1086. Divisor Game

难度: Easy

题目描述

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

解题思路

代码实现

解决方案

java

class Solution {
    public boolean divisorGame(int n) {

        boolean[] f = new boolean[n + 2];
        f[1] = false;
        f[2] = true;

        for (int i = 3; i <= n; i++) {
            for (int j = 1; j < i; ++j) {
                if (i % j == 0 && !f[i - j]) {
                    f[i] = true;
                    break;
                }
            }
        }

        return f[n];
    }

}