1706. Where Will the Ball Fall

Method 1

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.

Example 3

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]

Method 1

【O(n * m) time | O(n) space】

package Leetcode.Array;

import java.util.Arrays;

/**
 * @author zhengxingxing
 * @date 2025/02/15
 */
public class WhereWillTheBallFall {

    public static int[] findBall(int[][] grid) {
        // Get the width of the grid (number of columns)
        int n = grid[0].length;
        // Initialize result array to store the exit positions for each ball
        int[] ans = new int[n];

        // Simulate dropping a ball from each column
        for (int j = 0; j < n; j++) {
            // Track current column position of the ball
            // Initially, ball starts from column j
            int curCol = j;

            // Iterate through each row of the grid
            for (int[] row: grid) {
                // Get the direction of the current board
                // d = 1: board directs ball to right
                // d = -1: board directs ball to left
                int d = row[curCol];

                // Move ball to next position based on board direction
                curCol += d;

                // Check if ball gets stuck:
                // 1. curCol < 0: ball hits left boundary
                // 2. curCol == n: ball hits right boundary
                // 3. row[curCol] != d: forms V-shape with adjacent board
                //    Example: Current board goes right (1) but next position board goes left (-1)
                //    or current board goes left (-1) but next position board goes right (1)
                if (curCol < 0 || curCol == n || row[curCol] != d) {
                    // Ball is stuck, mark position as -1
                    curCol = -1;
                    // Stop simulating this ball's path
                    break;
                }
            }
            // Store final position for ball dropped from column j
            ans[j] = curCol;
        }
        return ans;
    }

    
    public static void main(String[] args) {
        // Test Case 1: Complex path with multiple directions
        int[][] grid1 = {
                {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}
        };
        System.out.println("Test Case 1: " + Arrays.toString(findBall(grid1)));

        // Test Case 2: Simplest case with single cell
        int[][] grid2 = { { -1 } };
        System.out.println("Test Case 2: " + Arrays.toString(findBall(grid2)));

        // Test Case 3: Alternating rows of same direction
        int[][] grid3 = {
                {1, 1, 1, 1, 1, 1},
                {-1, -1, -1, -1, -1, -1},
                {1, 1, 1, 1, 1, 1},
                {-1, -1, -1, -1, -1, -1}
        };
        System.out.println("Test Case 3: " + Arrays.toString(findBall(grid3)));
    }
}

Method 1

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