Create chalkboard-xor-game.py

Author: kamyu104

Python/chalkboard-xor-game.py

@@ -0,0 +1,43 @@
+# Time:  O(n)
+# Space: O(1)
+
+# We are given non-negative integers nums[i] which are written on a chalkboard.
+# Alice and Bob take turns erasing exactly one number from the chalkboard,
+# with Alice starting first.  If erasing a number causes the bitwise XOR of
+# all the elements of the chalkboard to become 0, then that player loses.
+# (Also, we'll say the bitwise XOR of one element is that element itself,
+#  and the bitwise XOR of no elements is 0.)
+#
+# Also, if any player starts their turn with the bitwise XOR of all the elements
+# of the chalkboard equal to 0, then that player wins.
+#
+# Return True if and only if Alice wins the game, assuming both players play optimally.
+#
+# Example:
+# Input: nums = [1, 1, 2]
+# Output: false
+# Explanation: 
+# Alice has two choices: erase 1 or erase 2. 
+# If she erases 1, the nums array becomes [1, 2]. The bitwise XOR of
+# all the elements of the chalkboard is 1 XOR 2 = 3.
+# Now Bob can remove any element he wants, because Alice will be the one
+# to erase the last element and she will lose. 
+# If Alice erases 2 first, now nums becomes [1, 1]. The bitwise XOR of
+# all the elements of the chalkboard is 1 XOR 1 = 0. Alice will lose.
+#
+# Notes:
+# - 1 <= N <= 1000. 
+# - 0 <= nums[i] <= 2^16.
+
+from operator import xor
+from functools import reduce
+
+
+class Solution(object):
+    def xorGame(self, nums):
+        """
+        :type nums: List[int]
+        :rtype: bool
+        """
+        return reduce(xor, nums) == 0 or \
+               len(nums) % 2 == 0