# 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
                
```


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://hao-fu-1.gitbook.io/oj/exhaustive-search/1706.-where-will-the-ball-fall.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.