1025. Divisor Game

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1025. Divisor Game

Difficulty: Easy

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

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class Solution {
    public boolean divisorGame(int N) {
        boolean[] result = new boolean[N + 1];
        
        result[0] = false;
        result[1] = false;
        
        for (int i = 2; i <= N; i ++) {
            for (int j = 1; j < i; j ++) {
                if (result[i - j] == false && i % j == 0) {
                    result[i] = true;
                    break;
                }
            }
        }
        
        return result[N];
    }
}