1706. Where Will the Ball Fall

https://leetcode.com/problems/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:

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。

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