## 857. Minimum Cost to Hire K Workers

There are `N` workers.  The `i`-th worker has a `quality[i]` and a minimum wage expectation `wage[i]`.

Now we want to hire exactly `K` workers to form a paid group.  When hiring a group of K workers, we must pay them according to the following rules:

1. Every worker in the paid group should be paid in the ratio of their quality compared to other workers in the paid group.
2. Every worker in the paid group must be paid at least their minimum wage expectation.

Return the least amount of money needed to form a paid group satisfying the above conditions.

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-th 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-th and 3-th workers seperately.
```

Note:

1. `1 <= K <= N <= 10000`, where `N = quality.length = wage.length`
2. `1 <= quality[i] <= 10000`
3. `1 <= wage[i] <= 10000`
4. Answers within `10^-5` of the correct answer will be considered correct.

## Rust Solution

``````struct Solution;

use std::collections::BinaryHeap;

impl Solution {
fn mincost_to_hire_workers(quality: Vec<i32>, wage: Vec<i32>, k: i32) -> f64 {
let k = k as usize;
let n = quality.len();
let mut workers: Vec<usize> = (0..n).collect();
let rate: Vec<f64> = (0..n).map(|i| wage[i] as f64 / quality[i] as f64).collect();
workers.sort_by(|&i, &j| rate[i].partial_cmp(&rate[j]).unwrap());
let mut res = std::f64::MAX;
let mut queue: BinaryHeap<i32> = BinaryHeap::new();
let mut sum = 0;
for i in workers {
let r = rate[i];
let q = quality[i];
queue.push(q);
sum += q;
if queue.len() > k {
sum -= queue.pop().unwrap();
}
if queue.len() == k {
res = res.min(r * sum as f64);
}
}
res
}
}

#[test]
fn test() {
use assert_approx_eq::assert_approx_eq;
let quality = vec![10, 20, 5];
let wage = vec![70, 50, 30];
let k = 2;
let res = 105.00000;
assert_approx_eq!(Solution::mincost_to_hire_workers(quality, wage, k), res);
let quality = vec![3, 1, 10, 10, 1];
let wage = vec![4, 8, 2, 2, 7];
let k = 3;
let res = 30.666667;
assert_approx_eq!(Solution::mincost_to_hire_workers(quality, wage, k), res);
}
``````

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