Introduction

In this blog post, we will explore how to solve the LeetCode problem "3360" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

Alice and Bob are playing a game where they take turns removing stones from a pile, with Alice going first. Alice starts by removing exactly 10 stones on her first turn. For each subsequent turn, each player removes exactly 1 fewer stone than the previous opponent. The player who cannot make a move loses the game. Given a positive integer n, return true if Alice wins the game and false otherwise. Example 1: Input: n = 12 Output: true Explanation: Alice removes 10 stones on her first turn, leaving 2 stones for Bob. Bob cannot remove 9 stones, so Alice wins. Example 2: Input: n = 1 Output: false Explanation: Alice cannot remove 10 stones, so Alice loses. Constraints: 1 <= n <= 50

Explanation

Here's the solution:

• Determine Win/Loss: Simulate the game according to the given rules. If Alice can make the first move and force a situation where Bob cannot make a move, then Alice wins.
• Recursive Approach: Utilize a recursive function to model the turns. The function takes the remaining stones, the stones to be removed by the current player, and a boolean indicating whose turn it is.

• Base Cases: The base cases handle scenarios where either the player cannot make a move (they lose) or the pile is exhausted.

• Runtime Complexity: O(n), where n is the initial number of stones. Storage Complexity: O(n) due to the recursion depth.

Code

    def stoneGame(n: int) -> bool:
    """
    Determines if Alice wins the stone game.

    Args:
        n: The initial number of stones.

    Returns:
        True if Alice wins, False otherwise.
    """

    def can_win(stones, remove, alice_turn):
        if stones < remove:
            return not alice_turn  # Current player cannot move, other player wins

        if alice_turn:  # Alice's turn
            return can_win(stones - remove, remove - 1, not alice_turn)
        else:  # Bob's turn
            return can_win(stones - remove, remove - 1, not alice_turn)

    if n < 10:
        return False
    else:
        return can_win(n - 10, 9, False)  # Alice starts by removing 10