Total Cost to Hire K Workers

class Solution {
    public long calculateMinimumCost(int[] pricing, int numWorkers, int numCandidates) {
        // Priority queue based on cost and index for tie-breaking
        PriorityQueue<int[]> queue = new PriorityQueue<>((worker1, worker2) -> {
            if (worker1[0] == worker2[0]) {
                return worker1[1] - worker2[1];
            }
            return worker1[0] - worker2[0];
        });
    
        // Initialize priority queue with first `numCandidates` from start and end
        for (int i = 0; i < numCandidates; i++) {
            queue.offer(new int[] {pricing[i], 0});
        }
        for (int i = Math.max(numCandidates, pricing.length - numCandidates); i < pricing.length; i++) {
            queue.offer(new int[] {pricing[i], 1});
        }
    
        long sum = 0;
        int forwardIndex = numCandidates;
        int backwardIndex = pricing.length - 1 - numCandidates;
    
        for (int i = 0; i < numWorkers; i++) {
            int[] currentWorker = queue.poll();
            int price = currentWorker[0], sectionId = currentWorker[1];
            sum += price;
    
            // Add next available workers based on the section
            if (forwardIndex <= backwardIndex) {
                if (sectionId == 0) {
                    queue.offer(new int[]{pricing[forwardIndex], 0});
                    forwardIndex++;
                } else {
                    queue.offer(new int[]{pricing[backwardIndex], 1});
                    backwardIndex--;
                }
            }
        }
    
        return sum;
    }
}

The code in question uses a Java class method calculateMinimumCost to calculate the minimum total cost of hiring a specific number of workers (numWorkers) from a given pool of candidates defined in the pricing array. The candidates are chosen from both the start and the end of the given array, taking into consideration numCandidates.

This method involves:

• Utilizing a priority queue (min-heap) to efficiently select candidates based on their pricing while maintaining a balance between those considered from the beginning versus the end of the list. Workers are compared first by price, and ties are resolved using their index.

• Initializing this queue by adding the first numCandidates from both the beginning and the end of the array.

• Iterating through the workers needed (numWorkers), dequeueing the lowest-priced candidate, adding his price to a running total sum, and then if more candidates are needed, pulling the next candidate from the relevant section of the array based on the location of the last dequeued candidate.

The process ensures that selection is cost-effective yet balanced from different sections of the candidate pool for a diverse selection. You successfully manage costs and achieve the target hiring numbers using efficient data structures like a priority queue, which streamlines the selection process significantly.

class Calculator:
    def computeTotalExpense(self, expenseList: List[int], count: int, numCandidates: int) -> int:
        priority_queue = []
        for index in range(numCandidates):
            priority_queue.append((expenseList[index], 0))
        for index in range(max(numCandidates, len(expenseList) - numCandidates), len(expenseList)):
            priority_queue.append((expenseList[index], 1))
    
        heapify(priority_queue)
            
        total_expense = 0
        next_front, next_end = numCandidates, len(expenseList) - 1 - numCandidates 
    
        for _ in range(count): 
            current_cost, section_id = heappop(priority_queue)
            total_expense += current_cost
            if next_front <= next_end: 
                if section_id == 0:
                    heappush(priority_queue, (expenseList[next_front], 0))
                    next_front += 1
                else:
                    heappush(priority_queue, (expenseList[next_end], 1))
                    next_end -= 1
                        
        return total_expense

The code provided in Python determines the total expense of hiring a specified number of workers (count) from a list of potential hire expenses (expenseList). The Calculator class contains the method computeTotalExpense, which implements a priority queue to efficiently manage and compute the hiring cost.

The algorithm operates as follows:

1. Initialize an empty list priority_queue to store each candidate's expense and a section identifier indicating their position in the original list.
2. The first numCandidates elements from expenseList have their costs added to the priority_queue with a section identifier of 0.
3. Additional elements from expenseList, beyond the first numCandidates up to the remaining list size minus numCandidates, are then added with a section identifier of 1.
4. The list is transformed into a heap structure to ensure that the smallest elements can be accessed quickly.
5. Intialize total_expense to 0, and calculate two indices, next_front and next_end, which help track the next candidates from the initial and latter sections of the list respectively.
6. Iterate over the number of hires (count), remove the lowest expense from the heap using heappop and add this to total_expense.
7. Depending on which section the removed element belongs to, push the next appropriate candidate into the heap from either the beginning or end of the list while adjusting the tracking indices (next_front or next_end).

This method efficiently minimizes the total hiring cost by always selecting the next lowest available expense from the list. The use of a priority queue (heap) allows the algorithm to efficiently manage and retrieve minimum values, which is vital to achieving a cost-effective solution for hiring multiple workers.