3DProjectionArea.go

/*
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 main

import (
	"fmt"
)

func main() {
	tests := [][][]int{{{2}}, {{1, 2}, {3, 4}}, {{1, 0}, {0, 2}}, {{1, 1, 1}, {1, 0, 1}, {1, 1, 1}}, {{2, 2, 2}, {2, 1, 2}, {2, 2, 2}}}

	for _, test := range tests {
		fmt.Println(projectionArea(test))
	}
}

func projectionArea(grid [][]int) int {
	// total projection are in all three planes
	totalProjectionArea := 0

	// list of tallest columns when viewd from North/South (XY) side
	xyAreas := []int{}

	areaZXDebug := 0
	areaYZDebug := 0

	// calculate West/East (yz) projection area
	for i := 0; i < len(grid); i++ {
		// tallest found in grid[i] - West/East		
		areaYZ := 0

		for j := 0; j < len(grid[i]); j++ {
			if grid[i][j] > areaYZ {
				areaYZ = grid[i][j]
			}

			if grid[i][j] > 0 {
				// add to Up/Down projection area (each nonzero cube column would form an up/won projection area of one unit)
				totalProjectionArea += 1
				areaZXDebug += 1
			}

			// update north/south areas list
			if len(xyAreas) < (i + 1) {
				xyAreas = append(xyAreas, grid[i][j])
			} else if xyAreas[i] < grid[i][j] {
				xyAreas[i] = grid[i][j]
			}
		}

		// add West/East (YZ) area component to total
		areaYZDebug += areaYZ
		totalProjectionArea += areaYZ
		
	}

	// add north/south are to total
	areaXYDebug := 0
	for _, xyAreaVal := range xyAreas {
		totalProjectionArea += xyAreaVal
		areaXYDebug += xyAreaVal
	}
	fmt.Printf("Input: %v\n", grid)
	fmt.Printf("\tAreaYZ: %d\n", areaYZDebug)
	fmt.Printf("\tAreaXY: %d\n", areaXYDebug)
	fmt.Printf("\tAreaZX: %d\n", areaZXDebug)

	return totalProjectionArea

}