How do different priority queue implementations compare?

How do different priority queue implementations compare?

There are several implementations of priority queues, such as binary heaps, Fibonacci heaps, and unsorted arrays. Each has its own strengths and weaknesses.

What are the time complexities for these implementations?

For a binary heap, insertion and deletion take O(log n), while for a Fibonacci heap, they can be amortized to O(1) for insertion and O(log n) for deletion.

Which implementation is the most efficient for large datasets?

Fibonacci heaps are often more efficient for large datasets due to their better amortized time complexities, especially in scenarios with many decrease-key operations.

Are there any practical applications where one is preferred over the others?

Yes, for example, Dijkstra's algorithm often benefits from using a priority queue implemented as a binary heap, while network optimization problems may use Fibonacci heaps.