2462 - Total Cost to Hire K Workers.

Medium

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

• 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 <ins>17,12,10,2</ins>,7,<ins>2,11,20,8</ins>. 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 <ins>17,12,10,7</ins>,<ins>2,11,20,8</ins>. The lowest cost is 2 (index 4). The total cost = 2 + 2 = 4.

• In the third hiring round we choose the worker from <ins>17,12,10,7,11,20,8</ins>. 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 <ins>1,2,4,1</ins>. 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 <ins>2,4,1</ins>. 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 <ins>2,4</ins>. The lowest cost is 2 (index 0).

The total cost = 2 + 2 = 4. The total hiring cost is 4.

Constraints:

• <code>1 <= costs.length <= 10⁵</code>

• <code>1 <= costsi<= 10⁵</code>

• 1 <= k, candidates <= costs.length