Threaded Binary Tree | Insertion

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;

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

  // True 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.

C++

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// Insertion in Threaded Binary Search Tree.
#include<bits/stdc++.h>
using namespace std;
  
struct Node
{
    struct Node *left, *right;
    int info;
  
    // True if left pointer points to predecessor
    // in Inorder Traversal
    bool lthread;
  
    // True if right pointer points to predecessor
    // 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;
}

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Java

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// Java program Insertion in Threaded Binary Search Tree. 
import java.util.*;
class solution
{
static class Node 
     Node left, right; 
    int info; 
    
    // True if left pointer points to predecessor 
    // in Inorder Traversal 
    boolean lthread; 
    
    // True if right pointer points to predecessor 
    // 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

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Python3

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# Insertion in Threaded Binary Search Tree. 
class newNode:
    def __init__(self, key):
      
        # True if left pointer points to 
        # predecessor in Inorder Traversal 
        self.info = key
        self.left = None
        self.right =None
        self.lthread = True
      
        # True if right pointer points to 
        # predecessor 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

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C#

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using System;
  
// C# program Insertion in Threaded Binary Search Tree.  
public class solution
{
public class Node
{
     public Node left, right;
    public int info;
  
    // True if left pointer points to predecessor  
    // in Inorder Traversal  
    public bool lthread;
  
    // True if right pointer points to predecessor  
    // 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

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Output:

5 10 13 14 16 17 20 30 

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