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Where Will the Ball Fall

Problem Description​

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.

Examples​

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

Solution for 1706. Where Will the Ball Fall​

Approach​

We drop the ball at grid[0][i] and track ball position i1, which initlized as i.

An observation is that, if the ball wants to move from i1 to i2, we must have the board direction grid[j][i1] == grid[j][i2]

Code in Different Languages​

Written by @agarwalhimanshugaya
        def findBall(self, grid):
m, n = len(grid), len(grid[0])

def test(i):
for j in xrange(m):
i2 = i + grid[j][i]
if i2 < 0 or i2 >= n or grid[j][i2] != grid[j][i]:
return -1
i = i2
return i
return map(test, range(n))

Complexity Analysis​

  • Time Complexity: O(N∗M)O(N*M)
  • Space Complexity: O(N) O(N)

References​