How to insert a node in Binary Search Tree using Iteration Last Updated : 17 Aug, 2022 Comments Improve Suggest changes Like Article Like Report You are given a binary search tree (BST) and a value to insert into the tree. Print inorder traversal of the BST after the insertion.Example: Input:To the given BST insert 40 Output: Explanation:The new node 40 is a leaf node. Start searching from the root till a leaf node is hit, i.e while searching if a new value is greater than current node move to right child else to left child. Input:To the given BST insert 600 Output: Explanation: The new node 600 is a leaf node. Start searching from the root till a leaf node is hit, i.e while searching if a new value is greater than current node move to right child else to left child. Approach: As we all know that a new key is always inserted at the leaf node. so we start searching a key from root till we hit a leaf node. Once a leaf node is found, the new node is added as a child of the leaf node with the given value, while searching if the value of current node is greater then the given value then move to the left , else move to right Follow the steps mentioned below to implement the idea: Start from the root and run a loop until a null pointer is reached.Keep the previous pointer of the current node stored.If the current node is null then create and insert the new node there and make it as one of the children of the parent/previous node depending on its value.If the value of current node is less than the new value then move to the right child of current node else move to the left child. Below is the implementation of the above approach: C++ // C++ program to demonstrate insert operation // in binary search tree #include <bits/stdc++.h> using namespace std; // BST node struct Node { int key; struct Node *left, *right; }; // Utility function to create a new node Node* newNode(int data) { Node* temp = new Node; temp->key = data; temp->left = NULL; temp->right = NULL; return temp; } // A utility function to insert a new // Node with given key in BST Node* insert(Node* root, int key) { // Create a new Node containing // the new element Node* newnode = newNode(key); // Pointer to start traversing from root and // traverses downward path to search // where the new node to be inserted Node* x = root; // Pointer y maintains the trailing // pointer of x Node* y = NULL; while (x != NULL) { y = x; if (key < x->key) x = x->left; else x = x->right; } // If the root is NULL i.e the tree is empty // The new node is the root node if (y == NULL) y = newnode; // If the new key is less than the leaf node key // Assign the new node to be its left child else if (key < y->key) y->left = newnode; // else assign the new node its right child else y->right = newnode; // Returns the pointer where the // new node is inserted return y; } // A utility function to do inorder // traversal of BST void Inorder(Node* root) { if (root == NULL) return; else { Inorder(root->left); cout << root->key << " "; Inorder(root->right); } } // Driver code int main() { /* Let us create following BST 50 / \ 30 70 / \ / \ 20 40 60 80 */ Node* root = NULL; root = insert(root, 50); insert(root, 30); insert(root, 20); insert(root, 40); insert(root, 70); insert(root, 60); insert(root, 80); // Print inorder traversal of the BST Inorder(root); return 0; } Java // Java program to demonstrate insert operation // in binary search tree import java.util.*; class solution { // BST node static class Node { int key; Node left, right; }; // Utility function to create a new node static Node newNode(int data) { Node temp = new Node(); temp.key = data; temp.left = null; temp.right = null; return temp; } // A utility function to insert a new // Node with given key in BST static Node insert(Node root, int key) { // Create a new Node containing // the new element Node newnode = newNode(key); // Pointer to start traversing from root and // traverses downward path to search // where the new node to be inserted Node x = root; // Pointer y maintains the trailing // pointer of x Node y = null; while (x != null) { y = x; if (key < x.key) x = x.left; else x = x.right; } // If the root is null i.e the tree is empty // The new node is the root node if (y == null) y = newnode; // If the new key is less than the leaf node key // Assign the new node to be its left child else if (key < y.key) y.left = newnode; // else assign the new node its right child else y.right = newnode; // Returns the pointer where the // new node is inserted return y; } // A utility function to do inorder // traversal of BST static void Inorder(Node root) { if (root == null) return; else { Inorder(root.left); System.out.print(root.key + " "); Inorder(root.right); } } // Driver code public static void main(String args[]) { /* Let us create following BST 50 / \ 30 70 / \ / \ 20 40 60 80 */ Node root = null; root = insert(root, 50); insert(root, 30); insert(root, 20); insert(root, 40); insert(root, 70); insert(root, 60); insert(root, 80); // Print inorder traversal of the BST Inorder(root); } } // contributed by Arnab Kundu Python3 """Python3 program to demonstrate insert operation in binary search tree """ # A Binary Tree Node # Utility function to create a # new tree node class newNode: # Constructor to create a newNode def __init__(self, data): self.key = data self.left = None self.right = self.parent = None # A utility function to insert a new # Node with given key in BST def insert(root, key): # Create a new Node containing # the new element newnode = newNode(key) # Pointer to start traversing from root # and traverses downward path to search # where the new node to be inserted x = root # Pointer y maintains the trailing # pointer of x y = None while (x != None): y = x if (key < x.key): x = x.left else: x = x.right # If the root is None i.e the tree is # empty. The new node is the root node if (y == None): y = newnode # If the new key is less than the leaf node key # Assign the new node to be its left child elif (key < y.key): y.left = newnode # else assign the new node its # right child else: y.right = newnode # Returns the pointer where the # new node is inserted return y # A utility function to do inorder # traversal of BST def Inorder(root): if (root == None): return else: Inorder(root.left) print(root.key, end=" ") Inorder(root.right) # Driver Code if __name__ == '__main__': """ Let us create following BST 50 / \ 30 70 / \ / \ 20 40 60 80 """ root = None root = insert(root, 50) insert(root, 30) insert(root, 20) insert(root, 40) insert(root, 70) insert(root, 60) insert(root, 80) # Pr inorder traversal of the BST Inorder(root) # This code is contributed by # SHUBHAMSINGH10 C# // C# program to demonstrate insert // operation in binary search tree using System; class GFG { // BST node class Node { public int key; public Node left, right; }; // Utility function to create a new node static Node newNode(int data) { Node temp = new Node(); temp.key = data; temp.left = null; temp.right = null; return temp; } // A utility function to insert a new // Node with given key in BST static Node insert(Node root, int key) { // Create a new Node containing // the new element Node newnode = newNode(key); // Pointer to start traversing from root and // traverses downward path to search // where the new node to be inserted Node x = root; // Pointer y maintains the trailing // pointer of x Node y = null; while (x != null) { y = x; if (key < x.key) x = x.left; else x = x.right; } // If the root is null i.e the tree is empty // The new node is the root node if (y == null) y = newnode; // If the new key is less than the leaf node key // Assign the new node to be its left child else if (key < y.key) y.left = newnode; // else assign the new node its right child else y.right = newnode; // Returns the pointer where the // new node is inserted return y; } // A utility function to do inorder // traversal of BST static void Inorder(Node root) { if (root == null) return; else { Inorder(root.left); Console.Write(root.key + " "); Inorder(root.right); } } // Driver code public static void Main(String[] args) { /* Let us create following BST 50 / \ 30 70 / \ / \ 20 40 60 80 */ Node root = null; root = insert(root, 50); insert(root, 30); insert(root, 20); insert(root, 40); insert(root, 70); insert(root, 60); insert(root, 80); // Print inorder traversal of the BST Inorder(root); } } // This code is contributed 29AjayKumar JavaScript <script> // javascript program to demonstrate insert // operation in binary search tree // BST node class Node { constructor() { this.key = 0; this.left = null; this.right = null; } }; // Utility function to create a new node function newNode(data) { var temp = new Node(); temp.key = data; temp.left = null; temp.right = null; return temp; } // A utility function to insert a new // Node with given key in BST function insert(root, key) { // Create a new Node containing // the new element var newnode = newNode(key); // Pointer to start traversing from root and // traverses downward path to search // where the new node to be inserted var x = root; // Pointer y maintains the trailing // pointer of x var y = null; while (x != null) { y = x; if (key < x.key) x = x.left; else x = x.right; } // If the root is null i.e the tree is empty // The new node is the root node if (y == null) y = newnode; // If the new key is less than the leaf node key // Assign the new node to be its left child else if (key < y.key) y.left = newnode; // else assign the new node its right child else y.right = newnode; // Returns the pointer where the // new node is inserted return y; } // A utility function to do inorder // traversal of BST function Inorder(root) { if (root == null) return; else { Inorder(root.left); document.write( root.key +" "); Inorder(root.right); } } // Driver code /* Let us create following BST 50 / \ 30 70 / \ / \ 20 40 60 80 */ var root = null; root = insert(root, 50); insert(root, 30); insert(root, 20); insert(root, 40); insert(root, 70); insert(root, 60); insert(root, 80); // Print inorder traversal of the BST Inorder(root); // This code is contributed by itsok. </script> Output20 30 40 50 60 70 80 Time Complexity: O(H), where H is the height of the BST. Auxiliary Space: O(1) Comment More infoAdvertise with us T tufan_gupta2000 Follow Improve Article Tags : Tree Binary Search Tree DSA Data Structures-Tree Traversals Practice Tags : Binary Search TreeTree Similar Reads Basics & PrerequisitesLogic Building ProblemsLogic building is about creating clear, step-by-step methods to solve problems using simple rules and principles. It’s the heart of coding, enabling programmers to think, reason, and arrive at smart solutions just like we do.Here are some tips for improving your programming logic: Understand the pro 2 min read Analysis of AlgorithmsAnalysis of Algorithms is a fundamental aspect of computer science that involves evaluating performance of algorithms and programs. Efficiency is measured in terms of time and space.BasicsWhy is Analysis Important?Order of GrowthAsymptotic Analysis Worst, Average and Best Cases Asymptotic NotationsB 1 min read Data StructuresArray Data StructureIn this article, we introduce array, implementation in different popular languages, its basic operations and commonly seen problems / interview questions. An array stores items (in case of C/C++ and Java Primitive Arrays) or their references (in case of Python, JS, Java Non-Primitive) at contiguous 3 min read String in Data StructureA string is a sequence of characters. The following facts make string an interesting data structure.Small set of elements. Unlike normal array, strings typically have smaller set of items. For example, lowercase English alphabet has only 26 characters. ASCII has only 256 characters.Strings are immut 2 min read Hashing in Data StructureHashing is a technique used in data structures that efficiently stores and retrieves data in a way that allows for quick access. Hashing involves mapping data to a specific index in a hash table (an array of items) using a hash function. It enables fast retrieval of information based on its key. The 2 min read Linked List Data StructureA linked list is a fundamental data structure in computer science. It mainly allows efficient insertion and deletion operations compared to arrays. Like arrays, it is also used to implement other data structures like stack, queue and deque. Here’s the comparison of Linked List vs Arrays Linked List: 2 min read Stack Data StructureA Stack is a linear data structure that follows a particular order in which the operations are performed. The order may be LIFO(Last In First Out) or FILO(First In Last Out). LIFO implies that the element that is inserted last, comes out first and FILO implies that the element that is inserted first 2 min read Queue Data StructureA Queue Data Structure is a fundamental concept in computer science used for storing and managing data in a specific order. It follows the principle of "First in, First out" (FIFO), where the first element added to the queue is the first one to be removed. It is used as a buffer in computer systems 2 min read Tree Data StructureTree Data Structure is a non-linear data structure in which a collection of elements known as nodes are connected to each other via edges such that there exists exactly one path between any two nodes. Types of TreeBinary Tree : Every node has at most two childrenTernary Tree : Every node has at most 4 min read Graph Data StructureGraph Data Structure is a collection of nodes connected by edges. It's used to represent relationships between different entities. If you are looking for topic-wise list of problems on different topics like DFS, BFS, Topological Sort, Shortest Path, etc., please refer to Graph Algorithms. Basics of 3 min read Trie Data StructureThe Trie data structure is a tree-like structure used for storing a dynamic set of strings. It allows for efficient retrieval and storage of keys, making it highly effective in handling large datasets. Trie supports operations such as insertion, search, deletion of keys, and prefix searches. In this 15+ min read AlgorithmsSearching AlgorithmsSearching algorithms are essential tools in computer science used to locate specific items within a collection of data. In this tutorial, we are mainly going to focus upon searching in an array. When we search an item in an array, there are two most common algorithms used based on the type of input 2 min read Sorting AlgorithmsA Sorting Algorithm is used to rearrange a given array or list of elements in an order. For example, a given array [10, 20, 5, 2] becomes [2, 5, 10, 20] after sorting in increasing order and becomes [20, 10, 5, 2] after sorting in decreasing order. There exist different sorting algorithms for differ 3 min read Introduction to RecursionThe process in which a function calls itself directly or indirectly is called recursion and the corresponding function is called a recursive function. A recursive algorithm takes one step toward solution and then recursively call itself to further move. The algorithm stops once we reach the solution 14 min read Greedy AlgorithmsGreedy algorithms are a class of algorithms that make locally optimal choices at each step with the hope of finding a global optimum solution. At every step of the algorithm, we make a choice that looks the best at the moment. To make the choice, we sometimes sort the array so that we can always get 3 min read Graph AlgorithmsGraph is a non-linear data structure like tree data structure. The limitation of tree is, it can only represent hierarchical data. For situations where nodes or vertices are randomly connected with each other other, we use Graph. Example situations where we use graph data structure are, a social net 3 min read Dynamic Programming or DPDynamic Programming is an algorithmic technique with the following properties.It is mainly an optimization over plain recursion. Wherever we see a recursive solution that has repeated calls for the same inputs, we can optimize it using Dynamic Programming. The idea is to simply store the results of 3 min read Bitwise AlgorithmsBitwise algorithms in Data Structures and Algorithms (DSA) involve manipulating individual bits of binary representations of numbers to perform operations efficiently. These algorithms utilize bitwise operators like AND, OR, XOR, NOT, Left Shift, and Right Shift.BasicsIntroduction to Bitwise Algorit 4 min read AdvancedSegment TreeSegment Tree is a data structure that allows efficient querying and updating of intervals or segments of an array. It is particularly useful for problems involving range queries, such as finding the sum, minimum, maximum, or any other operation over a specific range of elements in an array. The tree 3 min read Pattern SearchingPattern searching algorithms are essential tools in computer science and data processing. These algorithms are designed to efficiently find a particular pattern within a larger set of data. Patten SearchingImportant Pattern Searching Algorithms:Naive String Matching : A Simple Algorithm that works i 2 min read GeometryGeometry is a branch of mathematics that studies the properties, measurements, and relationships of points, lines, angles, surfaces, and solids. From basic lines and angles to complex structures, it helps us understand the world around us.Geometry for Students and BeginnersThis section covers key br 2 min read Interview PreparationInterview CornerThis article serves as your one-stop guide to interview preparation, designed to help you succeed across different experience levels and company expectations. Here is what you should expect in a Tech Interview, please remember the following points:Tech Interview Preparation does not have any fixed s 3 min read GfG160Are you preparing for technical interviews and would like to be well-structured to improve your problem-solving skills? Well, we have good news for you! GeeksforGeeks proudly presents GfG160, a 160-day coding challenge starting on 15th November 2024. In this event, we will provide daily coding probl 3 min read Practice ProblemGeeksforGeeks Practice - Leading Online Coding PlatformGeeksforGeeks Practice is an online coding platform designed to help developers and students practice coding online and sharpen their programming skills with the following features. GfG 160: This consists of most popular interview problems organized topic wise and difficulty with with well written e 6 min read Problem of The Day - Develop the Habit of CodingDo you find it difficult to develop a habit of Coding? If yes, then we have a most effective solution for you - all you geeks need to do is solve one programming problem each day without any break, and BOOM, the results will surprise you! Let us tell you how:Suppose you commit to improve yourself an 5 min read Like