How do you solve Find the Winner of the Circular Game on LeetCode?

Find the Winner of the Circular Game (LeetCode #1823) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: Understanding the circular counting mechanism is crucial.

What is the time complexity of Find the Winner of the Circular Game?

The optimal solution for Find the Winner of the Circular Game runs in O(n) time and uses O(1) space. The time complexity is O(n) due to the recursive calls, while the space complexity is O(1) as we only use a few variables for tracking.

What is the brute force solution for Find the Winner of the Circular Game?

The brute force approach for Find the Winner of the Circular Game is Brute Force, with O(n²) time complexity and O(1) space complexity. This approach simulates the game directly by maintaining a list of friends and removing them one by one as they lose. It is straightforward but inefficient as it requires multiple passes through the list. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Find the Winner of the Circular Game?

Find the Winner of the Circular Game uses the following concepts: Array, Math, Recursion, Queue, Simulation. The recommended patterns to study are: Recursion, Mathematical Induction.

What are the interview tips for Find the Winner of the Circular Game?

Always clarify the problem constraints and edge cases before starting. Discuss your thought process and approach before jumping into coding. Test your solution with different inputs to ensure it handles all scenarios.

What are common mistakes when solving Find the Winner of the Circular Game?

Failing to correctly handle the wrap-around counting. Not considering the base case in recursive solutions.

#1823

Find the Winner of the Circular Game

Medium

ArrayMathRecursionQueueSimulationRecursionMathematical Induction

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n)Space O(1)

This approach uses a mathematical recursive formula known as the Josephus problem, which allows us to determine the winner without simulating the entire game. It significantly reduces the time complexity.

⚙️

Algorithm

3 steps

1Step 1: Define a recursive function that returns the position of the winner for n friends and k steps.
2Step 2: Base case: if there's only one friend, they are the winner (return 0).
3Step 3: For more than one friend, calculate the winner's position recursively using the formula: (josephus(n - 1, k) + k) % n.

solution.py8 lines

1# Full working Python code
2
3def findTheWinner(n, k):
4    def josephus(n, k):
5        if n == 1:
6            return 0
7        return (josephus(n - 1, k) + k) % n
8    return josephus(n, k) + 1

ℹ

Complexity note: The time complexity is O(n) due to the recursive calls, while the space complexity is O(1) as we only use a few variables for tracking.

1Understanding the circular counting mechanism is crucial.
2Recognizing the recursive nature of the problem can lead to a more efficient solution.

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