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 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 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What is a 2-3 Tree in Data Structure?

Tree Data structure

The information about the tree is self-explanatory. Trees are ordered and, therefore, not linear. But they are actually designed differently. Tree A node-based data model that represents and supports the structure as a structure. In an asynchronous database, data is stored in a tree data structure called a database. All data types are stored in a central location. Each line of text is called the lower branch of the data type tree.

Two types of plants. This is limited to confidential information. Because this data processing is an individual process. So, there can be more than two children. This means that a binary plant can produce 0, 1 or, 2 seeds at any time. Binary search trees can quickly parse nested and linked expressions. This allows binary trees to provide values ??from list and associate arrays. This makes it easier to find hidden items (because it is a powerful data structure).

Properties of a tree

  1. Number of edges – A connection between two nodes in a tree data structure is called an edge. There is only one path between two file tree nodes. A positive number in this data structure is equal to -1 if all nodes in the tree data structure are equal.
  2. The circle level is the sum of all subtrees defined in the tree data structure of the selected node, called the node level. The root node level (also known as the tree level) should be the highest level relative to other nodes in the tree data structure. The leaf level of the data tree must be zero (0).
  3. Tree Level – The root node level is the tree level.

Types of trees in data structures

Now that we know what trees are let us now learn the different types of trees in data structures.

There are six types of trees in the data structure, and they are mentioned below:

  1. General tree
  2. Binary tree
  3. Binary search tree
  4. AVL tree (Adelson, Velskii, & Landis Tree)
  5. Red-Black tree
  6. N array tree

Binary trees

These types of trees have constraints (rules) on their hierarchy. All the nodes of a binary tree either have two or zero (0) child nodes. The two child nodes of a binary tree are treated as the left child node and right child node, respectively. The binary trees are the most popular trees among all the other trees in data structures. Other trees like BST (Binary search tree) and AVL tree (Adelson, Velskii, & Landis Tree) are formed from binary trees by applying some specific constraints.

These types of trees have constraints (rules) on their hierarchy. All the nodes of a binary tree either have two or zero (0) child nodes. The two child nodes of a binary tree are treated as the left child node and right child node, respectively. The binary trees are the most popular trees among all the other trees in data structures. Other trees like BST (Binary search tree) and AVL tree (Adelson, Velskii, & Landis Tree) are formed from binary trees by applying some specific constraints. AVL trees (Adelson, Velskii, & Landis Tree) are formed from binary trees by applying some constraints.

Note:

Height balanced tree

A height-balanced tree is a type of binary tree. If the absolute difference between the heights of the left and right subtree is less than or equal to 1, then the given binary tree is considered a height-balanced binary tree. This height-balanced tree includes the AVL tree (Adelson, Velskii & Landis Tree) and the red-black tree.

Note:

Best case

The possibility of solving an algorithm in its shortest time is known as the best case.

Average case

The possibility of solving an algorithm in its average time is known as the average case.

Worst case

The possibility of solving an algorithm in its greatest period is known as the worst case.

Note:

B+ tree

A specialized m – way tree, which is popularly used for disc access, is known as a B tree. The B+ tree is considered an extension of the B tree. It allows efficiency in search, deletion, and insertion operations.

B- tree

B- trees are self-balancing trees in data structures. It not only allows search deletions in logarithmic time, insertions, and sequential access but also maintains sorted data. Binary search trees are a part of B- trees (Binary search trees must have a maximum of only two children for each node, while B- trees can have more than two children for all the nodes present in the tree). B- trees differ from other self-balancing trees due to their efficient storage systems that write as well as read huge blocks of data (for example, in file systems, databases, etc.)

2 – 3 Trees

We know that the average case consumption of time to perform deletion, insertion, and search operations in a binary tree is given by O (log N) [Where N represents the number of nodes present in a given tree]. We also know that the worst-case consumption of time to perform deletion, insertion, and search operations in a binary tree is given by O (log N) [Where N represents the number of nodes present in a given tree].

2 – 3 tree is a height-balanced tree-like AVL tree (Adelson, Velskii, & Landis Tree), B tree, and Red-black tree.

We can consider a 2-3 tree as a B-tree with an order of 3.

Properties of 2 3 tree:

The properties of a 2 3 tree are mentioned below:

  1. The parent nodes of a 2-3 tree that have 2 child nodes are called 2–nodes. They possess two child nodes and one data value.
  2. The parent nodes of a 2-3 tree that have 3 child nodes are called 3–nodes. They possess three child nodes and two data values.
  3. The data of that is present in a 2-3 tree is stored in a sorted manner.
  4. 2 3 trees are balanced trees.
  5. All the leaf nodes of a 2 3 tree are present at a common level.
  6. In a 2 3 tree, each one among all the nodes belongs to one of the following categories: 3–node, 2–node, or leaf node.
  7. The insertion operation in a 2–3 tree is done at the leaf nodes of the tree.
  8. We follow two steps, namely base cases and recursive calls to perform search operations in a given 2–3 tree.
  9. We can perform the insertion operation in a 2–3 tree with 3 possible cases: insertion operation on a node that has one data value, insertion operation on a node that has two data values and its parent node contains one data value, insertion operation on a node that has two data values, and its parent node also contains two data values.
  10. We can also perform deletion operations in a 2–3 tree.
  11. The 2-3 tree is not a binary tree.
  12. All the nodes in a 2–3 tree that are not external nodes contain either two or three child nodes.