divisor_game

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1025. Divisor Game (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. 1 <= N <= 1000

Related Topics

[Math] [Dynamic Programming]

Hints

Hint 1

If the current number is even, we can always subtract a 1 to make it odd. If the current number is odd, we must subtract an odd number to make it even.