Question
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 <= N <= 1000
解题思路：本题通过动态规划
假设N=1，爱丽丝失败；先走输
假设N=2，她可以选择x=1，来使鲍勃遇到的N=2-1=1，无法操作，爱丽丝获胜；
先走胜
假设N=3，她只能选择x=1，鲍勃遇到的N=2，鲍勃获胜；
假设N=4，她可以选择x=1，来使鲍勃遇到的N=3，爱丽丝获胜
假设N=5，她可以选择X=1，来使鲍勃遇到的N=4，鲍勃获胜
然后往上计算
class Solution {
public boolean divisorGame(int N) {
boolean[] dp = new boolean[N + 1];
dp[1] = false;
for (int i = 2; i <= N; i++) {
for (int j = 1; j < i; j++) {
if (i % j == 0 && dp[i - j] == false) {
dp[i] = true;
}
}
}
return dp[N];
}
}
