#2462

Total Cost to Hire K Workers

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array · two pointers · heap (priority queue) · simulation

Description

You are given a 0-indexed integer array costs where costs[i] is the cost of hiring the i^th worker.

You are also given two integers k and candidates. We want to hire exactly k workers according to the following rules:

- You will run k sessions and hire exactly one worker in each session.

- In each hiring session, choose the worker with the lowest cost from either the first candidates workers or the last candidates workers. Break the tie by the smallest index.

- For example, if costs = [3,2,7,7,1,2] and candidates = 2, then in the first hiring session, we will choose the 4^th worker because they have the lowest cost [3,2,7,7,1,2].

- In the second hiring session, we will choose 1^st worker because they have the same lowest cost as 4^th worker but they have the smallest index [3,2,7,7,2]. Please note that the indexing may be changed in the process.

- If there are fewer than candidates workers remaining, choose the worker with the lowest cost among them. Break the tie by the smallest index.

- A worker can only be chosen once.

Return the total cost to hire exactly k workers.

Example 1:

Input: costs = [17,12,10,2,7,2,11,20,8], k = 3, candidates = 4

Output: 11

Explanation: We hire 3 workers in total. The total cost is initially 0.

- In the first hiring round we choose the worker from [17,12,10,2,7,2,11,20,8]. The lowest cost is 2, and we break the tie by the smallest index, which is 3. The total cost = 0 + 2 = 2.

- In the second hiring round we choose the worker from [17,12,10,7,2,11,20,8]. The lowest cost is 2 (index 4). The total cost = 2 + 2 = 4.

- In the third hiring round we choose the worker from [17,12,10,7,11,20,8]. The lowest cost is 7 (index 3). The total cost = 4 + 7 = 11. Notice that the worker with index 3 was common in the first and last four workers.

The total hiring cost is 11.

Example 2:

Input: costs = [1,2,4,1], k = 3, candidates = 3

Output: 4

Explanation: We hire 3 workers in total. The total cost is initially 0.

- In the first hiring round we choose the worker from [1,2,4,1]. The lowest cost is 1, and we break the tie by the smallest index, which is 0. The total cost = 0 + 1 = 1. Notice that workers with index 1 and 2 are common in the first and last 3 workers.

- In the second hiring round we choose the worker from [2,4,1]. The lowest cost is 1 (index 2). The total cost = 1 + 1 = 2.

- In the third hiring round there are less than three candidates. We choose the worker from the remaining workers [2,4]. The lowest cost is 2 (index 0). The total cost = 2 + 2 = 4.

The total hiring cost is 4.

Solution