883. 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:

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

Example 4:

Input: grid = [[1,1,1],[1,0,1],[1,1,1]]
Output: 14

Example 5:

Input: grid = [[2,2,2],[2,1,2],[2,2,2]]
Output: 21

 

Constraints:

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

Rust Solution

struct Solution;

impl Solution {
    fn projection_area(grid: Vec<Vec<i32>>) -> i32 {
        let mut sum_z: i32 = 0;
        let n = grid.len();
        let m = grid[0].len();
        let mut x = vec![0; n];
        let mut y = vec![0; m];
        for i in 0..n {
            for j in 0..m {
                if grid[i][j] != 0 {
                    sum_z += 1;
                }
                x[i] = i32::max(x[i], grid[i][j]);
                y[j] = i32::max(y[j], grid[i][j]);
            }
        }

        let sum_x: i32 = x.iter().sum();
        let sum_y: i32 = y.iter().sum();
        sum_x + sum_y + sum_z
    }
}

#[test]
fn test() {
    let grid: Vec<Vec<i32>> = vec_vec_i32![[2]];
    let res = 5;
    assert_eq!(Solution::projection_area(grid), res);
    let grid: Vec<Vec<i32>> = vec_vec_i32![[1, 2], [3, 4]];
    let res = 17;
    assert_eq!(Solution::projection_area(grid), res);
    let grid: Vec<Vec<i32>> = vec_vec_i32![[1, 0], [0, 2]];
    let res = 8;
    assert_eq!(Solution::projection_area(grid), res);
    let grid: Vec<Vec<i32>> = vec_vec_i32![[1, 1, 1], [1, 0, 1], [1, 1, 1]];
    let res = 14;
    assert_eq!(Solution::projection_area(grid), res);
    let grid: Vec<Vec<i32>> = vec_vec_i32![[2, 2, 2], [2, 1, 2], [2, 2, 2]];
    let res = 21;
    assert_eq!(Solution::projection_area(grid), res);
}