Data Structures Tutorial

Data Structures Tutorial Asymptotic Notation Structure and Union Array Data Structure Linked list Data Structure Type of Linked list Advantages and Disadvantages of linked list Queue Data Structure Implementation of Queue Stack Data Structure Implementation of Stack Sorting Insertion sort Quick sort Selection sort Heap sort Merge sort Bucket sort Count sort Radix sort Shell sort Tree Traversal of the binary tree Binary search tree Graph Spanning tree Linear Search Binary Search Hashing Collision Resolution Techniques

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Priority Queue in Data Structure Deque in Data Structure Difference Between Linear And Non Linear Data Structures Queue Operations In Data Structure About Data Structures Data Structures Algorithms Types of Data Structures Big O Notations Introduction to Arrays Introduction to 1D-Arrays Operations on 1D-Arrays Introduction to 2D-Arrays Operations on 2D-Arrays Strings in Data Structures String Operations Application of 2D array Bubble Sort Insertion Sort Sorting Algorithms What is DFS Algorithm What Is Graph Data Structure What is the difference between Tree and Graph What is the difference between DFS and BFS Bucket Sort Dijkstra’s vs Bellman-Ford Algorithm Linear Queue Data Structure in C Stack Using Array Stack Using Linked List Recursion in Fibonacci Stack vs Array What is Skewed Binary Tree Primitive Data Structure in C Dynamic memory allocation of structure in C Application of Stack in Data Structures Binary Tree in Data Structures Heap Data Structure Recursion - Factorial and Fibonacci What is B tree what is B+ tree Huffman tree in Data Structures Insertion Sort vs Bubble Sort Adding one to the number represented an array of digits Bitwise Operators and their Important Tricks Blowfish algorithm Bubble Sort vs Selection Sort Hashing and its Applications Heap Sort vs Merge Sort Insertion Sort vs Selection Sort Merge Conflicts and ways to handle them Difference between Stack and Queue AVL tree in data structure c++ Bubble sort algorithm using Javascript Buffer overflow attack with examples Find out the area between two concentric circles Lowest common ancestor in a binary search tree Number of visible boxes putting one inside another Program to calculate the area of the circumcircle of an equilateral triangle Red-black Tree in Data Structures Strictly binary tree in Data Structures 2-3 Trees and Basic Operations on them Asynchronous advantage actor-critic (A3C) Algorithm Bubble Sort vs Heap Sort Digital Search Tree in Data Structures Minimum Spanning Tree Permutation Sort or Bogo Sort Quick Sort vs Merge Sort Boruvkas algorithm Bubble Sort vs Quick Sort Common Operations on various Data Structures Detect and Remove Loop in a Linked List How to Start Learning DSA Print kth least significant bit number Why is Binary Heap Preferred over BST for Priority Queue Bin Packing Problem Binary Tree Inorder Traversal Burning binary tree Equal Sum What is a Threaded Binary Tree? What is a full Binary Tree? Bubble Sort vs Merge Sort B+ Tree Program in Q language Deletion Operation from A B Tree Deletion Operation of the binary search tree in C++ language Does Overloading Work with Inheritance Balanced Binary Tree Binary tree deletion Binary tree insertion Cocktail Sort Comb Sort FIFO approach Operations of B Tree in C++ Language Recaman’s Sequence Tim Sort Understanding Data Processing Applications of trees in data structures Binary Tree Implementation Using Arrays Convert a Binary Tree into a Binary Search Tree Create a binary search tree Horizontal and Vertical Scaling Invert binary tree LCA of binary tree Linked List Representation of Binary Tree Optimal binary search tree in DSA Serialize and Deserialize a Binary Tree Tree terminology in Data structures Vertical Order Traversal of Binary Tree What is a Height-Balanced Tree in Data Structure Convert binary tree to a doubly linked list Fundamental of Algorithms Introduction and Implementation of Bloom Filter Optimal binary search tree using dynamic programming Right side view of binary tree Symmetric binary tree Trim a binary search tree What is a Sparse Matrix in Data Structure What is a Tree in Terms of a Graph What is the Use of Segment Trees in Data Structure What Should We Learn First Trees or Graphs in Data Structures All About Minimum Cost Spanning Trees in Data Structure Convert Binary Tree into a Threaded Binary Tree Difference between Structured and Object-Oriented Analysis FLEX (Fast Lexical Analyzer Generator) Object-Oriented Analysis and Design Sum of Nodes in a Binary Tree What are the types of Trees in Data Structure What is a 2-3 Tree in Data Structure What is a Spanning Tree in Data Structure What is an AVL Tree in Data Structure Given a Binary Tree, Check if it's balanced

What is a Threaded Binary Tree?

When we consider those binary trees that are interlinked with each other, we do come across the fact that the fields present in there do consist of NULL values that ultimately lead to the damage and wastage of the storage space that we use for the tree. If we have a binary tree that comprises n number of nodes, then the n+1 link fields would definitely have the NULL values.

In order to save and manage the wastage of this storage space, a new convention was introduced by two people named Perlis and Thornton. In this particular method, the links which were previously filled with NULL are significantly replaced by threads. So, the binary trees that contains threads as a replacement, those binary trees are termed threaded binary trees. Each and every node in a threaded binary tree either contain a link to their child node or thread to various other nodes present in the tree.

Types of threaded binary tree

There are majorly two types of the threaded binary trees. They are given below: -

  • One-way threaded binary tree
  • Two-way threaded binary tree

Now, we will explain each of these trees one by one in the given section.

One-way threaded binary tree

In this type of threaded binary tree, the thread usually occurs either at the left or right link of the field of a given node. If, for example, say the link pops up at the right link of the field, then it will ultimately lead and point to the next adjacent node that will appear and perform the inorder traversal operation on the tree.

Such types of trees are vividly known as the Right threaded binary trees. Whereas on the other hand, if suppose the link pops out at the left link of a given node, then it will ultimately lead and point to the next adjacent node that will appear and perform the inorder predecessor operation on the tree. Such types of trees are known as the left threaded binary trees. In such kind of threaded binary trees, the right link of the last node and the left link of the first node generally occupies a NULL value.


A question arises here how do we distinguish links from threads so the answer to the same question is that threads are generally denoted by dotted lines and are pretty visible to human eyes as well.


The above picture depicts that the inorder traversal and exploration of the threaded binary tree turns out to be vivid with the nodes D, B, E, A, C, and F. When this given tree is represented as the right threaded binary tree, the right link present on the tree placed on the leaf node D that also contains NULL value is generally exchanged with a thread which is represented by a dotted line. This node directly heads out and points to node B, which is the successor of node D. Likewise, in the same way, all the other trees are allotted threads.

Two-way threaded binary tree

In this type of threaded binary tree, the right link of the node which contains the NULL value is generally changed by the thread that usually enacts and points out to the nodes that are inorder successor and the left link of the node which also contains the NULL value is generally replaced by the thread. It points out the nodes that are present in the inorder predecessor.


Take a look at the above picture that shows us the inorder traversal of the threaded binary tree having the vertices D, B, E, G, A, C, and F. If we look at this threaded binary tree, the node that is named E that contains the value NULL is generally interchanged by a simple thread which is a dotted line to its inorder former which node B.

Likewise, the node G that we see in the above picture contains left and right field links that already contain NULL values that are also exchanged by threads which are represented by dotted lines. This is done in such a way that the right link field generally points inorder successor, and in the same manner the left link heads out to the inorder predecessor. In the same manner, all the nodes that are present in the field are allotted threads.