Given a BST, the task is to insert a new node in this BST.
Example:
Insertion in Binary Search Tree
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 found, the new node is added as a child of the leaf node. The below steps are followed while we try to insert a node into a binary search tree:
- Check the value to be inserted (say X) with the value of the current node (say val) we are in:
- If X is less than val move to the left subtree.
- Otherwise, move to the right subtree.
- Once the leaf node is reached, insert X to its right or left based on the relation between X and the leaf node’s value.
Follow the below illustration for a better understanding:
Illustration:
Insertion in BST
Insertion in BST
Insertion in BST
Insertion in BST
Insertion in BST
Insertion in Binary Search Tree using Recursion:
Below is the implementation of the insertion operation using recursion.
C++14
// C++ program to demonstrate insertion// in a BST recursively#include <bits/stdc++.h>using namespace std;class BST { int data; BST *left, *right;public: // Default constructor. BST(); // Parameterized constructor. BST(int); // Insert function. BST* Insert(BST*, int); // Inorder traversal. void Inorder(BST*);};// Default Constructor definition.BST::BST() : data(0) , left(NULL) , right(NULL){}// Parameterized Constructor definition.BST::BST(int value){ data = value; left = right = NULL;}// Insert function definition.BST* BST::Insert(BST* root, int value){ if (!root) { // Insert the first node, if root is NULL. return new BST(value); } // Insert data. if (value > root->data) { // Insert right node data, if the 'value' // to be inserted is greater than 'root' node data. // Process right nodes. root->right = Insert(root->right, value); } else if (value < root->data) { // Insert left node data, if the 'value' // to be inserted is smaller than 'root' node data. // Process left nodes. root->left = Insert(root->left, value); } // Return 'root' node, after insertion. return root;}// Inorder traversal function.// This gives data in sorted order.void BST::Inorder(BST* root){ if (!root) { return; } Inorder(root->left); cout << root->data << " "; Inorder(root->right);}// Driver codeint main(){ BST b, *root = NULL; root = b.Insert(root, 50); b.Insert(root, 30); b.Insert(root, 20); b.Insert(root, 40); b.Insert(root, 70); b.Insert(root, 60); b.Insert(root, 80); b.Inorder(root); return 0;} |
C
// C program to demonstrate insert// operation in binary// search tree.#include <stdio.h>#include <stdlib.h>struct node { int key; struct node *left, *right;};// A utility function to create a new BST nodestruct node* newNode(int item){ struct node* temp = (struct node*)malloc(sizeof(struct node)); temp->key = item; temp->left = temp->right = NULL; return temp;}// A utility function to do inorder traversal of BSTvoid inorder(struct node* root){ if (root != NULL) { inorder(root->left); printf("%d ", root->key); inorder(root->right); }}// A utility function to insert// a new node with given key in BSTstruct node* insert(struct node* node, int key){ // If the tree is empty, return a new node if (node == NULL) return newNode(key); // Otherwise, recur down the tree if (key < node->key) node->left = insert(node->left, key); else if (key > node->key) node->right = insert(node->right, key); // Return the (unchanged) node pointer return node;}// Driver Codeint main(){ /* Let us create following BST 50 / \ 30 70 / \ / \ 20 40 60 80 */ struct 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 treeimport java.io.*;public class BinarySearchTree { // Class containing left // and right child of current node // and key value class Node { int key; Node left, right; public Node(int item) { key = item; left = right = null; } } // Root of BST Node root; // Constructor BinarySearchTree() { root = null; } BinarySearchTree(int value) { root = new Node(value); } // This method mainly calls insertRec() void insert(int key) { root = insertRec(root, key); } // A recursive function to // insert a new key in BST Node insertRec(Node root, int key) { // If the tree is empty, // return a new node if (root == null) { root = new Node(key); return root; } // Otherwise, recur down the tree else if (key < root.key) root.left = insertRec(root.left, key); else if (key > root.key) root.right = insertRec(root.right, key); // Return the (unchanged) node pointer return root; } // This method mainly calls InorderRec() void inorder() { inorderRec(root); } // A utility function to // do inorder traversal of BST void inorderRec(Node root) { if (root != null) { inorderRec(root.left); System.out.print(root.key + " "); inorderRec(root.right); } } // Driver Code public static void main(String[] args) { BinarySearchTree tree = new BinarySearchTree(); /* Let us create following BST 50 / \ 30 70 / \ / \ 20 40 60 80 */ tree.insert(50); tree.insert(30); tree.insert(20); tree.insert(40); tree.insert(70); tree.insert(60); tree.insert(80); // Print inorder traversal of the BST tree.inorder(); }}// This code is contributed by Ankur Narain Verma |
Python3
# Python program to demonstrate# insert operation in binary search tree# A utility class that represents# an individual node in a BSTclass Node: def __init__(self, key): self.left = None self.right = None self.val = key# A utility function to insert# a new node with the given keydef insert(root, key): if root is None: return Node(key) else: if root.val == key: return root elif root.val < key: root.right = insert(root.right, key) else: root.left = insert(root.left, key) return root# A utility function to do inorder tree traversaldef inorder(root): if root: inorder(root.left) print(root.val, end=" ") inorder(root.right)# Driver program to test the above functionsif __name__ == '__main__': # Let us create the following BST # 50 # / \ # 30 70 # / \ / \ # 20 40 60 80 r = Node(50) r = insert(r, 30) r = insert(r, 20) r = insert(r, 40) r = insert(r, 70) r = insert(r, 60) r = insert(r, 80) # Print inorder traversal of the BST inorder(r) |
C#
// C# program to demonstrate// insert operation in binary// search treeusing System;class BinarySearchTree { // Class containing left and // right child of current node // and key value public class Node { public int key; public Node left, right; public Node(int item) { key = item; left = right = null; } } // Root of BST Node root; // Constructor BinarySearchTree() { root = null; } BinarySearchTree(int value) { root = new Node(value); } // This method mainly calls insertRec() void insert(int key) { root = insertRec(root, key); } // A recursive function to insert // a new key in BST Node insertRec(Node root, int key) { // If the tree is empty, // return a new node if (root == null) { root = new Node(key); return root; } // Otherwise, recur down the tree if (key < root.key) root.left = insertRec(root.left, key); else if (key > root.key) root.right = insertRec(root.right, key); // Return the (unchanged) node pointer return root; } // This method mainly calls InorderRec() void inorder() { inorderRec(root); } // A utility function to // do inorder traversal of BST void inorderRec(Node root) { if (root != null) { inorderRec(root.left); Console.Write(root.key + " "); inorderRec(root.right); } } // Driver Code public static void Main(String[] args) { BinarySearchTree tree = new BinarySearchTree(); /* Let us create following BST 50 / \ 30 70 / \ / \ 20 40 60 80 */ tree.insert(50); tree.insert(30); tree.insert(20); tree.insert(40); tree.insert(70); tree.insert(60); tree.insert(80); // Print inorder traversal of the BST tree.inorder(); }}// This code is contributed by aashish1995 |
Javascript
<script>// javascript program to demonstrate // insert operation in binary// search tree /* * Class containing left and right child of current node and key value */ class Node { constructor(item) { this.key = item; this.left = this.right = null; } } // Root of BST var root = null; // This method mainly calls insertRec() function insert(key) { root = insertRec(root, key); } // A recursive function to insert a new key in BST function insertRec(root, key) { // If the tree is empty, return a new node if (root == null) { root = new Node(key); return root; } // Otherwise, recur down the tree if (key < root.key) root.left = insertRec(root.left, key); else if (key > root.key) root.right = insertRec(root.right, key); // Return the (unchanged) node pointer return root; } // This method mainly calls InorderRec() function inorder() { inorderRec(root); } // A utility function to // do inorder traversal of BST function inorderRec(root) { if (root != null) { inorderRec(root.left); document.write(root.key+"<br/>"); inorderRec(root.right); } }// Driver Code /* Let us create following BST 50 / \ 30 70 / \ / \ 20 40 60 80 */ insert(50); insert(30); insert(20); insert(40); insert(70); insert(60); insert(80); // Print inorder traversal of the BST inorder();// This code is contributed by Rajput-Ji</script> |
Output
20 30 40 50 60 70 80
Time Complexity:
- The worst-case time complexity of insert operations is O(h) where h is the height of the Binary Search Tree.
- In the worst case, we may have to travel from the root to the deepest leaf node. The height of a skewed tree may become n and the time complexity of insertion operation may become O(n).
Auxiliary Space: The auxiliary space complexity of insertion into a binary search tree is O(1)
Insertion in Binary Search Tree using Iterative approach:
Instead of using recursion, we can also implement the insertion operation iteratively using a while loop. Below is the implementation using a while loop.
C++
// C++ Code to insert node and to print inorder traversal// using iteration#include <bits/stdc++.h>using namespace std;// BST Nodeclass Node {public: int val; Node* left; Node* right; Node(int val) : val(val) , left(NULL) , right(NULL) { }};// Utility function to insert node in BSTvoid insert(Node*& root, int key){ Node* node = new Node(key); if (!root) { root = node; return; } Node* prev = NULL; Node* temp = root; while (temp) { if (temp->val > key) { prev = temp; temp = temp->left; } else if (temp->val < key) { prev = temp; temp = temp->right; } } if (prev->val > key) prev->left = node; else prev->right = node;}// Utility function to print inorder traversalvoid inorder(Node* root){ Node* temp = root; stack<Node*> st; while (temp != NULL || !st.empty()) { if (temp != NULL) { st.push(temp); temp = temp->left; } else { temp = st.top(); st.pop(); cout << temp->val << " "; temp = temp->right; } }}// Driver codeint main(){ Node* root = NULL; insert(root, 30); insert(root, 50); insert(root, 15); insert(root, 20); insert(root, 10); insert(root, 40); insert(root, 60); // Function call to print the inorder traversal inorder(root); return 0;} |
Java
// Java code to implement the insertion// in binary search treeimport java.io.*;import java.util.*;class GFG { // Driver code public static void main(String[] args) { BST tree = new BST(); tree.insert(30); tree.insert(50); tree.insert(15); tree.insert(20); tree.insert(10); tree.insert(40); tree.insert(60); tree.inorder(); }}class Node { Node left; int val; Node right; Node(int val) { this.val = val; }}class BST { Node root; // Function to insert a key public void insert(int key) { Node node = new Node(key); if (root == null) { root = node; return; } Node prev = null; Node temp = root; while (temp != null) { if (temp.val > key) { prev = temp; temp = temp.left; } else if (temp.val < key) { prev = temp; temp = temp.right; } } if (prev.val > key) prev.left = node; else prev.right = node; } // Function to print the inorder value public void inorder() { Node temp = root; Stack<Node> stack = new Stack<>(); while (temp != null || !stack.isEmpty()) { if (temp != null) { stack.add(temp); temp = temp.left; } else { temp = stack.pop(); System.out.print(temp.val + " "); temp = temp.right; } } }} |
Python3
# Python 3 code to implement the insertion# operation iterativelyclass GFG: @staticmethod def main(args): tree = BST() tree.insert(30) tree.insert(50) tree.insert(15) tree.insert(20) tree.insert(10) tree.insert(40) tree.insert(60) tree.inorder()class Node: left = None val = 0 right = None def __init__(self, val): self.val = valclass BST: root = None # Function to insert a key in the BST def insert(self, key): node = Node(key) if (self.root == None): self.root = node return prev = None temp = self.root while (temp != None): if (temp.val > key): prev = temp temp = temp.left elif(temp.val < key): prev = temp temp = temp.right if (prev.val > key): prev.left = node else: prev.right = node # Function to print the inorder traversal of BST def inorder(self): temp = self.root stack = [] while (temp != None or not (len(stack) == 0)): if (temp != None): stack.append(temp) temp = temp.left else: temp = stack.pop() print(str(temp.val) + " ", end="") temp = temp.rightif __name__ == "__main__": GFG.main([])# This code is contributed by rastogik346. |
C#
// Function to implement the insertion// operation iterativelyusing System;using System.Collections.Generic;public class GFG { // Driver code public static void Main(String[] args) { BST tree = new BST(); tree.insert(30); tree.insert(50); tree.insert(15); tree.insert(20); tree.insert(10); tree.insert(40); tree.insert(60); // Function call to print the inorder traversal tree.inorder(); }}public class Node { public Node left; public int val; public Node right; public Node(int val) { this.val = val; }}public class BST { public Node root; // Function to insert a new key in the BST public void insert(int key) { Node node = new Node(key); if (root == null) { root = node; return; } Node prev = null; Node temp = root; while (temp != null) { if (temp.val > key) { prev = temp; temp = temp.left; } else if (temp.val < key) { prev = temp; temp = temp.right; } } if (prev.val > key) prev.left = node; else prev.right = node; } // Function to print the inorder traversal of BST public void inorder() { Node temp = root; Stack<Node> stack = new Stack<Node>(); while (temp != null || stack.Count != 0) { if (temp != null) { stack.Push(temp); temp = temp.left; } else { temp = stack.Pop(); Console.Write(temp.val + " "); temp = temp.right; } } }}// This code is contributed by Rajput-Ji |
Javascript
// JavaScript code to implement the insertion// in binary search treeclass Node { constructor(val) { this.left = null; this.val = val; this.right = null; }}class BST { constructor() { this.root = null; } // Function to insert a key insert(key) { let node = new Node(key); if (this.root == null) { this.root = node; return; } let prev = null; let temp = this.root; while (temp != null) { if (temp.val > key) { prev = temp; temp = temp.left; } else if (temp.val < key) { prev = temp; temp = temp.right; } } if (prev.val > key) prev.left = node; else prev.right = node; } // Function to print the inorder value inorder() { let temp = this.root; let stack = []; while (temp != null || stack.length > 0) { if (temp != null) { stack.push(temp); temp = temp.left; } else { temp = stack.pop(); console.log(temp.val + " "); temp = temp.right; } } }}let tree = new BST();tree.insert(30);tree.insert(50);tree.insert(15);tree.insert(20);tree.insert(10);tree.insert(40);tree.insert(60);tree.inorder();// this code is contributed by devendrasolunke |
Output
10 15 20 30 40 50 60
The time complexity of inorder traversal is O(n), as each node is visited once.
The Auxiliary space is O(n), as we use a stack to store nodes for recursion.
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