1706. Where Will the Ball Fall

Problem

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.

https://leetcode.cn/problems/where-will-the-ball-fall/

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]

Constraints:

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

Test Cases

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class Solution:
    def findBall(self, grid: List[List[int]]) -> List[int]:

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import pytest

from solution import Solution


@pytest.mark.parametrize('grid, expected', [
    ([[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]], [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],[-1,-1,-1,-1,-1,-1]], [0,1,2,3,4,-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,-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,-1,1,1,1,-1,-1,-1,1,-1,-1,1,1,1,1,1,1,-1,1,-1,-1,-1,-1,-1,1,-1,1,-1,-1,-1,-1,1,1,-1,1,1],[1,-1,-1,-1,-1,1,-1,1,1,1,1,1,1,1,-1,1,-1,-1,-1,1,-1,-1,1,-1,1,-1,1,-1,-1,1,-1,1,-1,1,1,-1,-1,1,1,-1,1,-1]],
        [-1,-1,1,-1,-1,-1,-1,10,11,-1,-1,12,13,-1,-1,-1,-1,-1,17,-1,-1,20,-1,-1,-1,-1,-1,-1,-1,-1,27,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],
    ),
])
@pytest.mark.parametrize('sol', [Solution()])
def test_solution(sol, grid, expected):
    assert sol.findBall(grid) == expected

Thoughts

直接用模拟法，模拟每个球的移动路径，计算出最终落到哪里。

如果一个球落入 grid 中某一行 row 的第 src 列，那么球会往 dest = src + row[src] 列滚动。但如果 dest 超出 [0, n) 区间，就会被左右边界挡住并停在那里。类似地，如果 grid[dest] ≠ grid[src]，说明形成了一个 “V”，也就停住了。其他情况，球会落入下一行的 dest 列，重复同样的判断直到球在某行被卡住或者从最后一行漏下去为止。

每个球最多需要 O(m) 时间。总共时间复杂度 O(m * n)，附加的空间复杂度 O(1)。

Code

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class Solution:
    def findBall(self, grid: list[list[int]]) -> list[int]:
        n = len(grid[0])
        result = []
        for src in range(n):
            for row in grid:
                dest = src + row[src]
                if dest < 0 or dest >= n or row[dest] != row[src]:
                    result.append(-1)
                    break
                src = dest
            else:
                result.append(src)

        return result

许可协议

本文除了题目描述（Problem）部分之外，其他内容由 Calf 原创，采用 CC BY-NC-SA 4.0 许可协议，转载请注明出处。

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