1025. Divisor Game

Description

Alice and Bob take turns playing a game, with Alice starting first.

Initially, there is a number n on the chalkboard. On each player’s turn, that player makes a move consisting of:

• Choosing any integer x with 0 < x < n and n % x == 0.
• Replacing the number n on the chalkboard with n - x.

Also, if a player cannot make a move, they lose the game.

Return true if and only if Alice wins the game, assuming both players play optimally.

Example 1:

• Input: n = 2
• Output: true
• Explanation: Alice chooses 1, and Bob has no more moves.

Example 2:

• Input: n = 3
• Output: false
• Explanation: Alice chooses 1, Bob chooses 1, and Alice has no more moves.

Constraints:

• 1 <= n <= 1000

💡 Hint 1:
If the current number is even, we can always subtract a 1 to make it odd. If the current number is odd, we must subtract an odd number to make it even.

Submitted Code

class Solution:
    def divisorGame(self, n: int) -> bool:
        return n % 2 == 0

Runtime: 0 ms | Beats 100.00%
Memory: 17.76 MB | Beats 60.93%

짝수로 시작하면 n - 1로 밥에게 홀수를 넘길 수 있고, 마지막에 n이 1일 때 받는 플레이어가 지게 되기 때문에 앨리스가 무조건 이길 수 있다. 반대로 홀수로 시작하면 x로 홀수만 선택 가능하기 때문에 홀수 - 홀수가 되서 밥에게 짝수를 넘겨줄 수 밖에 없고, 결국 앨리스가 지게 된다.