How do priority queues and heaps differ?

What are the main differences between a priority queue and a heap?

A priority queue is an abstract data type where each element has a priority. A heap is a specific implementation of a priority queue, typically using a binary tree structure.

Can you explain how heaps are structured?

Heaps are usually implemented as binary trees where each parent node has a value less than or equal to its children (min-heap) or greater than or equal to its children (max-heap). This structure allows for efficient priority retrieval.

What are the time complexities for inserting and deleting elements in both?

In a priority queue implemented with a heap, both insertion and deletion operations have a time complexity of O(log n). However, a simple array-based priority queue can have O(n) for deletion.

Are there any real-world applications for priority queues?

Yes, priority queues are used in various applications like scheduling tasks in operating systems, managing bandwidth in networks, and in algorithms like Dijkstra's for shortest path finding.