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

Misc Topic:

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 B Tree in Data Structure Convert Sorted List to Binary Search Tree Flattening a Linked List Given a Perfect Binary Tree, Reverse Alternate Levels Left View of Binary Tree What are Forest Trees in Data Structure Compare Balanced Binary Tree and Complete Binary Tree Diameter of a Binary Tree Given a Binary Tree Check the Zig Zag Traversal Given a Binary Tree Print the Shortest Path Given a Binary Tree Return All Root To Leaf Paths Given a Binary Tree Swap Nodes at K Height Given a Binary Tree Find Its Minimum Depth Given a Binary Tree Print the Pre Order Traversal in Recursive Given a Generate all Structurally Unique Binary Search Trees Perfect Binary Tree Threaded Binary Trees Function to Create a Copy of Binary Search Tree Function to Delete a Leaf Node from a Binary Tree Function to Insert a Node in a Binary Search Tree Given Two Binary Trees, Check if it is Symmetric A Full Binary Tree with n Nodes Applications of Different Linked Lists in Data Structure B+ Tree in Data Structure Construction of B tree in Data Structure Difference between B-tree and Binary Tree Finding Rank in a Binary Search Tree Finding the Maximum Element in a Binary Tree Finding the Minimum and Maximum Value of a Binary Tree Finding the Sum of All Paths in a Binary Tree Time Complexity of Selection Sort in Data Structure How to get Better in Data Structures and Algorithms Binary Tree Leaf Nodes Classification of Data Structure Difference between Static and Dynamic Data Structure Find the Union and Intersection of the Binary Search Tree Find the Vertical Next in a Binary Tree Finding a Deadlock in a Binary Search Tree Finding all Node of k Distance in a Binary Tree Finding Diagonal Sum in a Binary Tree Finding Diagonal Traversal of The Binary Tree Finding In-Order Successor Binary Tree Finding the gcd of Each Sibling of the Binary Tree Greedy Algorithm in Data Structure How to Calculate Space Complexity in Data Structure How to find missing numbers in an Array Kth Ancestor Node of Binary Tree Minimum Depth Binary Tree Mirror Binary Tree in Data Structure Red-Black Tree Insertion Binary Tree to Mirror Image in Data Structure Calculating the Height of a Binary Search Tree in Data Structure Characteristics of Binary Tree in Data Structure Create a Complete Binary Tree from its Linked List Field in Tree Data Structure Find a Specified Element in a binary Search Tree Find Descendant in Tree Data Structure Find Siblings in a Binary Tree Given as an Array Find the Height of a Node in a Binary Tree Find the Second-Largest Element in a Binary Tree Find the Successor Predecessor of a Binary Search Tree Forest of a Tree in Data Structure In Order Traversal of Threaded Binary Tree Introduction to Huffman Coding Limitations of a Binary Search Tree Link State Routing Algorithm in Data Structure Map Reduce Algorithm for Binary Search Tree in Data Structure Non-Binary Tree in Data Structure Quadratic Probing Example in Hashing Scope and Lifetime of Variables in Data Structure Separate Chaining in Data Structure What is Dynamic Data Structure Separate Chaining vs Open Addressing Time and Space Complexity of Linear Data Structures Abstract Data Types in Data Structures Binary Tree to Single Linked List Count the Number of Nodes in the Binary Tree Count Total No. of Ancestors in a Binary Search Tree Elements of Dynamic Programming in Data Structures Find cost of tree with prims algorithm in data structures Find Preorder Successor in a Threaded Binary Tree Find Prime Nodes Sum Count in Non-Binary Tree Find the Right Sibling of a Binary Tree with Parent Pointers Find the Width of the Binary Search Tree Forest trees in Data Structures Free Tree in Data Structures Frequently asked questions in Tree Data Structures Infix, Postfix and Prefix Conversion Time Complexity of Fibonacci Series What is Weighted Graph in Data Structure What is the Advantage of Linear Search?

Threaded Binary Trees

Recursion or the usage of an auxiliary stack can both be used for in-order binary tree traversal. The goal of threaded binary trees is to speed up in-order traversal without using a stack or recursion. Making all right child pointers that would typically lead to NULL point to the node's inorder successor allows you to thread a binary tree (if it exists).

Threaded Binary Trees

Threaded binary trees come in two different varieties.

  1. Single-threaded: if successor exists.
  2. Double-threaded: When a process is double-threaded, its left and right NULL pointers are made to point, respectively, to its in-order predecessor and in-order successor. For postorder traversal and reverse inorder traversal, the predecessor threads are helpful.

The threads can also be used to access a node's ancestors quickly.

The single-threaded binary tree example is in the following diagram. The dotted lines depict threads.

Threaded Binary Trees

The boolean variable right thread is used to specify whether the right pointer points to the right child or the in-order successor since the right pointer serves two functions. We can add a left thread similarly for a binary tree with two threads.

Types of threaded binary trees.

The types of threaded Binary Trees are:

  1. One-way Threaded Binary Tree.
  2. Two-way Threaded Binary Tree.

One–way threaded binary Tree

Threaded Binary Trees

Right-threaded binary trees are these types of trees. A thread will point to the node's predecessor if it occurs in the left area of the node.

Threaded Binary Trees

Additionally, a NULL value will be present for other nodes with values in the correct link field.

Two–way threaded binary tree

Threaded Binary Trees
Threaded Binary Trees

A, C, F, D, B, E, and G are the results of this binary Tree's inorder traversal, as seen in the above figure. Similarly, threads are used to replace node G's right and left linked fields such that the correct link field points to the node's inorder successor and the left link field point to the node's inorder predecessor. Other nodes with link fields with NULL values are similarly populated with threads.

Threaded Binary Trees

They lack an in-order predecessor and a successor, respectively, which explains this. Threads pointing in circles are a sign of this. Consequently, we keep a unique node known as the header node to preserve the uniformity of threads.

Operations in the threaded binary tree

A threaded binary tree can be used for three different types of operations:

  1. Insert
  2. Search
  3. Delete

Let's take a closer look at each of these operations, where I'm utilizing a double-threaded binary tree:

Insertion in the threaded binary tree

  1. The insert operation can add a new node to a threaded binary tree.

Case 1: In an empty threaded binary search tree, whenever a new node is added, its left and right pointers are set to null pointers. This process is the same for both binaries and threaded binary search trees.

Threaded Binary Trees

Case 2: When a new node is put into a binary search tree as a left child of an existing node, we conduct two operations on the parent node's struct and two operations on the child node's struct, for instance:

For the parent node, the right pointer now points to the newly added node, setting the parent's bool variable to true to indicate that a right child exists.

The complexity of time and space for insertion

O(logn) space complexity, O(log N) time complexity (1)

Search operation by a threaded binary tree

Threaded Binary Trees
If search key < root, then.
   Go to the left thread.
   Go to the right thread.

We must repeat the process described above if we successfully find the required node.

It takes a while to look.

Time complexity gets an O (logn).

Deletion operation by a threaded binary tree

In the Threaded Binary Tree, delete

Case 1: In that case, the left thread of the parent node must be made to point to the left thread of the child after deletion, and the parent's leftThread must be set to false to indicate the parent is pointing to an out-of-order predecessor.

Threaded Binary Trees

Similarly, if we delete the right child, the right thread is set to false, and the parent's right is made to point to the kid's right thread.

Threaded Binary Trees

Advantages of threaded binary tree

  1. This Tree's ability to traverse components linearly.
  2. Because it uses linear traversal instead of stacks,
  3. Allows for the automatic usage of the parent pointer when locating the parent node.
  4. Nodes hold pointers to in-order predecessor and successor nodes, allowing for forward and backward traversal of nodes in an orderly way according to a threaded tree.