LeetCode 1025 Divisor Game (博弈)

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

Example 2:

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

Note:

1. 1 <= N <= 1000

题目链接：https://leetcode.com/problems/divisor-game/

题目分析：手推几个可以发现偶数是先手必胜，奇数是先手必败，下面证明

奇数的约数肯定是奇数（显然），那么面对奇数，一次操作完后必然变成偶数，先手如果是偶数，只需要每次都把这个数字变成奇数（减1即可），这样下去开始的后手最终必然会将数字变成2

class Solution {
    public boolean divisorGame(int N) {
        return N % 2 == 0;
    }
}