Total Cost to Hire K Workers

Heap / Priority Queue
Key Ideas
The key idea to solve this problem is to use a heap (priority queue) to keep track of the minimum and maximum costs while iterating through the array of worker costs.
Problem Number
Problem Summary
Problem Summary: The problem is to find the minimum total cost to hire K workers from a group of workers, where each worker has a certain quality and wage. The cost is determined by multiplying the wage of each worker by a ratio of their qualities. The goal is to minimize the total cost while meeting the condition that the K workers have the lowest possible ratio of quality to wage. Key Pitfalls: - It is important to consider all possible combinations of K workers to find the minimum cost. This can be done using a priority queue or heap data structure. - Be careful with dividing by zero or handling very large numbers, as this can lead to incorrect results or overflow errors. - Consider edge cases where K is equal to the number of workers or when the number of workers is less than K.
Solution Summary
The best solution for the given problem is to use a two-pointer approach combined with a heap (priority queue). The two pointers are used to keep track of the current range of workers, while the heap is used to maintain the K workers with the highest costs. Initially, the workers are sorted by their cost in descending order. Then, the two pointers are moved to form a range of K workers. The sum of the costs of these K workers is calculated and stored as the current minimum cost. Next, the right pointer is incremented to include the next worker, while the left pointer is incremented until the range contains exactly K workers again. This process continues until all the workers have been considered. Finally, the minimum cost is returned as the total cost to hire K workers.
Two Pointers
Heap (Priority Queue)