Threaded Binary Tree | Insertion

Last Updated : 14 Sep, 2023

We have already discuss the Binary Threaded Binary Tree.
Insertion in Binary threaded tree is similar to insertion in binary tree but we will have to adjust the threads after insertion of each element.

C representation of Binary Threaded Node:

struct Node
{
  struct Node *left, *right;
  int info;

  // false if left pointer points to predecessor 
  // in Inorder Traversal
  boolean lthread; 

  // false if right pointer points to successor 
  // in Inorder Traversal
  boolean rthread; 
};

In the following explanation, we have considered Binary Search Tree (BST) for insertion as insertion is defined by some rules in BSTs.
Let tmp be the newly inserted node. There can be three cases during insertion:

Case 1: Insertion in empty tree

Both left and right pointers of tmp will be set to NULL and new node becomes the root.

root = tmp;
tmp -> left = NULL;
tmp -> right = NULL;

Case 2: When new node inserted as the left child

After inserting the node at its proper place we have to make its left and right threads points to inorder predecessor and successor respectively. The node which was inorder successor. So the left and right threads of the new node will be-

tmp -> left = par ->left;
tmp -> right = par;

Before insertion, the left pointer of parent was a thread, but after insertion it will be a link pointing to the new node.

par -> lthread = false;
par -> left = temp;

Following example show a node being inserted as left child of its parent.

After insertion of 13,

Predecessor of 14 becomes the predecessor of 13, so left thread of 13 points to 10.
Successor of 13 is 14, so right thread of 13 points to left child which is 13.
Left pointer of 14 is not a thread now, it points to left child which is 13.

Case 3: When new node is inserted as the right child

The parent of tmp is its inorder predecessor. The node which was inorder successor of the parent is now the inorder successor of this node tmp. So the left and right threads of the new node will be-

tmp -> left = par;
tmp -> right = par -> right;

Before insertion, the right pointer of parent was a thread, but after insertion it will be a link pointing to the new node.

par -> rthread = false;
par -> right = tmp;

Following example shows a node being inserted as right child of its parent.

After 15 inserted,

Successor of 14 becomes the successor of 15, so right thread of 15 points to 16
Predecessor of 15 is 14, so left thread of 15 points to 14.
Right pointer of 14 is not a thread now, it points to right child which is 15.

C++ implementation to insert a new node in Threaded Binary Search Tree:
Like standard BST insert, we search for the key value in the tree. If key is already present, then we return otherwise the new key is inserted at the point where search terminates. In BST, search terminates either when we find the key or when we reach a NULL left or right pointer. Here all left and right NULL pointers are replaced by threads except left pointer of first node and right pointer of last node. So here search will be unsuccessful when we reach a NULL pointer or a thread.

Implementation:

C++

// Insertion in Threaded Binary Search Tree. 
#include<bits/stdc++.h> 
using namespace std; 
  
struct Node 
{ 
    struct Node *left, *right; 
    int info; 
  
    // False if left pointer points to predecessor 
    // in Inorder Traversal 
    bool lthread; 
  
    // False if right pointer points to successor 
    // in Inorder Traversal 
    bool rthread; 
}; 
  
// Insert a Node in Binary Threaded Tree 
struct Node *insert(struct Node *root, int ikey) 
{ 
    // Searching for a Node with given value 
    Node *ptr = root; 
    Node *par = NULL; // Parent of key to be inserted 
    while (ptr != NULL) 
    { 
        // If key already exists, return 
        if (ikey == (ptr->info)) 
        { 
            printf("Duplicate Key !\n"); 
            return root; 
        } 
  
        par = ptr; // Update parent pointer 
  
        // Moving on left subtree. 
        if (ikey < ptr->info) 
        { 
            if (ptr -> lthread == false) 
                ptr = ptr -> left; 
            else
                break; 
        } 
  
        // Moving on right subtree. 
        else
        { 
            if (ptr->rthread == false) 
                ptr = ptr -> right; 
            else
                break; 
        } 
    } 
  
    // Create a new node 
    Node *tmp = new Node; 
    tmp -> info = ikey; 
    tmp -> lthread = true; 
    tmp -> rthread = true; 
  
    if (par == NULL) 
    { 
        root = tmp; 
        tmp -> left = NULL; 
        tmp -> right = NULL; 
    } 
    else if (ikey < (par -> info)) 
    { 
        tmp -> left = par -> left; 
        tmp -> right = par; 
        par -> lthread = false; 
        par -> left = tmp; 
    } 
    else
    { 
        tmp -> left = par; 
        tmp -> right = par -> right; 
        par -> rthread = false; 
        par -> right = tmp; 
    } 
  
    return root; 
} 
  
// Returns inorder successor using rthread 
struct Node *inorderSuccessor(struct Node *ptr) 
{ 
    // If rthread is set, we can quickly find 
    if (ptr -> rthread == true) 
        return ptr->right; 
  
    // Else return leftmost child of right subtree 
    ptr = ptr -> right; 
    while (ptr -> lthread == false) 
        ptr = ptr -> left; 
    return ptr; 
} 
  
// Printing the threaded tree 
void inorder(struct Node *root) 
{ 
    if (root == NULL) 
        printf("Tree is empty"); 
  
    // Reach leftmost node 
    struct Node *ptr = root; 
    while (ptr -> lthread == false) 
        ptr = ptr -> left; 
  
    // One by one print successors 
    while (ptr != NULL) 
    { 
        printf("%d ",ptr -> info); 
        ptr = inorderSuccessor(ptr); 
    } 
} 
  
// Driver Program 
int main() 
{ 
    struct Node *root = NULL; 
  
    root = insert(root, 20); 
    root = insert(root, 10); 
    root = insert(root, 30); 
    root = insert(root, 5); 
    root = insert(root, 16); 
    root = insert(root, 14); 
    root = insert(root, 17); 
    root = insert(root, 13); 
  
    inorder(root); 
  
    return 0; 
} 

Java

// Java program Insertion in Threaded Binary Search Tree.  
import java.util.*; 
public class solution 
{ 
static class Node  
{  
     Node left, right;  
    int info;  
    
    // False if left pointer points to predecessor  
    // in Inorder Traversal  
    boolean lthread;  
    
    // False if right pointer points to successor  
    // in Inorder Traversal  
    boolean rthread;  
};  
    
// Insert a Node in Binary Threaded Tree  
static Node insert( Node root, int ikey)  
{  
    // Searching for a Node with given value  
    Node ptr = root;  
    Node par = null; // Parent of key to be inserted  
    while (ptr != null)  
    {  
        // If key already exists, return  
        if (ikey == (ptr.info))  
        {  
            System.out.printf("Duplicate Key !\n");  
            return root;  
        }  
    
        par = ptr; // Update parent pointer  
    
        // Moving on left subtree.  
        if (ikey < ptr.info)  
        {  
            if (ptr . lthread == false)  
                ptr = ptr . left;  
            else
                break;  
        }  
    
        // Moving on right subtree.  
        else
        {  
            if (ptr.rthread == false)  
                ptr = ptr . right;  
            else
                break;  
        }  
    }  
    
    // Create a new node  
    Node tmp = new Node();  
    tmp . info = ikey;  
    tmp . lthread = true;  
    tmp . rthread = true;  
      
    if (par == null)  
    {  
        root = tmp;  
        tmp . left = null;  
        tmp . right = null;  
    }  
    else if (ikey < (par . info))  
    {  
        tmp . left = par . left;  
        tmp . right = par;  
        par . lthread = false;  
        par . left = tmp;  
    }  
    else
    {  
        tmp . left = par;  
        tmp . right = par . right;  
        par . rthread = false;  
        par . right = tmp;  
    }  
    
    return root;  
}  
    
// Returns inorder successor using rthread  
static  Node inorderSuccessor( Node ptr)  
{  
    // If rthread is set, we can quickly find  
    if (ptr . rthread == true)  
        return ptr.right;  
    
    // Else return leftmost child of right subtree  
    ptr = ptr . right;  
    while (ptr . lthread == false)  
        ptr = ptr . left;  
    return ptr;  
}  
    
// Printing the threaded tree  
static void inorder( Node root)  
{  
    if (root == null)  
        System.out.printf("Tree is empty");  
    
    // Reach leftmost node  
     Node ptr = root;  
    while (ptr . lthread == false)  
        ptr = ptr . left;  
    
    // One by one print successors  
    while (ptr != null)  
    {  
        System.out.printf("%d ",ptr . info);  
        ptr = inorderSuccessor(ptr);  
    }  
}  
    
// Driver Program  
public static void main(String[] args) 
{  
     Node root = null;  
    
    root = insert(root, 20);  
    root = insert(root, 10);  
    root = insert(root, 30);  
    root = insert(root, 5);  
    root = insert(root, 16);  
    root = insert(root, 14);  
    root = insert(root, 17);  
    root = insert(root, 13);  
    
    inorder(root);  
}   
} 
//contributed by Arnab Kundu 
  
// This code is updated By Susobhan Akhuli

Python3

# Insertion in Threaded Binary Search Tree.  
class newNode: 
    def __init__(self, key): 
      
        # False if left pointer points to  
        # predecessor in Inorder Traversal  
        self.info = key 
        self.left = None
        self.right =None
        self.lthread = True
      
        # False if right pointer points to  
        # successor in Inorder Traversal  
        self.rthread = True
  
# Insert a Node in Binary Threaded Tree  
def insert(root, ikey): 
      
    # Searching for a Node with given value  
    ptr = root  
    par = None # Parent of key to be inserted  
    while ptr != None: 
          
        # If key already exists, return  
        if ikey == (ptr.info): 
            print("Duplicate Key !")  
            return root  
  
        par = ptr # Update parent pointer  
  
        # Moving on left subtree.  
        if ikey < ptr.info: 
            if ptr.lthread == False:  
                ptr = ptr.left  
            else: 
                break
  
        # Moving on right subtree.  
        else: 
            if ptr.rthread == False:  
                ptr = ptr.right  
            else: 
                break
  
    # Create a new node  
    tmp = newNode(ikey)  
  
    if par == None: 
        root = tmp  
        tmp.left = None
        tmp.right = None
    elif ikey < (par.info): 
        tmp.left = par.left  
        tmp.right = par  
        par.lthread = False
        par.left = tmp 
    else: 
        tmp.left = par  
        tmp.right = par.right  
        par.rthread = False
        par.right = tmp 
  
    return root 
  
# Returns inorder successor using rthread  
def inorderSuccessor(ptr): 
      
    # If rthread is set, we can quickly find  
    if ptr.rthread == True:  
        return ptr.right  
  
    # Else return leftmost child of  
    # right subtree  
    ptr = ptr.right  
    while ptr.lthread == False:  
        ptr = ptr.left  
    return ptr 
  
# Printing the threaded tree  
def inorder(root): 
    if root == None:  
        print("Tree is empty")  
  
    # Reach leftmost node  
    ptr = root  
    while ptr.lthread == False:  
        ptr = ptr.left  
  
    # One by one print successors  
    while ptr != None: 
        print(ptr.info,end=" ")  
        ptr = inorderSuccessor(ptr) 
  
# Driver Code 
if __name__ == '__main__': 
    root = None
  
    root = insert(root, 20)  
    root = insert(root, 10)  
    root = insert(root, 30)  
    root = insert(root, 5)  
    root = insert(root, 16)  
    root = insert(root, 14)  
    root = insert(root, 17)  
    root = insert(root, 13)  
  
    inorder(root)  
      
# This code is contributed by PranchalK 

C#

using System; 
  
// C# program Insertion in Threaded Binary Search Tree.   
public class solution 
{ 
public class Node 
{ 
     public Node left, right; 
    public int info; 
  
    // False if left pointer points to predecessor   
    // in Inorder Traversal   
    public bool lthread; 
  
    // False if right pointer points to successor   
    // in Inorder Traversal   
    public bool rthread; 
} 
  
// Insert a Node in Binary Threaded Tree   
public static Node insert(Node root, int ikey) 
{ 
    // Searching for a Node with given value   
    Node ptr = root; 
    Node par = null; // Parent of key to be inserted 
    while (ptr != null) 
    { 
        // If key already exists, return   
        if (ikey == (ptr.info)) 
        { 
            Console.Write("Duplicate Key !\n"); 
            return root; 
        } 
  
        par = ptr; // Update parent pointer 
  
        // Moving on left subtree.   
        if (ikey < ptr.info) 
        { 
            if (ptr.lthread == false) 
            { 
                ptr = ptr.left; 
            } 
            else
            { 
                break; 
            } 
        } 
  
        // Moving on right subtree.   
        else
        { 
            if (ptr.rthread == false) 
            { 
                ptr = ptr.right; 
            } 
            else
            { 
                break; 
            } 
        } 
    } 
  
    // Create a new node   
    Node tmp = new Node(); 
    tmp.info = ikey; 
    tmp.lthread = true; 
    tmp.rthread = true; 
  
    if (par == null) 
    { 
        root = tmp; 
        tmp.left = null; 
        tmp.right = null; 
    } 
    else if (ikey < (par.info)) 
    { 
        tmp.left = par.left; 
        tmp.right = par; 
        par.lthread = false; 
        par.left = tmp; 
    } 
    else
    { 
        tmp.left = par; 
        tmp.right = par.right; 
        par.rthread = false; 
        par.right = tmp; 
    } 
  
    return root; 
} 
  
// Returns inorder successor using rthread   
public static Node inorderSuccessor(Node ptr) 
{ 
    // If rthread is set, we can quickly find   
    if (ptr.rthread == true) 
    { 
        return ptr.right; 
    } 
  
    // Else return leftmost child of right subtree   
    ptr = ptr.right; 
    while (ptr.lthread == false) 
    { 
        ptr = ptr.left; 
    } 
    return ptr; 
} 
  
// Printing the threaded tree   
public static void inorder(Node root) 
{ 
    if (root == null) 
    { 
        Console.Write("Tree is empty"); 
    } 
  
    // Reach leftmost node   
     Node ptr = root; 
    while (ptr.lthread == false) 
    { 
        ptr = ptr.left; 
    } 
  
    // One by one print successors   
    while (ptr != null) 
    { 
        Console.Write("{0:D} ",ptr.info); 
        ptr = inorderSuccessor(ptr); 
    } 
} 
  
// Driver Program   
public static void Main(string[] args) 
{ 
     Node root = null; 
  
    root = insert(root, 20); 
    root = insert(root, 10); 
    root = insert(root, 30); 
    root = insert(root, 5); 
    root = insert(root, 16); 
    root = insert(root, 14); 
    root = insert(root, 17); 
    root = insert(root, 13); 
  
    inorder(root); 
} 
} 
  
  // This code is contributed by Shrikant13 

Javascript

<script> 
// javascript program Insertion in Threaded Binary Search Tree.  
     class Node { 
     constructor(){ 
this.left = null, this.right = null; 
        this.info = 0; 
  
        // False if left pointer points to predecessor 
        // in Inorder Traversal 
        this.lthread = false; 
  
        // False if right pointer points to successor 
        // in Inorder Traversal 
        this.rthread = false; 
    } 
    } 
  
    // Insert a Node in Binary Threaded Tree 
    function insert(root , ikey) { 
        // Searching for a Node with given value 
var ptr = root; 
var par = null; // Parent of key to be inserted 
        while (ptr != null) { 
            // If key already exists, return 
            if (ikey == (ptr.info)) { 
                document.write("Duplicate Key !\n"); 
                return root; 
            } 
  
            par = ptr; // Update parent pointer 
  
            // Moving on left subtree. 
            if (ikey < ptr.info) { 
                if (ptr.lthread == false) 
                    ptr = ptr.left; 
                else
                    break; 
            } 
  
            // Moving on right subtree. 
            else { 
                if (ptr.rthread == false) 
                    ptr = ptr.right; 
                else
                    break; 
            } 
        } 
  
        // Create a new node 
var tmp = new Node(); 
        tmp.info = ikey; 
        tmp.lthread = true; 
        tmp.rthread = true; 
  
        if (par == null) { 
            root = tmp; 
            tmp.left = null; 
            tmp.right = null; 
        } else if (ikey < (par.info)) { 
            tmp.left = par.left; 
            tmp.right = par; 
            par.lthread = false; 
            par.left = tmp; 
        } else { 
            tmp.left = par; 
            tmp.right = par.right; 
            par.rthread = false; 
            par.right = tmp; 
        } 
  
        return root; 
    } 
  
    // Returns inorder successor using rthread 
    function inorderSuccessor(ptr) { 
        // If rthread is set, we can quickly find 
        if (ptr.rthread == true) 
            return ptr.right; 
  
        // Else return leftmost child of right subtree 
        ptr = ptr.right; 
        while (ptr.lthread == false) 
            ptr = ptr.left; 
        return ptr; 
    } 
  
    // Printing the threaded tree 
    function inorder(root) { 
        if (root == null) 
            document.write("Tree is empty"); 
  
        // Reach leftmost node 
var ptr = root; 
        while (ptr.lthread == false) 
            ptr = ptr.left; 
  
        // One by one print successors 
        while (ptr != null) { 
            document.write(ptr.info+" "); 
            ptr = inorderSuccessor(ptr); 
        } 
    } 
  
    // Driver Program 
      
var root = null; 
  
        root = insert(root, 20); 
        root = insert(root, 10); 
        root = insert(root, 30); 
        root = insert(root, 5); 
        root = insert(root, 16); 
        root = insert(root, 14); 
        root = insert(root, 17); 
        root = insert(root, 13); 
  
        inorder(root); 
  
// This code contributed by aashish1995 
</script> 

Output

5 10 13 14 16 17 20 30

Time Complexity: O(log N)

Space Complexity: O(1), since no extra space used.

Threaded Binary Search Tree | Deletion

Anuj Chauhan

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Practice Tags :

Threaded Binary Tree | Insertion

C++

Java

Python3

C#

Javascript

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