Projection Area of 3D Shapes
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
1 2 3 4
Input
grid = [[1,2],[3,4]]Output
17The total area of the three projections of the shape is 17.
Example 2
2
Input
grid = [[2]]Output
5A single tower of height 2 contributes 1 from the top, 2 from the front, and 2 from the side.
Constraints
- n == grid.length == grid[i].length
- 1 <= n <= 50
- 0 <= grid[i][j] <= 50