• Difficulty Level : Medium
• Last Updated : 21 Dec, 2021

Inorder traversal of a Binary tree can either be done using recursion or with the use of a auxiliary stack. The idea of threaded binary trees is to make inorder traversal faster and do it without stack and without recursion. A binary tree is made threaded by making all right child pointers that would normally be NULL point to the inorder successor of the node (if it exists).
There are two types of threaded binary trees.
Single Threaded: Where a NULL right pointers is made to point to the inorder successor (if successor exists)
Double Threaded: Where both left and right NULL pointers are made to point to inorder predecessor and inorder successor respectively. The predecessor threads are useful for reverse inorder traversal and postorder traversal.
The threads are also useful for fast accessing ancestors of a node.
Following diagram shows an example Single Threaded Binary Tree. The dotted lines represent threads. C representation of a Threaded Node
Following is C representation of a single-threaded node.

C

 struct Node{    int data;    struct Node *left, *right;    bool rightThread; }

Java representation of a Threaded Node

Following is Java representation of a single-threaded node.

Java

 static class Node{    int data;    Node left, right;    boolean rightThread; } // This code contributed by aashish1995

Python3

 class Node:    def __init__(self, data,rightThread):        self.data = data;        self.left = None;        self.right = None;        self.rightThread = rightThread; # This code is contributed by umadevi9616

C#

 public class Node{   public int data;   public Node left, right;   public bool rightThread; } // This code is contributed by aashish1995

Javascript



Since right pointer is used for two purposes, the boolean variable rightThread is used to indicate whether right pointer points to right child or inorder successor. Similarly, we can add leftThread for a double threaded binary tree.
Following is code for inorder traversal in a threaded binary tree.

C

 // Utility function to find leftmost node in a tree rooted// with nstruct Node* leftMost(struct Node* n){    if (n == NULL)        return NULL;     while (n->left != NULL)        n = n->left;     return n;} // C code to do inorder traversal in a threaded binary treevoid inOrder(struct Node* root){    struct Node* cur = leftMost(root);    while (cur != NULL) {        printf("%d ", cur->data);         // If this node is a thread node, then go to        // inorder successor        if (cur->rightThread)            cur = cur->right;        else // Else go to the leftmost child in right             // subtree            cur = leftmost(cur->right);    }}

Java

 // Utility function to find leftmost node in a tree rooted// with nNode leftMost(Node n){    if (n == null)        return null;     while (n.left != null)        n = n.left;     return n;} // C code to do inorder traversal in a threaded binary treestatic void inOrder(Node root){    Node cur = leftMost(root);    while (cur != null) {        System.out.printf("%d ", cur.data);         // If this node is a thread node, then go to        // inorder successor        if (cur.rightThread)            cur = cur.right;        else // Else go to the leftmost child in right             // subtree            cur = leftmost(cur.right);    }} // This code contributed by aashish1995

Python3

 # Utility function to find leftmost Node in a tree rooted# with ndef leftMost(n):     if (n == None):        return None;     while (n.left != None):        n = n.left;     return n;  # C code to do inorder traversal in a threaded binary treedef inOrder(root):     cur = leftMost(root);    while (cur != None):        print(cur.data," ");         # If this Node is a thread Node, then go to        # inorder successor        if (cur.rightThread):            cur = cur.right;        else: # Else go to the leftmost child in right             # subtree            cur = leftmost(cur.right); # This code is contributed by Rajput-Ji

C#

 // Utility function to find leftmost node in a tree rooted// with nNode leftMost(Node n){  if (n == null)    return null;   while (n.left != null)    n = n.left;   return n;} // C code to do inorder traversal in a threaded binary treestatic void inOrder(Node root){  Node cur = leftMost(root);  while (cur != null)  {    Console.Write("{0} ", cur.data);     // If this node is a thread node, then go to    // inorder successor    if (cur.rightThread)      cur = cur.right;    else // Else go to the leftmost child in right      // subtree      cur = leftmost(cur.right);  }} // This code is contributed by gauravrajput1

Javascript



Following diagram demonstrates inorder order traversal using threads. We will soon be discussing insertion and deletion in threaded binary trees.
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