Projection Area of 3D Shapes

In this lab, you will be working on a problem involving the 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.

Your task is to create a function that returns the total area of all three projections.

Here are a few examples to clarify the problem:

Example 1:

Input: grid = [[1,2],[3,4]] Output: 17 Explanation: Here are the three projections ("shadows") of the shape made with each axis-aligned plane.

Example 2:

Input: grid = [[2]] Output: 5

Example 3:

Input: grid = [[1,0],[0,2]] Output: 8

Constraints:

• n == grid.length == grid[i].length
• 1 <= n <= 50
• 0 <= grid[i][j] <= 50

To solve this lab, you need to follow the instructions and rewrite the lab material according to the rules specified above.

Challenges:

1. Create a function and name it projectionArea. Export this function as ESM.
2. Write test cases for the projectionArea function to test various input cases and validate the results.

Evaluation script:

import fs from 'fs'
import { projectionArea } from '/home/damner/code/index.js'

const testlog = []

try {
  const result = projectionArea([[1, 2], [3, 4]])
  if (result === 17) {
    testlog.push({ status: 'pass' })
  } else {
    throw new Error('Incorrect result for example 1')
  }
} catch (error) {
  testlog.push({ status: 'error', error: error.message || 'Challenge failed' })
}

try {
  const result = projectionArea([[2]])
  if (result === 5) {
    testlog.push({ status: 'pass' })
  } else {
    throw new Error('Incorrect result for example 2')
  }
} catch (error) {
  testlog.push({ status: 'error', error: error.message || 'Challenge failed' })
}

fs.writeFileSync('/home/damner/code/.labtests/testlog.json', JSON.stringify(testlog))
fs.writeFileSync(process.env.UNIT_TEST_OUTPUT_FILE, JSON.stringify(testlog.map(result => result.status === 'pass')))

Adjust the evaluation script accordingly and make sure to complete the missing parts in the lab as per the instructions and rules given. Good luck!