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1706.WhereWillTheBallFall.py
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1706.WhereWillTheBallFall.py
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"""
1706. Where Will the Ball Fall
Medium
Array | Dynamic Programming | Depth-First Search | Matrix | Simulation
---
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.
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.
"""
from typing import List
# O(m * n) time | O(m * n) space
class Solution:
def findBall(self, grid: List[List[int]]) -> List[int]:
def dfs(row, col, grid):
if row == len(grid):
return col
nextCol = col + grid[row][col]
if nextCol < 0 or nextCol > len(grid[0]) - 1 or grid[row][col] != grid[row][nextCol]:
return -1
return dfs(row + 1, nextCol, grid)
res = []
for i in range(len(grid[0])):
res.append(dfs(0, i, grid))
return res