divide_players_into_teams_of_equal_skill.py

"""
You are given a positive integer array skill of even length n where skill[i] denotes the skill of the ith player. Divide the players into n / 2 teams of size 2 such that the total skill of each team is equal.

The chemistry of a team is equal to the product of the skills of the players on that team.

Return the sum of the chemistry of all the teams, or return -1 if there is no way to divide the players into teams such that the total skill of each team is equal.

 

Example 1:

Input: skill = [3,2,5,1,3,4]
Output: 22
Explanation: 
Divide the players into the following teams: (1, 5), (2, 4), (3, 3), where each team has a total skill of 6.
The sum of the chemistry of all the teams is: 1 * 5 + 2 * 4 + 3 * 3 = 5 + 8 + 9 = 22.
Example 2:

Input: skill = [3,4]
Output: 12
Explanation: 
The two players form a team with a total skill of 7.
The chemistry of the team is 3 * 4 = 12.
Example 3:

Input: skill = [1,1,2,3]
Output: -1
Explanation: 
There is no way to divide the players into teams such that the total skill of each team is equal.
 

Constraints:

2 <= skill.length <= 105
skill.length is even.
1 <= skill[i] <= 1000

"""

class Solution:
    def dividePlayers(self, skill: List[int]) -> int:
        skill.sort()

        left = 0
        right = len(skill) - 1
        ans = 0

        total = skill[left] + skill[right]
        while left <= right:
            if skill[left] + skill[right] != total:
                return -1
            ans = ans + (skill[left] * skill[right])
            left = left + 1
            right = right - 1
        
        return ans