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 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 a Spanning Tree in Data Structure

Data structures

Data management is called database management. This allows the computer to sort or organize the data for efficient retrieval. A data model is a system used to store, manage, and optimize computer resources. Data processing is not just about data storage. Almost every app or program has notices and updates about its version. Data structures are so simple and complex that it is difficult to program with a programming language that does not have data structures.

Data processing is the process of using intelligence and software to manage, organize, store and store information on a computer device or system. Data models provide visualization for easy data organization and management. Any basic process, program, or program has two parts: data and algorithms - the rules and regulations of data exchange and algorithms.

There are two types of data structures

  1. Linear Data structures
  2. Non-linear data structures

Linear Data structures

This data type adds data to the data type. It's all about the process. You can then delete the duplicate. There are four types of linear data, they are:

  1. Queue
  2. Stack
  3. Linked lists
  4. Array

Non-linear Data structures

Data formats can be created in a variety of ways. There are two types of interpersonal communication:

  1. Tree data structure
  2. Graph 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)

Graph data structure

The graph has two sets, which are considered V and E. These vertices are also called nodes, and edges are referred to as arcs connecting any two nodes in a graph. In a simple sentence, we can say that graph- is a set of vertices (V) and edges (E) which is denoted as G (V, E). These are usually accustomed to solving several real-time problems efficiently. These generally represent networks like a city's telephones, circuitry, and paths. These are also used on many social platforms like Facebook, LinkedIn, etc. Let us consider an example of each user or person on Facebook as a vertex (or node) in the graph. Each vertex has information about the user, like name, gender, etc., and the connection between each node or vertex is considered as edges or arcs. These are also used in the operating system as resource location graphs.

These are also used in Google maps to find the shortest distance between two places, these are also used in airlines to know the best effective route, used in transportation, in circuits it is used to represent the nodes or circuitry points, these are used to solve challenging puzzles like mazes, these are also used in computer networking, there are many advantages of using graphs like it is straightforward to work with the algorithms like DFS and BFS, it has many practical applications, because of its nature(non-linear data structure) it is used in solving many complex problems, it helps in understanding and visualizing complex issues. As we know, every coin has the other side. Similarly, graphs also have a few disadvantages; they generally use many pointers, which are very difficult to manage and require large memory.

Spanning tree

The subsets of graphs where all the vertices of the graphs are covered with the minimum number of edges that are possible are called spanning trees. Therefore, we can conclude that a spanning tree can have no cycles nor can be disconnected between any two vertices of the graph (It must be a connected graph)


Connected graph

A graph that has at least one possible path with connected edges between any two selected vertices of the same graph is known as a connected graph.

Disconnected graph

A graph that has at least two adjacent vertices of the same graph that are disconnected (do not have an edge between them) is known as a disconnected graph.

Based on the definition of a spanning tree, we can observe that all the uni-directed and connected graphs have at least one spanning tree. A disconnected graph does not have any spanning tree, as a path cannot be formed between the two disconnected vertices.


Uni-Directed graph

The graphs whose edges are directed in a single direction are treated as uni-direction graphs.

Cyclic graphs

The graphs whose edges form at least one cycle or loop are called cyclic graphs.

Acyclic graphs

The graphs whose edges do not form any cycles or loops are called acyclic graphs.

Therefore, it can be concluded that a single connected graph can possess more than one spanning tree. Spanning trees are subsets of the original graph, and disconnected graphs can never possess a spanning tree.

Properties of spanning trees

Let us look at the properties of spanning trees:

  1. A single connected graph can possess more than one spanning tree.
  2. The number of edges of all the spanning trees formed from a single graph G is equal.
  3. Spanning trees are acyclic in nature, i.e., they do not contain any loops.
  4. We depict a spanning tree to be minimally connected, i.e., if an edge is removed between any two vertices of a spanning tree, then it becomes disconnected.
  5. We also depict a spanning tree to be minimally acyclic, i.e., if an edge is added between any two vertices of a spanning tree, then it becomes cyclic in nature.

Mathematical Properties of spanning trees

Let us look at the mathematical properties of spanning trees:

  1. If a spanning tree has N number of vertices, then its number of edges is given by (n – 1)
  2. A spanning tree can be constructed by removing a maximum number of e – n + 1 edges from a given graph G.
  3. A maximum of n n – 2 number of spanning trees can be formed for a given complete graph.

Applications of spanning trees

Spanning trees have many applications in data structures. Some of the applications are given below:

  1. Spanning trees are used in civil network planning
  2. Spanning trees are used in computer network routing protocols.
  3. Spanning trees are used in cluster analysis.