Level 1: The time complexity of the given code is O(n), where n is the number of Department objects.
Level 2: The code retrieves all employees grouped by department asynchronously, and the time complexity is determined by the number of Department objects. The code first retrieves all departments from the database and orders them by their title. Then, it converts the queryset to a list asynchronously using the sync_to_async function. Finally, it returns the list of departments.
Level 3: The code retrieves all departments from the database using the Department.objects.all() method, which has a time complexity of O(n), where n is the number of Department objects. The retrieved departments are then ordered by their title using the order_by("title") method, which has a time complexity of O(n log n), as it performs a comparison-based sorting operation.
The sync_to_async function is used to asynchronously convert the queryset to a list. This function is typically used when working with asynchronous frameworks like Django Channels or asyncio. It wraps a synchronous function or method and allows it to be called asynchronously. In this case, it wraps the list function to convert the queryset to a list asynchronously.
The final step is to return the list of departments, which has a time complexity of O(1), as it simply returns the list.
Overall, the time complexity of the code is dominated by the retrieval and ordering of the Department objects, resulting in a time complexity of O(n log n).