x-of-a-kind-in-a-deck-of-cards.py

# Time:  O(n * (logn)^2)
# Space: O(n)

# In a deck of cards, each card has an integer written on it.
#
# Return true if and only if you can choose X >= 2 such that
# it is possible to split the entire deck into 1 or more groups of cards, where:
#
# Each group has exactly X cards.
# All the cards in each group have the same integer.
#
# Example 1:
#
# Input: [1,2,3,4,4,3,2,1]
# Output: true
# Explanation: Possible partition [1,1],[2,2],[3,3],[4,4]
# Example 2:
#
# Input: [1,1,1,2,2,2,3,3]
# Output: false
# Explanation: No possible partition.
# Example 3:
#
# Input: [1]
# Output: false
# Explanation: No possible partition.
# Example 4:
#
# Input: [1,1]
# Output: true
# Explanation: Possible partition [1,1]
# Example 5:
#
# Input: [1,1,2,2,2,2]
# Output: true
# Explanation: Possible partition [1,1],[2,2],[2,2]
#
# Note:
# - 1 <= deck.length <= 10000
# - 0 <= deck[i] < 10000

import collections


class Solution(object):
    def hasGroupsSizeX(self, deck):
        """
        :type deck: List[int]
        :rtype: bool
        """
        def gcd(a, b):  # Time: O((logn)^2)
            while b:
                a, b = b, a % b
            return a

        vals = collections.Counter(deck).values()
        return reduce(gcd, vals) >= 2