How do you solve Where Will the Ball Fall on LeetCode?

Where Will the Ball Fall (LeetCode #1706) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Understanding the grid's structure is crucial for simulating the ball's path.

What is the brute force solution for Where Will the Ball Fall?

The brute force approach for Where Will the Ball Fall is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach simulates the path of each ball dropped from the top of the grid. For each ball, we check its movement cell by cell until it either falls out or gets stuck. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Where Will the Ball Fall?

Where Will the Ball Fall uses the following concepts: Array, Matrix, Simulation. The recommended patterns to study are: Simulation, DFS, Memoization.

What are the interview tips for Where Will the Ball Fall?

Explain your thought process clearly while coding. Consider edge cases and test your solution with them. Use comments to clarify your logic, especially in complex sections.

What are common mistakes when solving Where Will the Ball Fall?

Not handling edge cases where the ball hits the walls correctly. Forgetting to reset the ball's position when it gets stuck.

#1706

Where Will the Ball Fall

Medium

ArrayMatrixSimulationSimulationDFSMemoization

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

The optimal solution uses a depth-first search (DFS) approach to simulate the ball's path efficiently. By caching results for each column, we avoid redundant calculations, leading to a faster solution.

⚙️

Algorithm

3 steps

1Step 1: Create a helper function to simulate the ball's path for a given column.
2Step 2: Use memoization to store results for each column to avoid recalculating paths.
3Step 3: For each ball, call the helper function and store the results.

solution.py23 lines

1# Full working Python code
2
3def findBall(grid):
4    m, n = len(grid), len(grid[0])
5    memo = [-2] * n
6    def dfs(col):
7        if memo[col] != -2:
8            return memo[col]
9        position = col
10        for row in range(m):
11            direction = grid[row][position]
12            next_position = position + direction
13            if direction == 1 and (next_position >= n or grid[row][next_position] == -1):
14                memo[col] = -1
15                return -1
16            if direction == -1 and (next_position < 0 or grid[row][next_position] == 1):
17                memo[col] = -1
18                return -1
19            position = next_position
20        memo[col] = position
21        return position
22    result = [dfs(col) for col in range(n)]
23    return result

ℹ

Complexity note: The time complexity is O(n) because each ball's path is calculated once and stored in memoization. The space complexity is O(n) due to the memo array used for caching results.

1Understanding the grid's structure is crucial for simulating the ball's path.
2Memoization can significantly reduce redundant calculations.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.