Binary Search Tree: Insertion

March 1, 2023

Insertion in a Binary Search Tree

Binary Search tree is fairly easy and we just need to know a few simple rules given below –

Binary Search Tree Insertion

Rules for Insertion in a Binary Search Tree (BST)

  • The left subtree for any given node will only contain nodes which are lesser than the current node
  • The right subtree for any given node will only contain nodes which are greater than the current node
  • Each subtree must also follow the above rules of BST

Pre Requisite to Insertion

Binary Search Tree_ Insertion 1

So, first, we will learn how to search a given node(value), in a binary search tree

Searching in a Binary Search Tree

Let us say we want to 9 in the binary search tree given in our example above, what approach we would follow?

Algorithm

  • Start from the root node
  • Compare the value with the root node, if same then found, return True
  • If the value is less than the root node, recurse to the left node. Else recurse to the right node
  • Do this recursively, until the value is found or not found

Example

Assuming we want to find 9 in the above example

  1. The root node is 15, (9 <15) thus recursing to the left node
  2. Now, the left node is 13, (9<14) thus again, recursing to the left node
  3. Now, the left node is 8, (9>8) thus, recursing to the right node
  4. Finally, the right node is 9, (9=9), thus value found, return true

Code to implement Search

// A sample C function to check if a given node exists in a binary search tree or not
struct node* search(struct node* root, int value) 
{ 
    // Check if the root is null or value is present at root itself
    if (root == NULL || root->value == value) 
       return root;

    // Root is smaller than value, go to right subtree's node, doing recusion here
    if (root->value < value) 
       return search(root->right, value); 

    // else only one case is left
    // i.e. Root is greater than value, go to left subtree's node, doing recusion here
    return search(root->left, value); 
}
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Priority Queue in C

Tree Traversals: Inorder Postorder Preorder

Inorder Tree Traversal in Binary Tree

Inorder Tree Traversal without Recursion

Preorder Tree Traversal without Recursion

Insertion in a Binary Search Tree

Insertion is fairly simple if you understood search perfectly

  • Try to search the BST for the node to be inserted
  • As the node wouldn’t exist we will hit the leaf node, with null as child node right!
  • Insert the new node here
  • Voila! Party, you’ve inserted

Code for Binary Search Tree Insertion

Run 
// PrepInsta's program to do insertion in a Binary Search Tree (BST)
#include<stdio.h> 
#include<stdlib.h>

// Basic struct of Tree 
struct node 
{ 
    int val; 
    struct node *left, *right; 
}; 
   
// Function to create a new Node
struct node* newNode(int item) 
{ 
    struct node* temp =  (struct node *)malloc(sizeof(struct node)); 
    temp->val = item; 
    temp->left = temp->right = NULL; 
    return temp; 
} 
   
// Function print the node in inorder format, when insertion is complete
void inorder(struct node* root) 
{ 
    if (root != NULL) 
    { 
        inorder(root->left); 
        printf("%d \n", root->val); 
        inorder(root->right); 
    } 
} 
   
// Here we are finding where to insert the new node so BST is followed
struct node* insert(struct node* node, int val) 
{ 
    /* If the tree(subtree) is empty, return a new node by calling newNode func.*/
    if (node == NULL) return newNode(val); 
  
    /* Else, we will do recursion down the tree to further subtrees */
    if (val < node->val) 
        node->left  = insert(node->left, val); 
    else if (val > node->val) 
        node->right = insert(node->right, val);    
  
    /* (Safety) return the node's pointer which is unchanged */
    return node; 
} 
   
int main() 
{ 
    /* Our BST will look like this 
              100 
           /     \ 
          40      140 
         /  \    /  \ 
       40   80  120  160 */
    struct node* root = NULL; 
    root = insert(root, 100); 
    insert(root, 60); 
    insert(root, 40); 
    insert(root, 80); 
    insert(root, 140); 
    insert(root, 120); 
    insert(root, 160);
    
   
    // Finally printing the tree using inorder
    inorder(root); 
   
    return 0; 
}

Output:

40 
60 
80 
100 
120 
140 
160

How it works?

  • In binary search trees, we use the INSERT function to add a new element in a tree.
  • Insertion is similar to searching wherein, we first check if the element is present in the given data or not. If not, the node is entered at that position.
  • If the data to be added is greater than the parent data node it is inserted towards the right of the parent; else it is inserted to the left of the parent.
  • In other words,
  • If  root > node, 

then the data node is added to the left sub-tree.

  • If  root < node, 

then the data node is added to the right sub-tree.

For Example: [15, 18, 13, 8, 14, 4, 16, 19, 9]

Binary Search Tree_ Insertion

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Introduction to Trees

Binary Trees

Binary Search Trees

Traversals

  • Traversal in Trees
  • Tree Traversals: Breadth-First Search (BFS) : C | C++ | Java
  • Tree Traversals: Depth First Search (DFS) : C | C++ | Java
  • Construct a Binary Tree from Postorder and Inorder

B – Trees

AVL Trees

  • AVL Trees
    • AVL Trees: Introduction
    • AVL Tree Insertion : C | C++ | Java
    • AVL Tree Deletion : C | C++ | Java
    • Insertion in a Binary Tree (Level Order) – C | C++ | Java
    • Searching in Binary Tree – C | C++ | Java
    • Searching in a Binary Search Tree – C | C++ | Java

Complete Programs for Trees

  • Depth First Traversals – C | C++ | Java
  • Level Order Traversal – C | C++ | Java
  • Construct Tree from given Inorder and Preorder traversals – C | C++ | Java
  • Construct Tree from given Postorder and Inorder traversals – C | C++ | Java
  • Construct Tree from given Postorder and Preorder traversal – C | C++ | Java
  • Find size of the Binary tree – C | C++ | Java
  • Find the height of binary tree – C | C++ | Java
  • Find maximum in binary tree – C | C++ | Java
  • Check whether two tree are identical- C| C++| Java
  • Spiral Order traversal of Tree- C | C++| Java
  • Level Order Traversal Line by Line – C | C++| Java
  • Hand shaking lemma and some Impotant Tree Properties.
  • Check If binary tree if Foldable or not.- C| C++| Java
  • check whether tree is Symmetric – C| C++| Java.
  • Check for Children-Sum in Binary Tree- C|C++| Java
  • Sum of all nodes in Binary Tree- C | C++ | Java
  • Lowest Common Ancestor in Binary Tree- C | C++ | Java

Introduction to Trees

Binary Trees

Binary Search Trees

Traversals

  • Traversal in Trees
  • Tree Traversals: Breadth-First Search (BFS) : C | C++ | Java
  • Tree Traversals: Depth First Search (DFS) : C | C++ | Java
  • Construct a Binary Tree from Postorder and Inorder

B – Trees

AVL Trees

  • AVL Trees
    • AVL Trees: Introduction
    • AVL Tree Insertion :  C | C++ | Java
    • AVL Tree Deletion : C | C++ | Java
    • Insertion in a Binary Tree (Level Order) – C | C++ | Java
    • Searching in Binary Tree – C | C++ | Java
    • Searching in a Binary Search Tree – C | C++ | Java

Complete Programs for Trees

  • Depth First Traversals – C | C++ | Java
  • Level Order Traversal – C | C++ | Java
  • Construct Tree from given Inorder and Preorder traversals – C | C++ | Java
  • Construct Tree from given Postorder and Inorder traversals – C | C++ | Java
  • Construct Tree from given Postorder and Preorder traversal – C | C++ | Java
  • Find size of the Binary tree – C | C++ | Java
  • Find the height of binary tree – C | C++ | Java
  • Find maximum in binary tree – C | C++ | Java
  • Check whether two tree are identical- C| C++| Java
  • Spiral Order traversal of Tree- C | C++| Java
  • Level Order Traversal LIne by Line – C | C++| Java
  • Hand shaking lemma and some Impotant Tree Properties.
  • Check If binary tree if Foldable or not.- C| C++| Java
  • check whether tree is Symmetric  C| C++| Java.
  • Check for Children-Sum in Binary Tree- C|C++| Java
  • Sum of all nodes in Binary Tree- C | C++ | Java
  • Lowest Common Ancestor in Binary Tree. C | C++ | Java