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.

Test Cases

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 = [[1,1,1,1,1,1],[-1,-1,-1,-1,-1,-1],[1,1,1,1,1,1],[-1,-1,-1,-1,-1,-1]]
Output: [0,1,2,3,4,-1]

Solution

C++ Java

class Solution {
public:
    vector<int> findBall(vector<vector<int>>& grid) {
        int n = grid.size(), m = grid[0].size();
        vector<int> res;
        for(int j=0; j<m; j++) {
            int startCol = j;
            for(int i=0; i<n; i++) {
                int endCol = startCol + grid[i][startCol];
                if (endCol < 0 || endCol >= m || grid[i][endCol] != grid[i][startCol]) {
                    startCol = -1;
                    break;
                }
                startCol = endCol;
            }
            res.push_back(startCol);
        }
        return res;
    }
};

class Solution {
    public int[] findBall(int[][] grid) {
        int n = grid.length, m = grid[0].length;
        int[] res = new int[m];
        for(int j=0; j<m; j++) {
            int startCol = j;
            for(int i=0; i<n; i++) {
                int endCol = startCol + grid[i][startCol];
                if (endCol < 0 || endCol >= m || grid[i][endCol] != grid[i][startCol]) {
                    startCol = -1;
                    break;
                }
                startCol = endCol;
            }
            res[j] = startCol;
        }
        return res;
    }
}