1025. Divisor Game

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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

题意：博弈问题，Alice先手。共N个石子，每个人可取x个石子，这里x要满足:(1)0<x<N (2)N%x=0 

思路：博弈问题关键在于根据题意，推敲规律。

    N=2时，Alice取1个，Bob不能再取，Alice胜。

    N=3时，Alice只能取1个，Bob取1个，Alice输。

    N=4时，Alice取1个，Bob面对3个石头的情况，由上知Bob必输，即Alice必胜。

    N=5时，Alice只能取1个，Bob面对4个石头的情况，由上知Alice必输。

    ......

   可知，当N为偶数时，Alice必胜，否则Alice必输。

class Solution {
public:
    bool divisorGame(int N) {
        if(N%2==0)
            return true;
        else 
            return false;
    }
};