grid): 
            res += max(row)
        return res