LeetCode-in-Java

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 ith worker and wage[i] is the minimum wage expectation for the ith 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:

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.

Given the integer k, return the least amount of money needed to form a paid group satisfying the above conditions. Answers within 10-5 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
• 1 <= k <= n <= 104
• 1 <= quality[i], wage[i] <= 104

Solution

import java.util.Arrays;
import java.util.Comparator;
import java.util.PriorityQueue;

public class Solution {
    public double mincostToHireWorkers(int[] quality, int[] wage, int k) {
        int n = quality.length;
        Worker[] workers = new Worker[n];
        for (int i = 0; i < n; i++) {
            workers[i] = new Worker(wage[i], quality[i]);
        }
        Arrays.sort(workers, Comparator.comparingDouble(Worker::ratio));

        PriorityQueue<Integer> maxHeap = new PriorityQueue<>((a, b) -> Integer.compare(b, a));
        int sumQuality = 0;
        double result = Double.MAX_VALUE;
        for (int i = 0; i < n; i++) {
            Worker worker = workers[i];
            sumQuality += worker.quality;
            maxHeap.add(worker.quality);
            if (maxHeap.size() > k) {
                sumQuality -= maxHeap.remove();
            }
            double groupRatio = worker.ratio();
            if (maxHeap.size() == k) {
                result = Math.min(sumQuality * groupRatio, result);
            }
        }
        return result;
    }

    static class Worker {
        int wage;
        int quality;

        double ratio() {
            return (double) wage / quality;
        }

        Worker(int wage, int quality) {
            this.wage = wage;
            this.quality = quality;
        }
    }
}

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