How do you solve Stone Removal Game on LeetCode?

Stone Removal Game (LeetCode #3360) 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: Alice's winning strategy can be derived from the number of stones left after her first move.

What is the time complexity of Stone Removal Game?

The optimal solution for Stone Removal 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 Stone Removal Game?

The brute force approach for Stone Removal Game is Brute Force, with O(n²) time complexity and O(1) space complexity. In this approach, we simulate the game by recursively checking all possible moves for both players. We start with Alice's turn and explore all outcomes until we determine if Alice can win or not. The optimal Optimal Solution approach improves this to O(1).

What algorithm or data structure is used to solve Stone Removal Game?

Stone Removal Game uses the following concepts: Math, Simulation. The recommended patterns to study are: Game Theory, Modulo Arithmetic.

What are the interview tips for Stone Removal Game?

Always consider edge cases, such as the minimum value of n. Look for patterns in game theory problems; they often lead to optimal solutions. Explain your thought process clearly, especially when transitioning from brute-force to optimal solutions.

What are common mistakes when solving Stone Removal Game?

Forgetting to handle the case where n < 10 correctly. Not recognizing the pattern in the game and relying solely on brute-force simulation.

#3360

Stone Removal Game

Easy

MathSimulationGame TheoryModulo Arithmetic

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(1)Space O(1)

Instead of simulating every possible move, we can derive a pattern based on the number of stones left. The game can be simplified to checking if the number of stones remaining after Alice's first move is a multiple of 11.

⚙️

Algorithm

4 steps

1Step 1: If n < 10, return false (Alice cannot make a valid move).
2Step 2: Calculate the remaining stones after Alice's first move: remaining = n - 10.
3Step 3: If remaining is less than 0, return true (Alice wins).
4Step 4: Check if remaining % 11 == 0. If true, Alice loses; otherwise, she wins.

solution.py2 lines

1def canAliceWin(n):
2    return n >= 10 and (n - 10) % 11 != 0

ℹ

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

1Alice's winning strategy can be derived from the number of stones left after her first move.
2The game can be simplified using modulo arithmetic to determine winning and losing positions.

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