1706. Where Will the Ball Fall

You have a 2-D grid of size m x n representing a box, and you have n balls. The box is open on the top and bottom sides.

Each cell in the box has a diagonal board spanning two corners of the cell that can redirect a ball to the right or to the left.

  • A board that redirects the ball to the right spans the top-left corner to the bottom-right corner and is represented in the grid as 1.
  • A board that redirects the ball to the left spans the top-right corner to the bottom-left corner and is represented in the grid as -1.

We drop one ball at the top of each column of the box. Each ball can get stuck in the box or fall out of the bottom. A ball gets stuck if it hits a "V" shaped pattern between two boards or if a board redirects the ball into either wall of the box.

Return an array answer of size n where answer[i] is the column that the ball falls out of at the bottom after dropping the ball from the ith column at the top, or -1 if the ball gets stuck in the box.

 

Example 1:

Input: grid = [[1,1,1,-1,-1],[1,1,1,-1,-1],[-1,-1,-1,1,1],[1,1,1,1,-1],[-1,-1,-1,-1,-1]]
Output: [1,-1,-1,-1,-1]
Explanation: This example is shown in the photo.
Ball b0 is dropped at column 0 and falls out of the box at column 1.
Ball b1 is dropped at column 1 and will get stuck in the box between column 2 and 3 and row 1.
Ball b2 is dropped at column 2 and will get stuck on the box between column 2 and 3 and row 0.
Ball b3 is dropped at column 3 and will get stuck on the box between column 2 and 3 and row 0.
Ball b4 is dropped at column 4 and will get stuck on the box between column 2 and 3 and row 1.

Example 2:

Input: grid = [[-1]]
Output: [-1]
Explanation: The ball gets stuck against the left wall.

 

Constraints:

  • m == grid.length
  • n == grid[i].length
  • 1 <= m, n <= 100
  • grid[i][j] is 1 or -1.

Rust Solution

struct Solution;

impl Solution {
    fn find_ball(grid: Vec<Vec<i32>>) -> Vec<i32> {
        let n = grid.len();
        let m = grid[0].len();
        let mut res = vec![];
        for j in 0..m {
            res.push(Self::dp(0, j, &grid, n, m));
        }
        res
    }

    fn dp(i: usize, j: usize, grid: &[Vec<i32>], n: usize, m: usize) -> i32 {
        if i == n {
            j as i32
        } else {
            if grid[i][j] == 1 && j + 1 < m && grid[i][j + 1] == 1 {
                return Self::dp(i + 1, j + 1, grid, n, m);
            }
            if grid[i][j] == -1 && j >= 1 && grid[i][j - 1] == -1 {
                return Self::dp(i + 1, j - 1, grid, n, m);
            }
            -1
        }
    }
}

#[test]
fn test() {
    let grid = vec_vec_i32![
        [1, 1, 1, -1, -1],
        [1, 1, 1, -1, -1],
        [-1, -1, -1, 1, 1],
        [1, 1, 1, 1, -1],
        [-1, -1, -1, -1, -1]
    ];
    let res = vec![1, -1, -1, -1, -1];
    assert_eq!(Solution::find_ball(grid), res);
}

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