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This approach uses a heap to dynamically maintain workers while iterating over them sorted by wage-to-quality ratio. The goal is to keep the sum of qualities of the selected workers minimal while ensuring all conditions are satisfied. We sort all workers by their wage-to-quality ratio because for each worker, to satisfy both their minimum wage and relative payment constraints, each selected worker must be paid at least this ratio times their quality.
Time Complexity: O(n log n) due to sorting, and O(n log k) for heap operations.
Space Complexity: O(n) for the sorted list of workers or the heap.
1using System;
2using System.Collections.Generic;
3
4public class Solution {
5 public double MincostToHireWorkers(int[] quality, int[] wage, int k) {
6 int n = wage.Length;
7 double[][] workers = new double[n][];
8
9 for (int i = 0; i < n; ++i)
10 workers[i] = new double[] { (double)wage[i] / quality[i], (double)quality[i] };
11
12 Array.Sort(workers, (a, b) => a[0].CompareTo(b[0]));
13
14 PriorityQueue<double, double> pq = new PriorityQueue<double, double>(Comparer<double>.Create((x, y) => y.CompareTo(x)));
15 double qualitySum = 0, result = double.MaxValue;
16
17 foreach (var worker in workers) {
18 qualitySum += worker[1];
19 pq.Enqueue(worker[1], worker[1]);
20
21 if (pq.Count > k)
22 qualitySum -= pq.Dequeue();
23
24 if (pq.Count == k)
25 result = Math.Min(result, qualitySum * worker[0]);
26 }
27
28 return result;
29 }
30}This C# solution manages to minimize costs using a priority queue to store the largest qualities. After sorting by wage-to-quality ratio, the smallest feasible payment is processed by iterating across possible k-group configurations utilizing qualities to keep down the requisite payment as low as possible.
This approach focuses on sorting workers by the ratio of their wage expectation to quality. By calculating this ratio, we can use it as a reference point to determine the required payment for every possible group of k workers. Selecting the right workers and calculating the minimum payment by understanding proportional wages can be done by iterating over sorted worker lists using two indices, capturing the required details and performing the necessary calculations.
Time Complexity: O(n log n) due to sorting, and O(n log n) due to managing heap.
Space Complexity: O(n) for worker list and heap storage.
Expressive JavaScript operations assisted by self-defined MaxHeap, smoothly sorting workers by efficiency standards, leveraged by quality tracking in heap formatting, rendering calculated results aligning to least fiscal expenditure categorically adjusted for set collections.