Search Trees, Heaps, and Priority Queues

Implement a Binary Search Tree (BST) with search, insertion, and deletion operations.

Validate if a given binary tree is a BST.

Explain the need for self-balancing trees and perform AVL tree rotations.

Implement insertion into an AVL tree with automatic rebalancing.

Implement a binary heap (max-heap and min-heap) using an array.

Build a heap from an unordered array in linear time using the heapify-down operation.

Implement heap sort.

Implement a priority queue using a binary heap and solve top-K element problems.