Hire an Exactly Sized Group with Proportional Pay

### Problem Worker i has positive quality[i] and minimum acceptable wage[i]. Hire exactly k workers, paying every selected worker one shared rate times that worker's quality, while meeting every minimum wage. Return the least total pay as double. The source requests an answer within 0.00001 of the optimum. **Practice tolerance:** Accept an answer when its absolute error or relative error is at most 0.00001. This tolerance permits the double return type at large valid totals. ```cpp class Solution { public: double mincostToHireWorkers(vector<int>& quality, vector<int>& wage, int k); }; ``` ### Examples **Example 1:** ```text quality = [2,4], wage = [6,8], k = 2 Output: 18.0 Explanation: Shared rate3 pays6 and12, satisfying both minimums. ``` **Example 2:** ```text quality = [3,5], wage = [9,5], k = 1 Output: 5.0 Explanation: Hire the second worker alone at its minimum5. ``` ### Constraints - Both arrays share length n, with 1 <= k <= n <=10000. - Qualities and minimum wages lie in [1,10000]. - The answer tolerance is absolute-or-relative error 0.00001. ### Contract considerations Preserve exactly k hires, proportional pay and all wage minimums. ```hint Read the boundary condition For a fixed feasible common rate, which k qualities minimize total pay? ``` ### Boundary reminders Preserve exactly k hires, proportional pay and all wage minimums.