**Insertion in Binary Search Tree**: Here, we will learn how to **insert a Node in Binary Search Tree**? In this article you will find algorithm, example in C++.

Submitted by Abhishek Jain, on July 30, 2017

**Binary Search Tree is one of the most important data structures in computer science.**

This data structure enables one to search for and find an element with an average running time **f(n)=O(log _{2} n)**. It also enables one to insert and delete (Deletion in Binary Search Tree) elements. This structure contrasts with the help of array and linked list.

Suppose **T** is a binary tree. Then **T** is called a binary search tree if each Node **N** of tree **T** has the following property: The value at **N** is greater than every value in the left subtree of **N** and is less than every value in the right subtree of **N**. (It is not difficult to see that the property guarantees that the inorder traversal of **T** will yield a sorted listing of the elements of **T**.)

**Algorithm (Outline):**

Suppose an ITEM of information is given. The following algorithm inserts ITEM as a new node in its appropriate place in the tree.

(a) Compare ITEM with the root node N of the tree. (i) If ITEM< N , Proceed to the left Child of N. (ii) If ITEM > N, proceed to the right child of N. (b)Repeat Step (a) until one of the following occurs: (i) We meet a node N such that ITEM=N. In this case the search is successful. (ii) We meet an empty subtree, which indicates that the search is unsuccessful, and we insert ITEM in place of the empty subtree.

**Consider the program:**

#include<iostream> using namespace std; struct node { int data; node* left; node* right; }; struct node* getNode(int data) { node* newNode=new node(); newNode->data=data; newNode->left=NULL; newNode->right=NULL; return newNode; } void inorder(struct node* root) { if (root != NULL) { inorder(root->left); cout<<root->data<<" "; inorder(root->right); } } struct node* Insert(struct node* root, int data) { if (root == NULL) return getNode(data); if (data < root->data) root->left = Insert(root->left, data); else if (data > root->data) root->right = Insert(root->right, data); return root; } int main() { node* root=NULL; root=Insert(root,20); Insert(root,15); Insert(root,25); Insert(root,18); Insert(root,10); Insert(root,16); Insert(root,19); cout<<"Before Insertion: "; cout<<"\nInorder: "; inorder(root); cout<<endl; root=Insert(root,17); cout<<"\nNode Inserted"<<endl; cout<<"\nAfter Insertion: "; cout<<"\nInorder: "; inorder(root); cout<<endl; return 0; }

Output

Before Insertion: Inorder: 10 15 16 18 19 20 25 Node Inserted After Insertion: Inorder: 10 15 16 17 18 19 20 25

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