# 1706. Where Will the Ball Fall

#### Medium

***

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:**

![](https://assets.leetcode.com/uploads/2019/09/26/ball.jpg)

<pre><code>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]]
<strong>Output:
</strong> [1,-1,-1,-1,-1]
<strong>Explanation:
</strong> 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.
</code></pre>

**Example 2:**

<pre><code>Input: grid = [[-1]]
<strong>Output:
</strong> [-1]
<strong>Explanation:
</strong> The ball gets stuck against the left wall.
</code></pre>

**Example 3:**

<pre><code>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]]
<strong>Output:
</strong> [0,1,2,3,4,-1]
</code></pre>

&#x20;

**Constraints:**

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

```python
class Solution:
    def findBall(self, grid: List[List[int]]) -> List[int]:
        rows, cols = len(grid), len(grid[0])
        @lru_cache(None)
        def recursion(row, col):
            if row == rows:
                return col
            elif grid[row][col] == 1 and col+1 < cols and grid[row][col+1] == 1:
                return recursion(row+1, col+1)
            elif grid[row][col] == -1 and col-1 >= 0 and grid[row][col-1] == -1:
                return recursion(row+1, col-1)
            return -1
        return [recursion(0, col) for col in range(cols)]
```