How do you solve Find the Child Who Has the Ball After K Seconds on LeetCode?

Find the Child Who Has the Ball After K Seconds (LeetCode #3178) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(1) time complexity and O(1) space complexity. Key insight: The ball's passing is periodic, which allows us to use modulo to simplify calculations.

What is the time complexity of Find the Child Who Has the Ball After K Seconds?

The optimal solution for Find the Child Who Has the Ball After K Seconds runs in O(1) time and uses O(1) space. The time complexity is O(1) because we perform a constant number of calculations, and the space complexity is O(1) since we only use a few variables.

What is the brute force solution for Find the Child Who Has the Ball After K Seconds?

The brute force approach for Find the Child Who Has the Ball After K Seconds is Brute Force, with O(k) time complexity and O(1) space complexity. We simulate the passing of the ball for each second until we reach k seconds. This approach is straightforward but inefficient for larger values of k. The optimal Optimal Solution approach improves this to O(1).

What algorithm or data structure is used to solve Find the Child Who Has the Ball After K Seconds?

Find the Child Who Has the Ball After K Seconds uses the following concepts: Math, Simulation. The recommended patterns to study are: Simulation, Mathematical Patterns.

What are the interview tips for Find the Child Who Has the Ball After K Seconds?

Always think about edge cases, such as the smallest and largest values for n and k. Explain your thought process clearly; it shows your understanding of the problem. Practice similar problems to recognize patterns in ball passing or movement.

What are common mistakes when solving Find the Child Who Has the Ball After K Seconds?

Forgetting to handle the direction change correctly when the ball reaches the ends. Not considering the periodic nature of the problem, leading to unnecessary simulations.

#3178

Find the Child Who Has the Ball After K Seconds

Easy

MathSimulationSimulationMathematical Patterns

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(k)	O(1)
Space	O(1)	O(1)

💡

Intuition

Time O(1)Space O(1)

Instead of simulating each second, we can determine the effective position using the modulo operation. The ball's movement is periodic, so we can find the position after k seconds without simulating each second.

⚙️

Algorithm

3 steps

1Step 1: Calculate the effective time as k % (2 * (n - 1)).
2Step 2: Determine the position based on the effective time and the direction of movement.
3Step 3: If the effective time is less than n, return the effective time; otherwise, calculate the position from the end.

solution.py8 lines

1# Full working Python code
2
3def find_child(n, k):
4    effective_time = k % (2 * (n - 1))
5    if effective_time < n:
6        return effective_time
7    else:
8        return (2 * (n - 1)) - effective_time

ℹ

Complexity note: The time complexity is O(1) because we perform a constant number of calculations, and the space complexity is O(1) since we only use a few variables.

1The ball's passing is periodic, which allows us to use modulo to simplify calculations.
2Understanding the direction change at the ends of the queue is crucial for determining the ball's position.

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