Binary Search Tree

A Binary Search Tree (BST) is a type of binary tree data structure in which each node contains a unique key and satisfies a specific ordering property:

• All nodes in the left subtree of a node contain values strictly less than the node’s value.
• All nodes in the right subtree of a node contain values strictly greater than the node’s value.

This structure enables efficient operations for searching, insertion, and deletion of elements, especially when the tree remains balanced.

• BSTs are widely used in database indexing, symbol tables, range queries, and are foundational for advanced structures like AVL tree and Red-Black tree. In problem solving, BSTs are used in problems where we need to maintain sorted stream of data.
• Operations like search, insertion, and deletion work in O(Log n) time for a balanced binary search tree. In the worst-case (unbalanced), these degrade to O(n). With self-balancing BSTs like AVL and Red Black Trees, we can ensure the worst case as O(Log n).

Basics

• Introduction
• Applications
• Insertion, Search and Delete
• Minimum and Maximum
• Floor and Ceil
• Inorder Successor and Inorder Predecessor
• Handling duplicates in BST

Easy Problems

• Second largest
• Sum of k smallest
• BST keys in given Range
• BST to Balanced BST
• Check for BST
• Binary Tree to BST
• Check if array is Inorder of BST
• Sorted Array to Balanced BST
• Check Equal BSTs
• BST to Min Heap
• Add all greater values in a BST
• Check if two BSTs have same elements

Medium Problems

• BST from Preorder
• Sorted Linked List to Balanced BST
• Transform a BST to greater sum tree
• BST to a Tree with sum of all smaller keys
• Construct BST from Level Order
• Check for Level Order of BST
• Max Sum with No Two Adjacent in BST
• LCA in a BST
• Distance between Two Nodes
• k-th Smallest in BST
• Largest BST in a Binary Tree | Set 2
• Remove all leaves from BST
• 2 sum in BST
• Max between two nodes of BST
• Largest BST Subtree
• 2 Sum in a Balanced BST
• Fix a BST with 2 swapped
• Leaf nodes from Preorder of a BST
• Check if an Array can represent BST

Hard Problems

• All possible BSTs for keys 1 to N
• In-place Convert BST into a Min-Heap
• Merge two BSTs
• K’th Largest in BST without change
• Check for Subsequence
• Max Subarray Unique Element
• Pairs with sum from two BSTs
• 3 Sum in a Balanced BST
• Replace with the least greater on right
• Leaf nodes from Preorder
• Minimum Possible value of |ai + aj – k|
• Special two digit numbers in a BST

Important Links

• Quiz on BST
• Quiz on Balanced BST
• Practice Problems’ on BST
• DSA Tutorial
• GfG 160: