**Minimum Cost to Hire K Workers ** There are `n`

workers. You are given two integer arrays `quality`

and `wage`

where `quality[i]`

is the quality of the `i`

worker and ^{th}`wage[i]`

is the minimum wage expectation for the `i`

worker.^{th}

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 `10`

of the actual answer will be accepted.^{-5}

**Example 1:**

Input:quality = [10,20,5], wage = [70,50,30], k = 2Output:105.00000Explanation: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 = 3Output:30.66667Explanation:We pay 4 to 0^{th}worker, 13.33333 to 2^{nd}and 3^{rd}workers separately.

**Constraints:**

`n == quality.length == wage.length`

`1 <= k <= n <= 10`

^{4}`1 <= quality[i], wage[i] <= 10`

^{4}

### Minimum Cost to Hire K Workers Solutions

✅**Time:** O(n)

✅**Space:** O(n)

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