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Projection Area of 3D Shapes - Math - Easy - LeetCode - MiniTV

Projection Area of 3D Shapes - Math - Easy - LeetCode - मिनी टीवी

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

public class Solution {
    public int ProjectionArea(int[][] grid) {
        int res = 0, n = grid.Length;
        for (int i = 0; i < n; ++i) {
            int x = 0, y = 0;
            for (int j = 0; j < n; ++j) {
                x = Math.Max(x, grid[i][j]);
                y = Math.Max(y, grid[j][i]);
                if (grid[i][j] > 0) ++res;
            }
            res += x + y;
        }
        return res;
    }
}

Time Complexity: O(n^2)

Space Complexity: O(1)

 

Explanation
front-back projection area on xz = sum(max value for every col)
right-left projection area on yz = sum(max value for every row)
top-down projection area on xy = sum(1 for every v > 0)