Assign the Minimum Fleet to Rental Reservations

Question

The question asks you to determine the minimum number of cars needed to fulfill a list of rental reservations, each with specific pickup and return times.

Codemia · Accepted Answer

To solve the problem of assigning the minimum fleet to rental reservations, we can use a greedy algorithm combined with a priority queue (or min-heap). The idea is to process the reservations in order of their pickup times and keep track of the cars currently in use. By managing the return times of the cars, we can efficiently determine when a car becomes available for a new reservation.

1. **Sort the reservations** by pickup time.
2. Initialize a min-heap to keep track of the return times of the cars currently in use.
3. Iterate through each reservation:
   - If the heap is not empty and the earliest return time is less than or equal to the current pickup time, remove the car from the heap (indicating it is now available).
   - Add the current reservation's return time to the heap, which represents assigning a car to this reservation.
4. The size of the heap at the end of the iteration will give the minimum number of cars needed.

The time complexity of this approach is O(n log n) due to the sorting step, where n is the number of reservations. The space complexity is O(k), where k is the number of cars used, which is at most n in the worst case.

```python
import heapq

def min_fleet(reservations):
    # Sort reservations by pickup time
    reservations.sort(key=lambda x: x[1])
    min_heap = []  # Min-heap to track return times
    car_assignment = {}  # Dictionary to store car assignments

for id, pickup, return_time in reservations:
        # Free up cars that have returned by the pickup time
        while min_heap and min_heap[0] <= pickup:
            heapq.heappop(min_heap)
        # Assign a new car for the current reservation
        heapq.heappush(min_heap, return_time)
        car_assignment[id] = len(min_heap)  # Assign car id based on heap size

return len(min_heap), car_assignment
```
This code defines a function that takes a list of reservations and returns the minimum number of cars needed along with their assignments.

Interviewers are looking for clarity in your thought process and the ability to break down the problem into manageable parts. They want to see how you approach the problem, the efficiency of your solution, and your understanding of data structures. Additionally, they may assess your ability to handle edge cases and consider the scalability of your solution.

Assign the Minimum Fleet to Rental Reservations

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