# 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:**

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

```
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`.

格子中有两种斜杠，当出现\\/时会卡住，否则会继续往下滑。问球分别从每列往下扔最后能到的位置。依次遍历列，并对每列再遍历行来模拟每次往斜下滑的过程，往左还是右取决于当前位置i1是/还是\，能否卡住取决于到达新位置i2和旧位置i1是否形成\\/，只要不卡住球就会自动往下层落。

代码参考了lee215。

```python
class Solution:
    def findBall(self, grid: List[List[int]]) -> List[int]:
        m, n = len(grid), len(grid[0])
        res = [0] * n
        for i in range(n):
            i1, i2 = i, 0
            for j in range(m):
                i2 = i1 + grid[j][i1]
                if i2 == n or i2 == -1 or grid[j][i2] != grid[j][i1]:
                    i1 = -1
                    break
                i1 = i2
            res[i] = i1
        return res
                
```