Smallest Sufficient Team

Problem Description

In a project, you have a list of required skills req_skills, and a list of people. The ith person people[i] contains a list of skills that the person has. Consider a sufficient team: a set of people such that for every required skill in req_skills, there is at least one person in the team who has that skill. We can represent these teams by the index of each person. Return any sufficient team of the smallest possible size, represented by the index of each person. You may return the answer in any order.

Key Insights

• A sufficient team must cover all required skills.
• Each person's skills can be represented as a bitmask, allowing us to efficiently track which skills are covered.
• We can use dynamic programming (DP) to find the smallest team by iterating through combinations of people.
• The maximum number of required skills is 16, which allows us to use a bitmask representation for skill coverage.

Space and Time Complexity

Time Complexity: O(2^m * n), where m is the number of required skills and n is the number of people. Space Complexity: O(2^m), for storing the minimum team size for each skill combination.

Solution

To solve the problem, we will:

1. Use a bitmask to represent the skills covered by each person.
2. Initialize a DP array to track the minimum team size needed to cover each combination of skills.
3. Iterate through each person and update the DP array based on the skills they contribute.
4. Finally, backtrack to find the indices of the people who form the smallest sufficient team.

Code Solutions