Non Linear Data Structure

A Binary Search Tree (BST) is a tree data structure in which each node has a maximum of two children: a left child with values less than the parent node and a right child with values more than the parent node. This structure facilitates fast searching, insertion, and deletion operations, normally carried out in O(log n) time in an evenly balanced tree. Nonetheless, in the worst scenario, an unbalanced BST can descend to O(n) time complexity. Insertion, deletion, search, and tree traversals like inorder, preorder, and postorder traversals are some of the most common BST operations that play a critical role in data retrieval and processing. BSTs have a vast array of applications, including database indexing, auto-completion systems, and file organization. An AVL Tree is a self-balancing binary search tree where balance factor (difference in height between left and right subtrees of any node) is at most 1. If the balance is broken with insertion or deletion, rotations (LL, RR, LR, RL) are used to correct the balance. AVL trees ensure a strict O(log n) time complexity for search, insertion, and deletion, which is much better than unbalanced BSTs in worst-case situations. AVL trees are used extensively in applications where search efficiency is of utmost importance, including database systems, memory management, and network routing.Though BSTs are easier to implement and require fewer rotations, if unbalanced, they can be inefficient. However, AVL trees maintain balance but have a higher rotation overhead. Knowing both structures assists in choosing the most appropriate tree for various computational requirements. Through the mastery of these concepts, students can maximize data storage and retrieval in actual applications