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.

Key Characteristics of a BST:

• Hierarchical Structure: A BST is composed of nodes, each having up to two children, forming a tree-like hierarchy with a single root node at the top.
• Ordering Property: For every node in the BST, all values in the left subtree are smaller, and all values in the right subtree are larger than the node’s value. This rule holds recursively for all subtrees.
• Efficient Operations: In a balanced BST, operations like search, insertion, and deletion can be performed in O(log n) time. 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).
• Recursive Nature: Each left or right subtree of a node in a BST is itself a BST, allowing recursive algorithms to naturally process the tree.
• Practical Applications: BSTs are widely used in database indexing, symbol tables, range queries, and are foundational for advanced structures like AVL trees, Red-Black trees. In problem solving, BSTs are used in problems where we need to maintain sorted stream of data.

Introduction to Binary Search:

• Introduction to BST
• Applications of BST

Basic Operations on BST:

• Insertion in BST
• Searching in BST
• Deletion in BST
• Minimum in BST
• Maximum in BST
• Floor in BST
• Ceil in BST
• Inorder Successor in BST
• Inorder Predecessor in BST
• Handling duplicates in BST

Easy Standard Problems on BST:

• Second largest in BST
• Sum of k smallest in BST
• 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 Same BSTs without constructing
• BST to Min Heap
• Add all greater values in a BST
• Check if two BSTs have same elements

Medium Standard Problems on BST:

• 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 if an array can represent Level Order of BST
• Max Sum with No Two Adjacent in BST
• LCA in a BST
• Distance between two nodes of a BST
• 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
• Two nodes of a BST are swapped, correct it
• Leaf nodes from Preorder of a BST

Hard Standard Problems on BST:

• Construct all possible BSTs for keys 1 to N
• In-place Convert BST into a Min-Heap
• Check given array of size n can represent BST of n levels or not
• Merge two BSTs with limited extra space
• K’th Largest Element in BST when modification to BST is not allowed
• Check if given sorted sub-sequence exists in binary search tree
• Maximum Unique Element in every subarray of size K
• Count pairs from two BSTs whose sum is equal to a given value x
• Find if there is a triplet in a Balanced BST that adds to zero
• Replace every element with the least greater element on its right
• Leaf nodes from Preorder of a Binary Search Tree
• Minimum Possible value of |ai + aj – k| for given array and k.
• Special two digit numbers in a Binary Search Tree
• Merge Two Balanced Binary Search Trees

Some Quizzes:

• ‘Quizzes’ on Binary Search Tree
• ‘Quizzes’ on Balanced Binary Search Trees

Quick Links :

• ‘Practice Problems’ on Binary Search Tree
• Videos on Binary Search Tree

Recommended:

• Learn Data Structure and Algorithms | DSA Tutorial