How to insert a node in Binary Search Tree using Iteration

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>

Output

20 30 40 50 60 70 80 

Time Complexity: O(H), where H is the height of the BST. 
Auxiliary Space: O(1)