nim-game.py

# Time:  O(1)
# Space: O(1)
#
# You are playing the following Nim Game with your friend:
# There is a heap of stones on the table, each time one of 
# you take turns to remove 1 to 3 stones.
# The one who removes the last stone will be the winner.
# You will take the first turn to remove the stones.
#
# Both of you are very clever and have optimal strategies for
# the game. Write a function to determine whether you can win 
# the game given the number of stones in the heap.
#
# For example, if there are 4 stones in the heap, then you will
# never win the game: no matter 1, 2, or 3 stones you remove,
# the last stone will always be removed by your friend.
#

class Solution(object):
    def canWinNim(self, n):
        """
        :type n: int
        :rtype: bool
        """
        return n % 4 != 0