1025.py

'''
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
'''

class Solution(object):
    def divisorGame(self, N):
        """
        :type N: int
        :rtype: bool
        """
        if N == 0:
            return False
    
        move = 0
        while N > 1:
            for num in range(1, N):
                if N%num == 0:
                    N -= num
                    move += 1
                    break
        # print move
        if move%2:
            return True
        return False