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
class Solution:
def projectionArea(self, grid):
"""
:type grid: List[List[int]]
:rtype: int
"""
front = [0] * len(grid)
side = [0] * len(grid)
top = 0
for i in range(len(grid)):
for j in range(len(grid[i])):
if grid[i][j] == 0:
continue
top += 1
front[i] = max(front[i],grid[i][j])
side[j] = max(side[j],grid[i][j])
return top + sum(front) + sum(side)