2491. Divide Players Into Teams of Equal Skill

Problem

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

C++

• class Solution {
  public:
      long long dividePlayers(vector<int>& skill) {
          sort(skill.begin(), skill.end());
          int n = skill.size();
          int t = skill[0] + skill[n - 1];
          long long ans = 0;
          for (int i = 0, j = n - 1; i < j; ++i, --j) {
              if (skill[i] + skill[j] != t) return -1;
              ans += 1ll * skill[i] * skill[j];
          }
          return ans;
      }
  };

PYTHON

• class Solution:
      def dividePlayers(self, skill: list[int]) -> int:
          skill.sort()
          total_product = 0
          target_sum = skill[0] + skill[-1]
          i, j = 0, len(skill) - 1
          while i < j:
              if skill[i] + skill[j] != target_sum:
                  return -1
              total_product += skill[i] * skill[j]
              i += 1
              j -= 1
          return total_product

JAVA

• class Solution {
      public long dividePlayers(int[] skill) {
          Arrays.sort(skill);
          int n = skill.length;
          int t = skill[0] + skill[n - 1];
          long ans = 0;
          for (int i = 0, j = n - 1; i < j; ++i, --j) {
              if (skill[i] + skill[j] != t) {
                  return -1;
              }
              ans += (long) skill[i] * skill[j];
          }
          return ans;
      }
  }