描述
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.
Example 1:
Input: [[2]]
Output: 5
Example 2:
Input: [[1,2],[3,4]]
Output: 17
Explanation:
Here are the three projections ("shadows") of the shape made with each axis-aligned plane.
Example 3:
Input: [[1,0],[0,2]]
Output: 8
Example 4:
Input: [[1,1,1],[1,0,1],[1,1,1]]
Output: 14
Example 5:
Input: [[2,2,2],[2,1,2],[2,2,2]]
Output: 21
Note:
1 <= grid.length = grid[0].length <= 50
0 <= grid[i][j] <= 50
解析
根据题意，可以找出正面、顶面，侧面的表面积求和即可。时间复杂度为 O(N^2)，空间复杂度为 O(1)。
解答
class Solution(object):
def projectionArea(self, grid):
"""
:type grid: List[List[int]]
:rtype: int
"""
M = len(grid)
N = len(grid[0])
top = sum( [1 if grid[i][j]!=0 else 0 for i in range(M) for j in range(N) ])
left = sum(map(max,grid))
front = sum(map(max,[[grid[i][j] for i in range(M)] for j in range(N)]))
return top + left + front
运行结果
Runtime: 60 ms, faster than 64.05% of Python online submissions for Projection Area of 3D Shapes.
Memory Usage: 11.9 MB, less than 11.36% of Python online submissions for Projection Area of 3D Shapes.
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