How do you solve Find the Winning Player in Coin Game on LeetCode?

Find the Winning Player in Coin Game (LeetCode #3222) 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: Understanding the game mechanics helps simplify the problem significantly.

What is the time complexity of Find the Winning Player in Coin Game?

The optimal solution for Find the Winning Player in Coin Game runs in O(1) time and uses O(1) space. The time complexity is O(1) because we are performing a constant number of operations regardless of the input size.

What is the brute force solution for Find the Winning Player in Coin Game?

The brute force approach for Find the Winning Player in Coin Game is Brute Force, with O(n²) time complexity and O(1) space complexity. In the brute force approach, we simulate each turn of the game, checking if Alice or Bob can make the required total of 115 with the available coins. We continue until one player cannot make the required total, determining the winner based on who made the last successful move. The optimal Optimal Solution approach improves this to O(1).

What algorithm or data structure is used to solve Find the Winning Player in Coin Game?

Find the Winning Player in Coin Game uses the following concepts: Math, Simulation, Game Theory. The recommended patterns to study are: Game Theory, Mathematical Simulation.

What are the interview tips for Find the Winning Player in Coin Game?

Always start with a brute-force solution to understand the problem better. Look for patterns or mathematical relationships that can simplify the problem. Discuss your thought process out loud during the interview to show your understanding.

What are common mistakes when solving Find the Winning Player in Coin Game?

Overcomplicating the problem by simulating each turn instead of calculating the maximum turns. Not considering the conditions under which a player can no longer play.

#3222

Find the Winning Player in Coin Game

Easy

MathSimulationGame TheoryGame TheoryMathematical Simulation

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(1)Space O(1)

In the optimal solution, we realize that the game can be reduced to a simple calculation. The maximum number of turns is determined by the limiting factor of coins available. The player who can make the last move wins, and we can calculate the total turns directly.

⚙️

Algorithm

2 steps

1Step 1: Calculate the maximum turns possible as min(x, y // 4).
2Step 2: If the total turns are odd, Alice wins; if even, Bob wins.

solution.py3 lines

1def find_winner(x, y):
2    turns = min(x, y // 4)
3    return 'Alice' if turns % 2 == 0 else 'Bob'

ℹ

Complexity note: The time complexity is O(1) because we are performing a constant number of operations regardless of the input size.

1Understanding the game mechanics helps simplify the problem significantly.
2Optimal play means calculating the maximum possible turns rather than simulating each turn.

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