Maximum Performance of a Team

Problem Description

You are given two integers n and k and two integer arrays speed and efficiency both of length n. There are n engineers numbered from 1 to n. speed[i] and efficiency[i] represent the speed and efficiency of the i-th engineer respectively.

Choose at most k different engineers out of the n engineers to form a team with the maximum performance. The performance of a team is the sum of its engineers' speeds multiplied by the minimum efficiency among its engineers.

Return the maximum performance of this team. Since the answer can be a huge number, return it modulo 10^9 + 7.

Key Insights

• The performance is influenced by both speed and efficiency; thus, we need to consider both attributes while forming a team.
• Sorting engineers by their efficiency allows us to focus on the most efficient ones first, which maximizes performance.
• Using a min-heap (priority queue) helps maintain the top k speeds efficiently, allowing for quick computation of the total speed.
• The overall performance for a specific efficiency level can be computed based on the current total speed and the minimum efficiency of the chosen engineers.

Space and Time Complexity

Time Complexity: O(n log n) - due to sorting the engineers based on efficiency and managing the min-heap for speed. Space Complexity: O(k) - for storing the speeds in the min-heap.

Solution

1. Pair up each engineer's speed with their efficiency.
2. Sort the engineers based on efficiency in descending order.
3. Use a min-heap to maintain the top k speeds.
4. For each engineer (starting from the most efficient), compute the current performance and update the maximum performance found.
5. Return the maximum performance modulo 10^9 + 7.

Code Solutions