857 - Minimum Cost to Hire K Workers.

Hard

There are n workers. You are given two integer arrays quality and wage where quality[i] is the quality of the <code>i^th</code> worker and wage[i] is the minimum wage expectation for the <code>i^th</code> worker.

We want to hire exactly k workers to form a paid group. To hire a group of k workers, we must pay them according to the following rules:

• Every worker in the paid group should be paid in the ratio of their quality compared to other workers in the paid group.

• Every worker in the paid group must be paid at least their minimum wage expectation.

Given the integer k, return the least amount of money needed to form a paid group satisfying the above conditions. Answers within <code>10^-5</code> of the actual answer will be accepted.

Example 1:

Input: quality = 10,20,5, wage = 70,50,30, k = 2

Output: 105.00000

Explanation: We pay 70 to 0^th worker and 35 to 2^nd worker.

Example 2:

Input: quality = 3,1,10,10,1, wage = 4,8,2,2,7, k = 3

Output: 30.66667

Explanation: We pay 4 to 0^th worker, 13.33333 to 2^nd and 3^rd workers separately.

Constraints:

• n == quality.length == wage.length

• <code>1 <= k <= n <= 10⁴</code>

• <code>1 <= qualityi, wagei<= 10⁴</code>