presentation of data structure

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Lecture Materials

If you wish, you can read through a seven-page course description . A 21-page topic summary is also available: Algorithms and data structures—topic summary .

This is a collection of PowerPoint (pptx) slides ("pptx") presenting a course in algorithms and data structures. Associated with many of the topics are a collection of notes ("pdf"). Some presentations may be associated with videos ("V") and homework questions ("Q"), possibly with answers ("A"). Some topics also links to corresponding Wikipedia page ("W"), entries in the NIST Dictionary of Algorithms and Data Structures (DADS) ("D"), and references to cplusplus.com ("C").

You will note that the section numbering in the notes is paralleled in the top left corner of the slides; thus, anyone watching the slides can follow along in the notes.

Spanish notes translated by Christian von Lücken.

Table of contents

• Introduction and review
• Algorithm analysis
• List, stacks and queues
• Trees and hierarchical orders
• Ordered trees
• Search trees
• Priority queues
• Sorting algorithms
• Hash functions and hash tables
• Equivalence relations and disjoint sets
• Graph algorithms
• Algorithm design
• Theory of computation
• Other topics
• Concluding remarks

1. Introduction and review

2. algorithm analysis, 3. lists, stacks, and queues, 4. trees and hierarchical orders.

Before we proceed with looking at data structures for storing linearly ordered data, we must take a diversion to look at trees. At first glance, it appears as if trees are most appropriate for storing hierarchically ordered data; however, we will later see how trees can also be used to allow efficient storage of linearly ordered data, as well.

5. Ordered trees

A general tree is appropriate for storing hierarchical orders, where the relationship is between the parent and the children. There are many cases, however, where the tree data structure is more useful if there is a fixed number of identifiable children. This topic looks at binary trees as well as perfect and complete binary trees, N-ary trees, the concept of balance, binomial trees, and left-child right-sibling binary trees (a technique for storing general trees as binary trees).

6. Search trees

This topic looks at storing linearly ordered data in search trees. The focus is to ensure that operations on individual elements stored in the tree run in Θ(ln( - )) time.

7. Priority queues

A priority queue stores linearly ordered data based on the priority; however, by restricting the operations, those operations can be optimized.

8. Sorting algorithms

9. hash functions and hash tables.

Note that previously I used to teach linear probing and double hashing; however, it has been brought to my attention that quadratic hashing is better—especially when we consider the effects of caching and the additional cost of cache misses.

10. Equivalence relations and disjoint sets

11. graph algorithms, 12. algorithm design, 13. theory of computation, 14. other topics, 15. concluding remarks.

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• Data Structures
• Linked List
• Binary Tree
• Binary Search Tree
• Segment Tree
• Disjoint Set Union
• Fenwick Tree
• Red-Black Tree
• Advanced Data Structures

Introduction to Data Structures

• Data Structure Types, Classifications and Applications

Overview of Data Structures

• Introduction to Linear Data Structures
• Introduction to Hierarchical Data Structure
• Overview of Graph, Trie, Segment Tree and Suffix Tree Data Structures

Different Types of Data Structures

• Array Data Structure Guide
• String in Data Structure
• Linked List Data Structure
• Stack Data Structure

Queue Data Structure

• Introduction to Tree - Data Structure and Algorithm Tutorials
• Heap Data Structure
• Hashing in Data Structure
• Graph Data Structure And Algorithms
• Matrix Data Structure
• Data Structure Alignment : How data is arranged and accessed in Computer Memory?
• Static Data Structure vs Dynamic Data Structure
• Static and Dynamic Data Structures
• Common operations on various Data Structures
• Real-life Applications of Data Structures and Algorithms (DSA)

Different Types of Advanced Data Structures

What is data structure.

A data structure is a particular way of organising data in a computer so that it can be used effectively. The idea is to reduce the space and time complexities of different tasks. 

The choice of a good data structure makes it possible to perform a variety of critical operations effectively. An efficient data structure also uses minimum memory space and execution time to process the structure. A data structure is not only used for organising the data. It is also used for processing, retrieving, and storing data. There are different basic and advanced types of data structures that are used in almost every program or software system that has been developed. So we must have good knowledge of data structures.

Need Of Data Structure:

The structure of the data and the synthesis of the algorithm are relative to each other. Data presentation must be easy to understand so the developer, as well as the user, can make an efficient implementation of the operation. Data structures provide an easy way of organising, retrieving, managing, and storing data.

Here is a list of the needs for data.

• Data structure modification is easy. 
• It requires less time. 
• Save storage memory space. 
• Data representation is easy. 
• Easy access to the large database

Classification/Types of Data Structures:

•     Linear Data Structure
•     Non-Linear Data Structure.

  Linear Data Structure:

• Elements are arranged in one dimension ,also known as linear dimension.
• Example: lists, stack, queue, etc.

 Non-Linear Data Structure

• Elements are arranged in one-many, many-one and many-many dimensions.
• Example: tree, graph, table, etc.

Most Popular Data Structures: 

An array is a collection of data items stored at contiguous memory locations. The idea is to store multiple items of the same type together. This makes it easier to calculate the position of each element by simply adding an offset to a base value, i.e., the memory location of the first element of the array (generally denoted by the name of the array). 

Array Data Structure

2. Linked Lists :

Like arrays, Linked List is a linear data structure. Unlike arrays, linked list elements are not stored at a contiguous location; the elements are linked using pointers. 

Linked Data Structure

Stack is a linear data structure which follows a particular order in which the operations are performed. The order may be LIFO(Last In First Out) or FILO(First In Last Out). In stack, all insertion and deletion are permitted at only one end of the list.

• push(): When this operation is performed, an element is inserted into the stack.
• pop(): When this operation is performed, an element is removed from the top of the stack and is returned.
• top(): This operation will return the last inserted element that is at the top without removing it.
• size(): This operation will return the size of the stack i.e. the total number of elements present in the stack.
• isEmpty(): This operation indicates whether the stack is empty or not.

Like Stack, Queue is a linear structure which follows a particular order in which the operations are performed. The order is First In First Out (FIFO). In the queue, items are inserted at one end and deleted from the other end. A good example of the queue is any queue of consumers for a resource where the consumer that came first is served first. The difference between stacks and queues is in removing. In a stack we remove the item the most recently added; in a queue, we remove the item the least recently added. 

Queue Operations:

• Enqueue(): Adds (or stores) an element to the end of the queue..
• Dequeue(): Removal of elements from the queue.
• Peek() or front(): Acquires the data element available at the front node of the queue without deleting it.
• rear(): This operation returns the element at the rear end without removing it.
• isFull(): Validates if the queue is full.
• isNull(): Checks if the queue is empty.

5. Binary Tree :

Unlike Arrays, Linked Lists, Stack and queues, which are linear data structures, trees are hierarchical data structures. A binary tree is a tree data structure in which each node has at most two children, which are referred to as the left child and the right child. It is implemented mainly using Links. 

A Binary Tree is represented by a pointer to the topmost node in the tree. If the tree is empty, then the value of root is NULL. A Binary Tree node contains the following parts. 

Binary Tree Data Structure

6. Binary Search Tree :

A Binary Search Tree is a Binary Tree following the additional properties: 

• The left part of the root node contains keys less than the root node key.
• The right part of the root node contains keys greater than the root node key.
• There is no duplicate key present in the binary tree.

A Binary tree having the following properties is known as Binary search tree (BST).

Binary Search Tree Data Structure

A Heap is a special Tree-based data structure in which the tree is a complete binary tree. Generally, Heaps can be of two types: 

• Max-Heap: In a Max-Heap the key present at the root node must be greatest among the keys present at all of its children. The same property must be recursively true for all sub-trees in that Binary Tree.
• Min-Heap: In a Min-Heap the key present at the root node must be minimum among the keys present at all of its children. The same property must be recursively true for all sub-trees in that Binary Tree.

Max and Min Heap

8. Hashing Data Structure :

Hashing is an important Data Structure which is designed to use a special function called the Hash function which is used to map a given value with a particular key for faster access of elements. The efficiency of mapping depends on the efficiency of the hash function used. 

Let a hash function H(x) maps the value x at the index x%10 in an Array. For example, if the list of values is [11, 12, 13, 14, 15] it will be stored at positions {1, 2, 3, 4, 5} in the array or Hash table respectively. 

Hash Data Structure

9. Matrix :

A matrix represents a collection of numbers arranged in an order of rows and columns. It is necessary to enclose the elements of a matrix in parentheses or brackets. 

A matrix with 9 elements is shown below. 

Trie is an efficient information retrieval data structure. Using Trie, search complexities can be brought to an optimal limit (key length). If we store keys in the binary search tree, a well-balanced BST will need time proportional to M * log N, where M is maximum string length and N is the number of keys in the tree. Using Trie, we can search the key in O(M) time. However, the penalty is on Trie storage requirements. 

Trie Data Structure

11. Graph :

Graph is a data structure that consists of a collection of nodes (vertices) connected by edges. Graphs are used to represent relationships between objects and are widely used in computer science, mathematics, and other fields. Graphs can be used to model a wide variety of real-world systems, such as social networks, transportation networks, and computer networks.

Graph Data Structure

Applications of Data Structures:

Data structures are used in various fields such as:

• Operating system
• Computer Design
• Image Processing
• Simulation,

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Trees in Data Structures

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Data Structure Visualization

Mar 15, 2019

270 likes | 777 Views

Data Structure Visualization. Vikrant Colaso Kunal Garach Anuj Shah. Why use animation for visualizing Data Structures?. Instead of students mentally running the algorithm, the animation helps rapid perception of the data structures.

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Presentation Transcript

Data Structure Visualization Vikrant Colaso Kunal Garach Anuj Shah

Why use animation for visualizing Data Structures? • Instead of students mentally running the algorithm, the animation helps rapid perception of the data structures. • They can also dynamically portray the changes in data structures as the algorithm evolves. • User can control speed of execution and thus learn at his own pace.

Previous Work Numerous attempts have been made to prove that Visualization helps in learning. Our Study Testing Retention of Information Gained using Different Media. (Animation, Standard Text and Both)

Tests • Phase 1 • Students from CS 2604 were given a time limit of 20 minutes to learn both DFS and BFS using either the text, tool or both. • A 10 minute, multiple choice test was taken at the end to evaluate their understanding of procedural as well as conceptual aspects of the algorithms. • Phase 2 • After a period of 15 days a second test was conducted to test the retention. • Tests were designed using HTML and JavaScript in order to record the time taken on each question.

Data Collected Demographic Survey: Name, GPA, Prior knowledge of Graph and Graph searching techniques. Post Test Questionnaire: Understanding of algorithms, prediction of score, helpfulness of presented material, comments on the material. Tests: Time taken on each question, total scored on each category of questions.

Data Analysis • Using Spotfire and Excel. • ANOVA, T- tests.

Results 82% confident that there is a significant difference between T+T and Text Average scores for the Text Group is the least.

Results Contd…. Decrease in Average Scores

Better Results Contd…. This indicates a trend that degradation for the Text group is the most. 79.83% confident that there is a difference in average scores for the second test

Results Contd…. Better 61.50% confident that there is a difference in average procedural scores for the second test This indicates a trend that degradation for plain text is the most.

Results Contd…. 99.88% confident that the Text + Tool combination is rated as the most helpful.

Results Contd…. 88.62% confident that the average GPA on Text+Tool was less than that on Text

Is this relevant? 91.68% confidence that the average time taken on conceptual questions is less for tool.

Summary of Trends in data • A poor average score for those who used the text on the 2nd test. • A poorer average score on procedural questions as well for those using the text. • The textual material was the least appreciated. • GPAs of students on the text were on an average higher than those using both • the text and the tool.

Conclusions • General Comments: • Almost all the students liked the Tool and felt that it was a novel method for teaching. • Those who got the Text felt they may have done better with a graphical visualization of the data structures. • Remembering the algorithms was difficult for almost all the students however those using the tool could remember some of the steps.

Further Work Recommend that students be given a longer time/Assignments with the tool to notice a trend. Recommend testing with review of material before taking the second test. Recommend using a tool with speed control, history and other enhancements. Studies should be conducted with a larger number of students and questions.

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