Total Cost to Hire K Workers

Total Cost to Hire K Workers

What is this problem about?

The "Total Cost to Hire K Workers coding problem" is a resource management challenge that involves selecting workers with the lowest costs under specific constraints. You are given an array of costs and two integers, k and candidates. In each of the k rounds, you hire the worker with the lowest cost from either the first candidates or the last candidates workers in the remaining pool. If there's a tie, the worker with the smaller index is chosen. Once a worker is hired, they are removed from the pool, and the boundaries for the next round are updated.

Why is this asked in interviews?

This "Total Cost to Hire K Workers interview question" is popular at companies like Microsoft and Meta because it tests your ability to manage dynamic datasets and prioritize elements efficiently. It evaluates your understanding of priority queues and the two-pointer technique to keep track of available candidates as the pool shrinks. This problem mimics real-world scenarios where resources must be allocated optimally from a changing set of options.

Algorithmic pattern used

The "Array, Two Pointers, Heap (Priority Queue), Simulation interview pattern" is the most effective approach here. We use two min-heaps: one for the front candidates and one for the back candidates. In each round, we compare the top of both heaps, pick the minimum, add it to our total cost, and then "refill" the corresponding heap from the remaining workers using two pointers. This ensures that we always have the correct set of candidates available for selection in $O(k \log (\text{candidates}))$ time.

Example explanation

Costs: [17, 12, 10, 2, 7, 2, 11, 20, 8], k=3, candidates=3.

1. Initial Heaps: Front=[10, 12, 17], Back=[8, 11, 20].
2. Round 1: Min is 8 (from back). Total=8. Remaining costs: [17, 12, 10, 2, 7, 2, 11, 20].
3. Back heap refilled: [11, 20, 2] -> [2, 11, 20].
4. Round 2: Min is 2 (from back). Total=10.
5. Back heap refilled: [11, 20, 7] -> [7, 11, 20].
6. Round 3: Min is 7 (from back). Total=17. Final cost: 17.

Common mistakes candidates make

One frequent mistake in the "Total Cost to Hire K Workers coding problem" is not handling the case where the front and back candidate ranges overlap. If they overlap, all remaining workers should be considered together in a single heap to avoid picking the same worker twice. Another error is not correctly breaking ties by index, which is often a specific requirement of the problem. Some candidates also struggle with the logic of moving the pointers and refilling the heaps correctly.

Interview preparation tip

To master the "Array, Two Pointers, Heap (Priority Queue), Simulation interview pattern," practice problems that involve "Top K" elements or "sliding window" heaps. Focus on maintaining the state of your heaps as you process the input. Being comfortable with heap operations in your chosen programming language is essential for these types of medium-difficulty problems.