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This approach involves sorting engineers by their efficiency in descending order, ensuring that each team's minimum efficiency is dominated by its highest-efficiency member being considered rather than doing a costly check of all members.
After this, we use a min-heap to keep track of the top 'k' speeds. The strategy is to iterate through each engineer (sorted by efficiency), compute potential team performance by inserting their speed into the speed sum (if advantageous), and then multiplying by the current engineer's efficiency (the smallest efficiency thus far in the sorted order).
Time Complexity: O(n log n) due to sorting and heap operations.
Space Complexity: O(k) for maintaining the min-heap.
1import heapq
2
3class Solution:
4 def maxPerformance(self, n, speed, efficiency, k):
5 engineers = list(zip(efficiency, speed))
6 engineers.sort(reverse=True)
7 speed_heap = []
8 speed_sum = max_perf = 0
9 for e, s in engineers:
10 heapq.heappush(speed_heap, s)
11 speed_sum += s
12 if len(speed_heap) > k:
13 speed_sum -= heapq.heappop(speed_heap)
14 max_perf = max(max_perf, speed_sum * e)
15 return max_perf % (10**9 + 7)
16This solution utilizes Python's heapq as a min-heap structure to efficiently handle and minimize the smallest elements when necessary. Engineers are sorted by efficiency, and possible teams are evaluated based on the current efficiency and speed set maintained in the heap.
Instead of using a heap, an alternative approach employs dynamic programming. For each engineer sorted by efficiency, we determine the maximum performance we can achieve using a binary search to find an optimal combination in an accumulated list of maximum speeds and efficiencies.
This involves recursively filling up a DP table with potential performance values, achieving optimization through binary search.
Time Complexity: O(n^2 log n) in a worst-case naive implementation.
Space Complexity: O(n) for the DP table.
Due to complexity, a full DP + binary search approach has intricate implementation specific details. A similar illustrative solution in pseudocode involves maintaining an array where calculating potential top speeds and efficiencies are iterated and evaluated using a DP-based recurrence relation.