BST 3.32

BST stands for Binary Search Tree, which is a commonly used data structure in computer science. It is a binary tree where each node has a key and satisfies the property that the key in any node is greater than the keys in all nodes in its left subtree and smaller than the keys in all nodes in its right subtree.

BST differs from other types of trees, such as AVL or red-black trees, primarily in terms of balancing criteria and complexity. While AVL or red-black trees maintain balance by considering factors like tree height or color, BST primarily focuses on maintaining the order of keys.

The main operations on a BST include insertion of new nodes, deletion of existing nodes, search for a specific key, and traversal of the tree for different purposes like printing or processing data.

To insert a new node into a BST, you compare the key of the new node with the key of the current node. If the new node's key is smaller, you move to the left child; if it's greater, you move to the right child. This process continues until an empty spot is found to insert the new node.

In most implementations, duplicate keys are not allowed in a BST. If an attempt is made to insert a duplicate key, it can either be rejected or handled differently based on specific requirements or more advanced variations of BSTs like AVL trees.

Deletion in a BST can be a bit more complex. It depends on the type of node being deleted. If the node to be deleted has no children, it can simply be removed. If it has one child, that child takes its place. If it has two children, the node's successor or predecessor is found and replaces the deleted node while maintaining the BST property.

BSTs have several advantages, such as efficient searching, insertion, and deletion operations with average time complexity of O(log n), compactness of representation compared to other tree types, support for ordered traversal and efficient range queries.

One potential drawback of using a BST is that in certain scenarios, when the tree is heavily unbalanced, the operations can degrade to O(n) time complexity. Balancing techniques or self-balancing variants like AVL or red-black trees can help mitigate this issue.

Yes, besides keys, BST nodes can store associated data or payload. This makes BSTs flexible for various applications, as you can associate additional information with each node.

BSTs find applications in many domains. Some examples include symbol tables in compilers, database systems, interval trees for efficient indexing of intervals, and binary search algorithms based on the concept of BSTs.