# Convert a Binary Tree to Threaded binary tree | Set 1 (Using Queue)

• Difficulty Level : Medium
• Last Updated : 31 Oct, 2022

We have discussed Threaded Binary Tree. The idea of threaded binary trees is to make inorder traversal faster and do it without stack and without recursion. In a simple threaded binary tree, the NULL right pointers are used to store inorder successor. Wherever a right pointer is NULL, it is used to store inorder successor.

The following diagram shows an example Single Threaded Binary Tree. The dotted lines represent threads.

The following is a structure of a single-threaded binary tree.

## C

 `struct` `Node {``    ``int` `key;``    ``Node *left, *right;` `    ``// Used to indicate whether the right pointer is a normal right``    ``// pointer or a pointer to inorder successor.``    ``bool` `isThreaded;``};`

## Java

 `static` `class` `Node {``    ``int` `key;``    ``Node left, right;` `    ``// Used to indicate whether the right pointer is a normal right``    ``// pointer or a pointer to inorder successor.``    ``boolean` `isThreaded;``};` `// This code is contributed by umadevi9616`

## Python3

 `class` `Node:``    ``def` `__init__(``self``):``        ``self``.Key ``=` `0``;``        ``self``.left ``=` `None``;``        ``self``.right ``=` `None``;``        ` `        ``# Used to indicate whether the right pointer is a normal right``        ``# pointer or a pointer to inorder successor.``        ``self``.isThreaded ``=` `False``;``    ` `# This code is contributed by Rajput-Ji`

## C#

 `class` `Node {``    ``int` `key;``    ``Node left, right;` `    ``// Used to indicate whether the right pointer is a normal right``    ``// pointer or a pointer to inorder successor.``    ``bool` `isThreaded;``};` `// This code is contributed by Rajput-Ji`

## Javascript

 `class Node``{``    ``constructor(item)``    ``{``        ``// Used to indicate whether the right pointer is a normal``          ``// right pointer or a pointer to inorder successor.``        ``let isThreaded;``        ``this``.data=item;``        ``this``.left = ``this``.right = ``null``;``       ` `    ``}``}`

How to convert a Given Binary Tree to Threaded Binary Tree?

We basically need to set NULL right pointers to inorder successor. We first do an inorder traversal of the tree and store it in a queue (we can use a simple array also) so that the inorder successor becomes the next node. We again do an inorder traversal and whenever we find a node whose right is NULL, we take the front item from queue and make it the right of current node. We also set isThreaded to true to indicate that the right pointer is a threaded link.
Following is the implementation of the above idea.

## C++

 `/* C++ program to convert a Binary Tree to Threaded Tree */``#include ``using` `namespace` `std;` `/* Structure of a node in threaded binary tree */``struct` `Node {``    ``int` `key;``    ``Node *left, *right;` `    ``// Used to indicate whether the right pointer is a``    ``// normal right pointer or a pointer to inorder``    ``// successor.``    ``bool` `isThreaded;``};` `// Helper function to put the Nodes in inorder into queue``void` `populateQueue(Node* root, std::queue* q)``{``    ``if` `(root == NULL)``        ``return``;``    ``if` `(root->left)``        ``populateQueue(root->left, q);``    ``q->push(root);``    ``if` `(root->right)``        ``populateQueue(root->right, q);``}` `// Function to traverse queue, and make tree threaded``void` `createThreadedUtil(Node* root, std::queue* q)``{``    ``if` `(root == NULL)``        ``return``;` `    ``if` `(root->left)``        ``createThreadedUtil(root->left, q);``    ``q->pop();` `    ``if` `(root->right)``        ``createThreadedUtil(root->right, q);` `    ``// If right pointer is NULL, link it to the``    ``// inorder successor and set 'isThreaded' bit.``    ``else` `{``        ``root->right = q->front();``        ``root->isThreaded = ``true``;``    ``}``}` `// This function uses populateQueue() and``// createThreadedUtil() to convert a given binary tree``// to threaded tree.``void` `createThreaded(Node* root)``{``    ``// Create a queue to store inorder traversal``    ``std::queue q;` `    ``// Store inorder traversal in queue``    ``populateQueue(root, &q);` `    ``// Link NULL right pointers to inorder successor``    ``createThreadedUtil(root, &q);``}` `// A utility function to find leftmost node in a binary``// tree rooted with 'root'. This function is used in``// inOrder()``Node* leftMost(Node* root)``{``    ``while` `(root != NULL && root->left != NULL)``        ``root = root->left;``    ``return` `root;``}` `// Function to do inorder traversal of a threaded binary``// tree``void` `inOrder(Node* root)``{``    ``if` `(root == NULL)``        ``return``;` `    ``// Find the leftmost node in Binary Tree``    ``Node* cur = leftMost(root);` `    ``while` `(cur != NULL) {``        ``cout << cur->key << ``" "``;` `        ``// If this Node is a thread Node, then go to``        ``// inorder successor``        ``if` `(cur->isThreaded)``            ``cur = cur->right;` `        ``else` `// Else go to the leftmost child in right``             ``// subtree``            ``cur = leftMost(cur->right);``    ``}``}` `// A utility function to create a new node``Node* newNode(``int` `key)``{``    ``Node* temp = ``new` `Node;``    ``temp->left = temp->right = NULL;``    ``temp->key = key;``    ``return` `temp;``}` `// Driver program to test above functions``int` `main()``{``    ``/*       1``            ``/ \``           ``2   3``          ``/ \ / \``         ``4  5 6  7     */``    ``Node* root = newNode(1);``    ``root->left = newNode(2);``    ``root->right = newNode(3);``    ``root->left->left = newNode(4);``    ``root->left->right = newNode(5);``    ``root->right->left = newNode(6);``    ``root->right->right = newNode(7);` `    ``createThreaded(root);` `    ``cout << ``"Inorder traversal of created threaded tree "``            ``"is\n"``;``    ``inOrder(root);``  ` `    ``return` `0;``}`

## Java

 `// Java program to convert binary tree to threaded tree``import` `java.util.LinkedList;``import` `java.util.Queue;` `/* Class containing left and right child of current`` ``node and key value*/``class` `Node {``    ``int` `data;``    ``Node left, right;` `    ``// Used to indicate whether the right pointer is a normal``    ``// right pointer or a pointer to inorder successor.``    ``boolean` `isThreaded;` `    ``public` `Node(``int` `item)``    ``{``        ``data = item;``        ``left = right = ``null``;``    ``}``}` `class` `BinaryTree {``    ``Node root;` `    ``// Helper function to put the Nodes in inorder into queue``    ``void` `populateQueue(Node node, Queue q)``    ``{``        ``if` `(node == ``null``)``            ``return``;``        ``if` `(node.left != ``null``)``            ``populateQueue(node.left, q);``        ``q.add(node);``        ``if` `(node.right != ``null``)``            ``populateQueue(node.right, q);``    ``}` `    ``// Function to traverse queue, and make tree threaded``    ``void` `createThreadedUtil(Node node, Queue q)``    ``{``        ``if` `(node == ``null``)``            ``return``;` `        ``if` `(node.left != ``null``)``            ``createThreadedUtil(node.left, q);``        ``q.remove();` `        ``if` `(node.right != ``null``)``            ``createThreadedUtil(node.right, q);` `        ``// If right pointer is NULL, link it to the``        ``// inorder successor and set 'isThreaded' bit.``        ``else` `{``            ``node.right = q.peek();``            ``node.isThreaded = ``true``;``        ``}``    ``}` `    ``// This function uses populateQueue() and``    ``// createThreadedUtil() to convert a given binary tree``    ``// to threaded tree.``    ``void` `createThreaded(Node node)``    ``{``        ``// Create a queue to store inorder traversal``        ``Queue q = ``new` `LinkedList();` `        ``// Store inorder traversal in queue``        ``populateQueue(node, q);` `        ``// Link NULL right pointers to inorder successor``        ``createThreadedUtil(node, q);``    ``}` `    ``// A utility function to find leftmost node in a binary``    ``// tree rooted with 'root'. This function is used in inOrder()``    ``Node leftMost(Node node)``    ``{``        ``while` `(node != ``null` `&& node.left != ``null``)``            ``node = node.left;``        ``return` `node;``    ``}` `    ``// Function to do inorder traversal of a threaded binary tree``    ``void` `inOrder(Node node)``    ``{``        ``if` `(node == ``null``)``            ``return``;` `        ``// Find the leftmost node in Binary Tree``        ``Node cur = leftMost(node);` `        ``while` `(cur != ``null``) {``            ``System.out.print(``" "` `+ cur.data + ``" "``);` `            ``// If this Node is a thread Node, then go to``            ``// inorder successor``            ``if` `(cur.isThreaded == ``true``)``                ``cur = cur.right;``            ``else` `// Else go to the leftmost child in right subtree``                ``cur = leftMost(cur.right);``        ``}``    ``}` `    ``// Driver program to test for above functions``    ``public` `static` `void` `main(String args[])``    ``{``        ``BinaryTree tree = ``new` `BinaryTree();``        ``tree.root = ``new` `Node(``1``);``        ``tree.root.left = ``new` `Node(``2``);``        ``tree.root.right = ``new` `Node(``3``);` `        ``tree.root.left.left = ``new` `Node(``4``);``        ``tree.root.left.right = ``new` `Node(``5``);``        ``tree.root.right.left = ``new` `Node(``6``);``        ``tree.root.right.right = ``new` `Node(``7``);` `        ``tree.createThreaded(tree.root);``        ``System.out.println(``"Inorder traversal of created threaded tree"``);``        ``tree.inOrder(tree.root);``    ``}``}` `// This code has been contributed by Mayank Jaiswal`

## Python3

 `# Python3 program to convert``# a Binary Tree to Threaded Tree` `# Structure of a node in threaded binary tree``class` `Node:` `    ``def` `__init__(``self``, key):``        ``self``.key ``=` `key``        ``self``.left ``=` `None``        ``self``.right ``=` `None``        ` `        ``# Used to indicate whether the right pointer``        ``# is a normal right pointer or a pointer to``        ``# inorder successor.``        ``self``.isThreaded ``=` `False` `# Helper function to put the Nodes``# in inorder into queue``def` `populateQueue(root, q):` `    ``if` `root ``=``=` `None``: ``return``    ``if` `root.left:``        ``populateQueue(root.left, q)``    ``q.append(root)``    ` `    ``if` `root.right:``        ``populateQueue(root.right, q)` `# Function to traverse queue,``# and make tree threaded``def` `createThreadedUtil(root, q):` `    ``if` `root ``=``=` `None``: ``return` `    ``if` `root.left:``        ``createThreadedUtil(root.left, q)``    ``q.pop(``0``)` `    ``if` `root.right:``        ``createThreadedUtil(root.right, q)` `    ``# If right pointer is None, link it to the``    ``# inorder successor and set 'isThreaded' bit.``    ``else``:``        ``if` `len``(q) ``=``=` `0``: root.right ``=` `None``        ``else``: root.right ``=` `q[``0``]``        ``root.isThreaded ``=` `True` `# This function uses populateQueue() and``# createThreadedUtil() to convert a given``# binary tree to threaded tree.``def` `createThreaded(root):` `    ``# Create a queue to store inorder traversal``    ``q ``=` `[]` `    ``# Store inorder traversal in queue``    ``populateQueue(root, q)` `    ``# Link None right pointers to inorder successor``    ``createThreadedUtil(root, q)` `# A utility function to find leftmost node``# in a binary tree rooted with 'root'.``# This function is used in inOrder()``def` `leftMost(root):` `    ``while` `root !``=` `None` `and` `root.left !``=` `None``:``        ``root ``=` `root.left``    ``return` `root` `# Function to do inorder traversal``# of a threaded binary tree``def` `inOrder(root):` `    ``if` `root ``=``=` `None``: ``return` `    ``# Find the leftmost node in Binary Tree``    ``cur ``=` `leftMost(root)` `    ``while` `cur !``=` `None``:``    ` `        ``print``(cur.key, end ``=` `" "``)` `        ``# If this Node is a thread Node,``        ``# then go to inorder successor``        ``if` `cur.isThreaded:``            ``cur ``=` `cur.right` `        ``# Else go to the leftmost child``        ``# in right subtree``        ``else``:``            ``cur ``=` `leftMost(cur.right)``    ` `# Driver Code``if` `__name__ ``=``=` `"__main__"``:` `    ``root ``=` `Node(``1``)``    ``root.left ``=` `Node(``2``)``    ``root.right ``=` `Node(``3``)``    ``root.left.left ``=` `Node(``4``)``    ``root.left.right ``=` `Node(``5``)``    ``root.right.left ``=` `Node(``6``)``    ``root.right.right ``=` `Node(``7``)` `    ``createThreaded(root)` `    ``print``(``"Inorder traversal of created"``,``                      ``"threaded tree is"``)``    ``inOrder(root)``    ` `# This code is contributed by Rituraj Jain`

## C#

 `// C# program to convert binary tree to threaded tree``using` `System;``using` `System.Collections.Generic;` `/* Class containing left and right child of current``node and key value*/``public` `class` `Node {``    ``public` `int` `data;``    ``public` `Node left, right;` `    ``// Used to indicate whether the right pointer is a normal``    ``// right pointer or a pointer to inorder successor.``    ``public` `bool` `isThreaded;` `    ``public` `Node(``int` `item)``    ``{``        ``data = item;``        ``left = right = ``null``;``    ``}``}` `public` `class` `BinaryTree {``    ``Node root;` `    ``// Helper function to put the Nodes in inorder into queue``    ``void` `populateQueue(Node node, Queue q)``    ``{``        ``if` `(node == ``null``)``            ``return``;``        ``if` `(node.left != ``null``)``            ``populateQueue(node.left, q);``        ``q.Enqueue(node);``        ``if` `(node.right != ``null``)``            ``populateQueue(node.right, q);``    ``}` `    ``// Function to traverse queue, and make tree threaded``    ``void` `createThreadedUtil(Node node, Queue q)``    ``{``        ``if` `(node == ``null``)``            ``return``;` `        ``if` `(node.left != ``null``)``            ``createThreadedUtil(node.left, q);``        ``q.Dequeue();` `        ``if` `(node.right != ``null``)``            ``createThreadedUtil(node.right, q);` `        ``// If right pointer is NULL, link it to the``        ``// inorder successor and set 'isThreaded' bit.``        ``else` `{``            ``if` `(q.Count != 0)``                ``node.right = q.Peek();``            ``node.isThreaded = ``true``;``        ``}``    ``}` `    ``// This function uses populateQueue() and``    ``// createThreadedUtil() to convert a given binary tree``    ``// to threaded tree.``    ``void` `createThreaded(Node node)``    ``{``        ``// Create a queue to store inorder traversal``        ``Queue q = ``new` `Queue();` `        ``// Store inorder traversal in queue``        ``populateQueue(node, q);` `        ``// Link NULL right pointers to inorder successor``        ``createThreadedUtil(node, q);``    ``}` `    ``// A utility function to find leftmost node in a binary``    ``// tree rooted with 'root'. This function is used in inOrder()``    ``Node leftMost(Node node)``    ``{``        ``while` `(node != ``null` `&& node.left != ``null``)``            ``node = node.left;``        ``return` `node;``    ``}` `    ``// Function to do inorder traversal of a threaded binary tree``    ``void` `inOrder(Node node)``    ``{``        ``if` `(node == ``null``)``            ``return``;` `        ``// Find the leftmost node in Binary Tree``        ``Node cur = leftMost(node);` `        ``while` `(cur != ``null``) {``            ``Console.Write(``" "` `+ cur.data + ``" "``);` `            ``// If this Node is a thread Node, then go to``            ``// inorder successor``            ``if` `(cur.isThreaded == ``true``)``                ``cur = cur.right;``            ``else` `// Else go to the leftmost child in right subtree``                ``cur = leftMost(cur.right);``        ``}``    ``}` `    ``// Driver code``    ``public` `static` `void` `Main(String[] args)``    ``{``        ``BinaryTree tree = ``new` `BinaryTree();``        ``tree.root = ``new` `Node(1);``        ``tree.root.left = ``new` `Node(2);``        ``tree.root.right = ``new` `Node(3);` `        ``tree.root.left.left = ``new` `Node(4);``        ``tree.root.left.right = ``new` `Node(5);``        ``tree.root.right.left = ``new` `Node(6);``        ``tree.root.right.right = ``new` `Node(7);` `        ``tree.createThreaded(tree.root);``        ``Console.WriteLine(``"Inorder traversal of created threaded tree"``);``        ``tree.inOrder(tree.root);``    ``}``}` `// This code has been contributed by 29AjayKumar`

## Javascript

 ``

Output

```Inorder traversal of created threaded tree is
4 2 5 1 6 3 7 ```

Time complexity: O(n)

Auxiliary space: O(n) // for queue q

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