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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.
1using System;
2using System.Collections.Generic;
3
4public class Solution {
5 public int MaxPerformance(int n, int[] speed, int[] efficiency, int k) {
6 var engineers = new List<(int eff, int spd)>();
7 for (int i = 0; i < n; i++) {
8 engineers.Add((efficiency[i], speed[i]));
9 }
10 engineers.Sort((a, b) => b.eff.CompareTo(a.eff));
11
12 var minHeap = new SortedSet<(int speed, int idx)>();
13 long speedSum = 0, maxPerf = 0;
14 int mod = 1000000007;
15
16 foreach (var engineer in engineers) {
17 speedSum += engineer.spd;
18 minHeap.Add((engineer.spd, engineers.IndexOf(engineer)));
19
20 if (minHeap.Count > k) {
21 speedSum -= minHeap.Min.speed;
22 minHeap.Remove(minHeap.Min);
23 }
24
25 maxPerf = Math.Max(maxPerf, speedSum * engineer.eff);
26 }
27
28 return (int)(maxPerf % mod);
29 }
30}
31Similar to other solutions, C# also allows us to make use of Collections such as SortedSet, which helps in automatically sorting and accessing the minimum elements efficiently. Each engineer consideration is done under sorted efficiencies, and selections adjust to track and output possible team performances.
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.