projectionArea.go

/* https://leetcode.com/problems/projection-area-of-3d-shapes/description/
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.
	https://s3-lc-upload.s3.amazonaws.com/uploads/2018/08/02/shadow.png

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
*/

package lmath

func projectionArea(grid [][]int) int {
	I, J := len(grid), len(grid[0])
	xx, xz, xy := 0, 0, 0
	for i := 0; i < I; i++ {
		tmpXZ, tmpXY := 0, 0
		for j := 0; j < J; j++ {
			if grid[i][j] != 0 {
				xx++
			}
			if grid[i][j] > tmpXZ {
				tmpXZ = grid[i][j]
			}
			if grid[j][i] > tmpXY {
				tmpXY = grid[j][i]
			}
		}
		xz += tmpXZ
		xy += tmpXY
	}
	return xx + xz + xy
}