1025. Divisor Game.py

class Solution:
    def divisorGame(self, n: int) -> bool:
        ctr = 0 # variable for counting every try of Alice and Bob
        while n!=1:
            ctr+=1
            n-=1

        if ctr%2==0:# -> Bob had the last move
            return False
        return True # -> else Alice wins
        
        
        # from discussion
        # return n%2 == 0
        
'''
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: 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
'''