575 Distribute Candies

Given an integer array with even length, where different numbers in this array represent different kinds of candies. Each number means one candy of the corresponding kind. You need to distribute these candies equally in number to brother and sister. Return the maximum number of kinds of candies the sister could gain.

Example 1:

Input:
 candies = [1,1,2,2,3,3]

Output:
 3

Explanation:

There are three different kinds of candies (1, 2 and 3), and two candies for each kind.
Optimal distribution: The sister has candies [1,2,3] and the brother has candies [1,2,3], too. 
The sister has three different kinds of candies.

Example 2:

Input:
 candies = [1,1,2,3]

Output:
 2

Explanation:
 For example, the sister has candies [2,3] and the brother has candies [1,1]. 
The sister has two different kinds of candies, the brother has only one kind of candies.

Note:

1. The length of the given array is in range [2, 10,000], and will be even.

2. The number in given array is in range [-100,000, 100,000].

The Idea: Since the input is always going to be even, we will always be able to distribute half. The only requirement to this problem is that each of 2 people get half the amount of candies, but one of them gets the most diverse group of candies. This would be the same as minimizing the type of candies to the other person, can then taking the complement. So the problem is to divide candies into two sets. One that has the most type of candies, and the other than does not. We know that the most diverse group of candies is the set(candies). If this number is == to half the amount of candies, then the means the other less diverse group of candies can be given to the other person. However, we have more unique candies than half the candies, we will always be limited into only giving half.

Complexity: O(n) time and space

class Solution:
    def distributeCandies(self, candies):
        """
        :type candies: List[int]
        :rtype: int
        """

        cc = set(candies)
        half = int(len(candies) / 2)
        return half if len(cc) >= half else len(cc)