Introduction to Binary Search Tree Last Updated : 12 Dec, 2024 Comments Improve Suggest changes Like Article Like Report Binary Search Tree is a data structure used in computer science for organizing and storing data in a sorted manner. Binary search tree follows all properties of binary tree and for every nodes, its left subtree contains values less than the node and the right subtree contains values greater than the node. This hierarchical structure allows for efficient Searching, Insertion, and Deletion operations on the data stored in the tree.Binary Search TreeProperties of Binary Search Tree:The left subtree of a node contains only nodes with keys less than the node's key.The right subtree of a node contains only nodes with keys greater than the node's key.The left and right subtree each must also be a binary search tree. There must be no duplicate nodes(BST may have duplicate values with different handling approaches).Test Your UnderstandingGiven a Binary Tree, find out if it is Binary Search Tree or not.Important Points about BSTA Binary Search Tree is useful for maintaining sorted stream of data. It allows search, insert, delete, ceiling, max and min in O(h) time. Along with these, we can always traverse the tree items in sorted order. With Self Balancing BSTs, we can ensure that the height of the BST is bound be Log n. Hence we achieve, the above mentioned O(h) operations in O(Log n) time.When we need only search, insert and delete and do not need other operations, we prefer Hash Table over BST as a Hash Table supports these operations in O(1) time on average.Next Articles:Applications, Advantages and Disadvantages of Binary Search TreeInsertion in Binary Search Tree (BST)Searching in Binary Search Tree (BST)Deletion in Binary Search Tree (BST) Comment More infoAdvertise with us Next Article Applications of BST K kartik Follow Improve Article Tags : Binary Search Tree Advanced Data Structure DSA Practice Tags : Advanced Data StructureBinary Search Tree Similar Reads 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 s 4 min read Introduction to Binary Search Tree Binary Search Tree is a data structure used in computer science for organizing and storing data in a sorted manner. Binary search tree follows all properties of binary tree and for every nodes, its left subtree contains values less than the node and the right subtree contains values greater than the 3 min read Applications of BST Binary Search Tree (BST) is a data structure that is commonly used to implement efficient searching, insertion, and deletion operations along with maintaining sorted sequence of data. Please remember the following properties of BSTs before moving forward.The left subtree of a node contains only node 3 min read Applications, Advantages and Disadvantages of Binary Search Tree A Binary Search Tree (BST) is a data structure used to storing data in a sorted manner. Each node in a Binary Search Tree has at most two children, a left child and a right child, with the left child containing values less than the parent node and the right child containing values greater than the p 2 min read Insertion in Binary Search Tree (BST) Given a BST, the task is to insert a new node in this BST.Example: How to Insert a value in a Binary Search Tree:A new key is always inserted at the leaf by maintaining the property of the binary search tree. We start searching for a key from the root until we hit a leaf node. Once a leaf node is fo 15 min read Searching in Binary Search Tree (BST) Given a BST, the task is to search a node in this BST. For searching a value in BST, consider it as a sorted array. Now we can easily perform search operation in BST using Binary Search Algorithm. Input: Root of the below BST Output: TrueExplanation: 8 is present in the BST as right child of rootInp 7 min read Deletion in Binary Search Tree (BST) Given a BST, the task is to delete a node in this BST, which can be broken down into 3 scenarios:Case 1. Delete a Leaf Node in BST Case 2. Delete a Node with Single Child in BSTDeleting a single child node is also simple in BST. Copy the child to the node and delete the node. Case 3. Delete a Node w 10 min read Binary Search Tree (BST) Traversals – Inorder, Preorder, Post Order Given a Binary Search Tree, The task is to print the elements in inorder, preorder, and postorder traversal of the Binary Search Tree. Input: A Binary Search TreeOutput: Inorder Traversal: 10 20 30 100 150 200 300Preorder Traversal: 100 20 10 30 200 150 300Postorder Traversal: 10 30 20 150 300 200 1 10 min read Balance a Binary Search Tree Given a BST (Binary Search Tree) that may be unbalanced, the task is to convert it into a balanced BST that has the minimum possible height.Examples: Input: Output: Explanation: The above unbalanced BST is converted to balanced with the minimum possible height.Input: Output: Explanation: The above u 10 min read Self-Balancing Binary Search Trees Self-Balancing Binary Search Trees are height-balanced binary search trees that automatically keep the height as small as possible when insertion and deletion operations are performed on the tree. The height is typically maintained in order of logN so that all operations take O(logN) time on average 4 min read Like