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LeetCode 1706 Where Will the Ball Fall

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LeetCode

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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 i<sup>th</sup> column at the top, or -1 if the ball gets stuck in the box.

Example 1:

<pre>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. </pre>

Example 2:

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

Example 3:

<pre>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] </pre>

Constraints:

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

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题目大意：

二维数组每一个cell都是1或者-1，分别表示一个玻璃板的放置方向，正对角线或者反对角线。球从每一个列投下，根据玻璃板的设置，若成功从底部滑出，输入列号，否则输入-1. 求这个结果数组。

解题思路：

这是Q&A题目。游戏模拟题大多用DFS，因为就是选择一条路径走到底。

解题步骤：

N/A

注意事项：

  1. 任何情况都是row + 1，而不是-1
  2. 题目要求若成功，输出球跌出的列号，而不是boolean = 1

Python代码：

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def findBall(self, grid: List[List[int]]) -> List[int]:
	return [self.dfs(grid, 0, j) for j in range(len(grid[0]))]

def dfs(self, grid, row, col):
	if row == len(grid):
		return col
	if grid[row][col] == 1:
		if col + 1 == len(grid[0]) or grid[row][col + 1] == -1:
			return -1
		else:
			return self.dfs(grid, row + 1, col + 1)
	else:
		if col - 1 < 0 or grid[row][col - 1] == 1:
			return -1
		else:
			return self.dfs(grid, row + 1, col - 1)

算法分析：

时间复杂度为O(nm)，空间复杂度O(1), n, m分别为行数和列数。

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