## Similar Problems

Similar Problems not available

# Total Cost To Hire K Workers - Leetcode Solution

LeetCode: Total Cost To Hire K Workers Leetcode Solution

Difficulty: Medium

Topics: two-pointers heap-priority-queue array simulation

The "Total Cost To Hire K Workers" problem on LeetCode is a problem that asks us to find the minimum cost of hiring K workers to complete a project. Each worker has a certain quality, and if we want to hire a worker with a higher quality, we need to pay them more. Additionally, there is a ratio that dictates the minimum salary we must pay a worker based on their quality.

To solve this problem, we need to first understand the given problem statement. There are N workers, each worker has a quality (qi) and a wage (wi). Additionally, there is a ratio (r) which suggests that if we want to hire a worker with quality Q2 and we have already hired a worker with quality Q1, then we must pay Q2*r salary to Q2 worker to maintain a fair ratio.

From the problem, we are to find the minimum cost that would be spent hiring K workers. To do this, we must first sort the workers based on their expected salaries (s), where s = wi/qi. The intuition behind this is to find the workers that offer the best value for money.

We then perform a sliding window search to obtain the K workers with the lowest expected salaries. During the sliding window search, we keep track of the sum of the salaries of the K workers. Additionally, since we want to maintain a fair ratio, we ensure that the ratio is met for each worker within the window.

The algorithm for solving this problem is as follows:

- Sort the workers based on their expected salaries s = wi/qi in ascending order.
- Initialize a priority queue and a variable to track the quality of the Kth worker seen so far.
- Initialize a variable to track the sum of salaries of the K workers seen so far. Set this to infinity as the initial value.
- Loop through each worker in the sorted workers:
- Add the current worker's quality to the priority queue.
- If the length of the priority queue is greater than K, remove the worker with the max quality from the queue. (since we want to keep only the K workers with the lowest expected salaries)
- If the length of the priority queue is K, calculate the sum of salaries of the K workers using the ratio r.
- If the sum of salaries is less than the current minimum sum seen so far, update the minimum sum.

- Return the minimum sum of salaries.

The time complexity of this algorithm is O(Nlog(N)) since we first sort the workers based on their expected salaries and then perform a sliding window search, where we add and remove elements from a priority queue. The space complexity is O(N) which is the size of the priority queue.

Here is the Python code that implements the algorithm:

```
import heapq
class Solution:
def mincostToHireWorkers(self, quality: List[int], wage: List[int], k: int) -> float:
workers = sorted([(w/q, q, w) for q, w in zip(quality, wage)]) # sort workers by expected salaries
heap = [] # initialize a priority queue
total_quality = 0 # initialize a variable for the quality of the Kth worker
min_cost = float('inf') # initialize the minimum cost variable
for s, q, w in workers:
heapq.heappush(heap, -q) # add current worker's quality to the priority queue
total_quality += q # update total quality
if len(heap) > k: # if priority queue contains more than K workers
total_quality += heapq.heappop(heap) # remove worker with the maximum quality
if len(heap) == k: # if priority queue contains K workers
cost = total_quality * s # calculate cost
min_cost = min(min_cost, cost) # update minimum cost
return min_cost
```

In summary, the "Total Cost To Hire K Workers" problem on LeetCode can be solved using a sliding window approach that involves the use of a priority queue. We first sort the workers by their expected salaries, and then we perform a sliding window search to obtain the K workers with the lowest expected salaries while ensuring that the ratio constraint is met.

## Total Cost To Hire K Workers Solution Code

`1`