C++: Heap vs. BST Performance

What are the performance differences between heaps and binary search trees in C++?

Heaps and binary search trees (BSTs) have different performance characteristics. Heaps are optimized for priority queue operations, providing O(log n) time complexity for insertions and deletions, while BSTs allow for O(log n) average time complexity for search, insert, and delete operations. However, BSTs can degrade to O(n) in the worst case if not balanced.

When should I use a heap instead of a BST?

You should use a heap when you need efficient access to the largest or smallest element, such as in priority queues. If you need to maintain a sorted order or perform frequent searches, a balanced BST would be more appropriate.

Can you give an example of when a BST would be more beneficial?

Certainly! A BST is more beneficial when you need to perform many search operations, like in a database where you frequently query for records. It allows for faster lookups compared to a heap.

What about memory usage? How do heaps and BSTs compare?

Heaps typically use an array-based structure, which can be more memory efficient due to contiguous memory allocation. In contrast, BSTs use nodes that may lead to higher memory overhead due to pointers, especially if the tree is unbalanced.