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 <= 105skill.length is even.1 <= skill[i] <= 1000This approach involves first sorting the skill array. The goal is to form teams such that each team has an equal total skill value.
By sorting the skills, the smallest and largest unpaired skills can be paired together to potentially form a valid team. This creates a straightforward method to iterate and compare pairs using two pointers, ensuring each team's total skill is consistent.
Utilize two pointers, one starting at the beginning of the sorted skills and the other at the end, to form teams by incrementing or decrementing as conditions require. Check if teams formed balance the array accurately for equal skill sums.
The given C code sorts the array and checks if each pair of smallest and largest skill elements add up to the same total skill value. It uses two pointers to iterate and compute the sum of chemistries.
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Time Complexity: O(n log n), due to the sorting step.
Space Complexity: O(1), as no additional space proportional to input size is used.
To solve the problem efficiently without sorting, utilize a hash map to count the frequency of each skill level. By arranging teams based on these frequencies, we can potentially balance skill totals across teams, verifying team chemistry conditions in the progress.
Each team should combine players of differing skill values such that their sum remains consistent each time. This involves iterating across the hash map keys and determining corresponding partners for forming valid teams.
The C solution uses a frequency array to count occurrences of each skill level. It finds valid pairings, checking if skills can sum up consistently. Chemistry is calculated by multiplying paired skill values, adjusting the frequency in-place.
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Time Complexity: O(n + k^2), where n is the number of skills and k is the unique skills' range.
Space Complexity: O(k), because of the frequency array for skills up to 1000.
| Approach | Complexity |
|---|---|
| Approach 1: Sorting and Two-Pointer Technique | Time Complexity: O(n log n), due to the sorting step. |
| Approach 2: Hash Map for Frequency Counting | Time Complexity: O(n + k^2), where n is the number of skills and k is the unique skills' range. |
Divide Players Into Teams of Equal Skill - Leetcode 2491 - Python • NeetCodeIO • 8,222 views views
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