883. Projection Area of 3D Shapes（easy） 

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

xy:從上往下看，相當於壓扁，只要[i,j]有格子，就有shadow

xz：從前往後看，第i行顯示的是第i行所有列最高的格子

yz：從左往右看，第j列顯示的是第j列所有行最高的格子

class Solution:
    def projectionArea(self, grid):
        """
        :type grid: List[List[int]]
        :rtype: int
        """
        xy , xz , yz = 0,0,0
        sum = 0
        for i in range(len(grid)):
            for j in  range(len(grid[0])):
                if grid[i][j]!= 0:
                    xy += 1
            xz += max(grid[i])
        for j in  range(len(grid[0])):
            yz += max([x[j] for x in grid])
                
        return xy+xz+yz