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

Last Updated : 10 Feb, 2023

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.

threadedBT

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 <bits/stdc++.h>
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<Node*>* 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<Node*>* 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<Node*> 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<Node> 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<Node> 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<Node> q = new LinkedList<Node>();
 
        // 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<Node> 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<Node> 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<Node> q = new Queue<Node>();
 
        // 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

<script>
 
// JavaScript program to convert 
// binary tree to threaded tree
 
/* Class containing left and right child of current 
 node and key value*/
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;
        
    }
}
 
let root;
// Helper function to put the Nodes in inorder into queue
function populateQueue(node,q)
{
     if (node == null)
            return;
        if (node.left != null)
            populateQueue(node.left, q);
        q.push(node);
        if (node.right != null)
            populateQueue(node.right, q);
}
 
 // Function to traverse queue, and make tree threaded
function createThreadedUtil(node,q)
{
     if (node == null)
            return;
   
        if (node.left != null)
            createThreadedUtil(node.left, q);
        q.shift();
   
        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[0];
            node.isThreaded = true;
        }
}
 
// This function uses populateQueue() and
// createThreadedUtil() to convert a given binary tree
// to threaded tree.
function createThreaded(node)
{
    // Create a queue to store inorder traversal
        let q = [];
   
        // 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()
function leftMost(node)
{
    while (node != null && node.left != null)
            node = node.left;
        return node;
}
 
// Function to do inorder traversal of a threaded binary tree
function inOrder(node)
{
    if (node == null)
            return;
   
        // Find the leftmost node in Binary Tree
        let cur = leftMost(node);
   
        while (cur != null) {
            document.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 program to test for above functions
root = new Node(1);
        root.left = new Node(2);
        root.right = new Node(3);
   
        root.left.left = new Node(4);
        root.left.right = new Node(5);
        root.right.left = new Node(6);
        root.right.right = new Node(7);
   
        createThreaded(root);
         
        document.write(
        "Inorder traversal of created threaded tree<br>"
        );
        inOrder(root);
 
 
// This code is contributed by rag2127
 
</script>

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

Convert a Binary Tree to Threaded binary tree | Set 2 (Efficient)

GeeksforGeeks

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Convert a Binary Tree to Threaded binary tree | Set 2 (Efficient)

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