10/11 每日一題(計算3維的陰影面積)

You are given an n x n grid where we place some 1 x 1 x 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 the cell (i, j).

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. 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: grid = [[1,2],[3,4]]
Output: 17
Explanation: Here are the three projections ("shadows") of the shape made with each axis-aligned plane.

Example 2:

Input: grid = [[2]]
Output: 5

Example 3:

Input: grid = [[1,0],[0,2]]
Output: 8

 

Constraints:

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

 class Solution:

    def projectionArea(self, grid: List[List[int]]) -> int:

        res=0

        #X-Y

        #X-Z

        m=len(grid[0])

       

        max_hight=0

        for i in grid:

            print(f'x-z 長={(max(i))}')

            res+=max(i)

       

       

        print(f'加上y-z前={res}')

        for i in range(len(grid)):

            y_z=0

            for j in range(m):

                y_z=max(y_z,grid[j][i])

                print(f'i={i},j={j},檢查的grid[j][i]={grid[j][i]}')

                if grid[i][j]!=0:

                    #處理x-y, 當有值得前提下才會有影子

                    res+=1

            print(f'y_z={y_z}')

            res+=y_z

        print(f'res={res}')

       

        return res