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Problem Solving with Algorithms and Data Structures using Python ¶

By Brad Miller and David Ranum, Luther College

There is a wonderful collection of YouTube videos recorded by Gerry Jenkins to support all of the chapters in this text.

• 1.1. Objectives
• 1.2. Getting Started
• 1.3. What Is Computer Science?
• 1.4. What Is Programming?
• 1.5. Why Study Data Structures and Abstract Data Types?
• 1.6. Why Study Algorithms?
• 1.7. Review of Basic Python
• 1.8.1. Built-in Atomic Data Types
• 1.8.2. Built-in Collection Data Types
• 1.9.1. String Formatting
• 1.10. Control Structures
• 1.11. Exception Handling
• 1.12. Defining Functions
• 1.13.1. A Fraction Class
• 1.13.2. Inheritance: Logic Gates and Circuits
• 1.14. Summary
• 1.15. Key Terms
• 1.16. Discussion Questions
• 1.17. Programming Exercises
• 2.1.1. A Basic implementation of the MSDie class
• 2.2. Making your Class Comparable
• 3.1. Objectives
• 3.2. What Is Algorithm Analysis?
• 3.3. Big-O Notation
• 3.4.1. Solution 1: Checking Off
• 3.4.2. Solution 2: Sort and Compare
• 3.4.3. Solution 3: Brute Force
• 3.4.4. Solution 4: Count and Compare
• 3.5. Performance of Python Data Structures
• 3.7. Dictionaries
• 3.8. Summary
• 3.9. Key Terms
• 3.10. Discussion Questions
• 3.11. Programming Exercises
• 4.1. Objectives
• 4.2. What Are Linear Structures?
• 4.3. What is a Stack?
• 4.4. The Stack Abstract Data Type
• 4.5. Implementing a Stack in Python
• 4.6. Simple Balanced Parentheses
• 4.7. Balanced Symbols (A General Case)
• 4.8. Converting Decimal Numbers to Binary Numbers
• 4.9.1. Conversion of Infix Expressions to Prefix and Postfix
• 4.9.2. General Infix-to-Postfix Conversion
• 4.9.3. Postfix Evaluation
• 4.10. What Is a Queue?
• 4.11. The Queue Abstract Data Type
• 4.12. Implementing a Queue in Python
• 4.13. Simulation: Hot Potato
• 4.14.1. Main Simulation Steps
• 4.14.2. Python Implementation
• 4.14.3. Discussion
• 4.15. What Is a Deque?
• 4.16. The Deque Abstract Data Type
• 4.17. Implementing a Deque in Python
• 4.18. Palindrome-Checker
• 4.19. Lists
• 4.20. The Unordered List Abstract Data Type
• 4.21.1. The Node Class
• 4.21.2. The Unordered List Class
• 4.22. The Ordered List Abstract Data Type
• 4.23.1. Analysis of Linked Lists
• 4.24. Summary
• 4.25. Key Terms
• 4.26. Discussion Questions
• 4.27. Programming Exercises
• 5.1. Objectives
• 5.2. What Is Recursion?
• 5.3. Calculating the Sum of a List of Numbers
• 5.4. The Three Laws of Recursion
• 5.5. Converting an Integer to a String in Any Base
• 5.6. Stack Frames: Implementing Recursion
• 5.7. Introduction: Visualizing Recursion
• 5.8. Sierpinski Triangle
• 5.9. Complex Recursive Problems
• 5.10. Tower of Hanoi
• 5.11. Exploring a Maze
• 5.12. Dynamic Programming
• 5.13. Summary
• 5.14. Key Terms
• 5.15. Discussion Questions
• 5.16. Glossary
• 5.17. Programming Exercises
• 6.1. Objectives
• 6.2. Searching
• 6.3.1. Analysis of Sequential Search
• 6.4.1. Analysis of Binary Search
• 6.5.1. Hash Functions
• 6.5.2. Collision Resolution
• 6.5.3. Implementing the Map Abstract Data Type
• 6.5.4. Analysis of Hashing
• 6.6. Sorting
• 6.7. The Bubble Sort
• 6.8. The Selection Sort
• 6.9. The Insertion Sort
• 6.10. The Shell Sort
• 6.11. The Merge Sort
• 6.12. The Quick Sort
• 6.13. Summary
• 6.14. Key Terms
• 6.15. Discussion Questions
• 6.16. Programming Exercises
• 7.1. Objectives
• 7.2. Examples of Trees
• 7.3. Vocabulary and Definitions
• 7.4. List of Lists Representation
• 7.5. Nodes and References
• 7.6. Parse Tree
• 7.7. Tree Traversals
• 7.8. Priority Queues with Binary Heaps
• 7.9. Binary Heap Operations
• 7.10.1. The Structure Property
• 7.10.2. The Heap Order Property
• 7.10.3. Heap Operations
• 7.11. Binary Search Trees
• 7.12. Search Tree Operations
• 7.13. Search Tree Implementation
• 7.14. Search Tree Analysis
• 7.15. Balanced Binary Search Trees
• 7.16. AVL Tree Performance
• 7.17. AVL Tree Implementation
• 7.18. Summary of Map ADT Implementations
• 7.19. Summary
• 7.20. Key Terms
• 7.21. Discussion Questions
• 7.22. Programming Exercises
• 8.1. Objectives
• 8.2. Vocabulary and Definitions
• 8.3. The Graph Abstract Data Type
• 8.4. An Adjacency Matrix
• 8.5. An Adjacency List
• 8.6. Implementation
• 8.7. The Word Ladder Problem
• 8.8. Building the Word Ladder Graph
• 8.9. Implementing Breadth First Search
• 8.10. Breadth First Search Analysis
• 8.11. The Knight’s Tour Problem
• 8.12. Building the Knight’s Tour Graph
• 8.13. Implementing Knight’s Tour
• 8.14. Knight’s Tour Analysis
• 8.15. General Depth First Search
• 8.16. Depth First Search Analysis
• 8.17. Topological Sorting
• 8.18. Strongly Connected Components
• 8.19. Shortest Path Problems
• 8.20. Dijkstra’s Algorithm
• 8.21. Analysis of Dijkstra’s Algorithm
• 8.22. Prim’s Spanning Tree Algorithm
• 8.23. Summary
• 8.24. Key Terms
• 8.25. Discussion Questions
• 8.26. Programming Exercises

Acknowledgements ¶

We are very grateful to Franklin Beedle Publishers for allowing us to make this interactive textbook freely available. This online version is dedicated to the memory of our first editor, Jim Leisy, who wanted us to “change the world.”

Indices and tables ¶

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Browse Course Material

Course info.

• Prof. Erik Demaine

Departments

• Electrical Engineering and Computer Science

As Taught In

• Algorithms and Data Structures

Learning Resource Types

Advanced data structures, assignments.

• There will be a weekly one-page assignment, 10 assignments in total.
• You may skip any one problem, or we will ignore the problem with the lowest grade. If you volunteered to scribe twice, we will ignore the lowest two grades.
• The answers must be typeset in LaTeX. The answers must fit in one page, or your solution will not be read. Use at least 10 pt font and 1 inch margins. This rule is meant to prepare you for writing research publications: one often has to explain great ideas in a very limited number of pages.
• Submissions must be made online and consist of a compiled PDF document.
• Grades and comments will be posted online.
• Solutions do not need to include all calculations, trivial details etc. Just prove to us that you found the solution, and you understand it well.
• 0 = You didn’t get it. Filling one page to the brim does not mean you can’t get zero. Please don’t write stuff you know is wrong.
• 1 = Your solution was ultimately a good one, but the write-up contained significant errors or omissions.
• 2 = (We think) you got it.

PROBLEM SETS	SOLUTIONS

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Announcements

We will be holding our office hours starting next week:

• Keith : Wednesdays, 3PM - 5PM in Durand 317.
• Kevin : Fridays, 2PM - 4PM in Huang Baseement.

Welcome to CS166, a course in the design, analysis, and implementation of data structures. We've got an exciting quarter ahead of us - the data structures we'll investigate are some of the most beautiful constructs I've ever come across - and I hope you're able to join us.

CS166 has two prerequisites - CS107 and CS161. From CS107, we'll assume that you're comfortable working from the command-line; designing, testing, and debugging nontrivial programs; manipulating pointers and arrays; using bitwise operators; and reasoning about the memory hierarchy. From CS161, we'll assume you're comfortable designing and analyzing nontrivial algorithms; using O, o, Θ, Ω, and ω notation; solving recurrences; working through standard graph and sequence algorithms; and structuring proofs of correctness.

We'll update this site with more information as we get closer to the start of the quarter. In the meantime, feel free to email me at [email protected] if you have any questions about the class!

Schedule and Readings

This syllabus is still under construction and is subject to change as we fine-tune the course. Stay tuned for more information and updates!

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. . run quickly, at least in an amortized sense. Today we'll see why this operation is so important, as well as how to make the operation run quickly by pulling together many ideas we've seen in the course of our exploration of amortization.

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Tuesday	Thursday
This first lecture explores word-level parallelism through a data structure for very small integers and a technique for computing most-significant bits in time O(1). It will lay the groundwork we'll use next time when exploring fusion trees. Slides: Readings: to compute most-significant bits in time O(1).
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• DSA Tutorial
• Data Structures
• Linked List
• Dynamic Programming
• Binary Tree
• Binary Search Tree
• Divide & Conquer
• Mathematical
• Backtracking
• Branch and Bound
• Pattern Searching

10 Best Data Structures and Algorithms Courses [2024]

With advancement, it’s important to walk with the trend. As you can see, the world is moving more towards IT, and everyone wants to upskill themselves with the best domains. And when we talk about the best IT domains, software development can’t be ignored. One thing that you must have a good grip on before entering the world of development is Data Structures and Algorithms . Undoubtedly, DSA is the most important skill that every good tech firm seeks in a software engineer or developer. 

Every leading tech giant, be it service-based to product-based (such as Google, Microsoft, Amazon, Meta, and Twitter) hires programmers/developers who are well-versed in the concepts of Data Structures and Algorithms. Also, DSA-based coding questions are asked in their tech interview rounds – thus, to crack their coding rounds, you must be good at DSA.

Learning DSA is quite important as Data Structures are the building block of software development and Algorithms provide efficiency while solving a problem. Hence, learning DSA will make you a better problem-solver and help you crack coding rounds in tech companies. To ease your learning, here are some of the best data structures and algorithms courses every developer must read. 

Table of Content

Best Courses for Data Structures and Algorithms(DSA)

1. data structures and algorithms – self-paced (geeksforgeeks), 2. advanced data structures (mit), 3. data structures and algorithms python – the complete bootcamp (udemy), 4. master the coding interview: data structures + algorithms (udemy), 5. algorithms, part i, and algorithms, part ii (princeton university), 6. algorithms specialization (stanford university), 7. algorithms course by iit bombay (edx), 8. data structures and algorithms (nptel), 9. data structures and algorithms in java (university of california san diego), 10. intro to data structures and algorithms (udacity).

The Data Structures and Algorithms – Self-Paced course , offered by GeeksforGeeks, is one of the most-recommended courses to learn Data Structures & Algorithms and requires no prior knowledge of DSA. The entire course has been covered using the two most demanding programming languages: C++ and Java. In this course, you’ll get premium video lectures by Mr. Sandeep Jain, Founder of GeeksforGeeks . It has recorded videos, practice problems, assessment tests, etc and you can learn at your own pace. This is a complete package that has been divided into 8 weeks of your learning period. It also comes at a pocket-friendly price. You can also get 24X7 doubt assistance for 6 months. If you’re a learner, you can also solve real-world tech problems. Hence, this course provided by GeeksforGeeks is a must-read course if you want to grow in your software development career. This Data Structures and Algorithms – Self-Paced course on GeeksforGeeks has already thousands of students land their dream jobs in tech giants like Microsoft, Amazon, Amdocs, etc.  

What Will You Learn:

• Basics (Time and Space Complexity, practice problems)
• Mathematics 
• Bitwise Operators
• Searching and Sorting
• Matrix, Hashing, and Strings
• Linked List, Stack, Queue, and Deque
• Tree, Heap, and, Graph
• Segment Tree
• Disjoint Set, etc. 

Are you an aspiring SDE? This course is specially designed for you to get placed in top tech companies like Google, Microsoft, and Amazon, here’s the right course for you. Covered with all these rich features, this is the best course for DSA. 

• Level: Beginner to Intermediate
• Price: Paid (at an affordable price)
• Certification: Available

Course Link: Data Structures and Algorithms – Self-Paced (GeeksforGeeks)

Another best course for Data Structure and Algorithms is Advanced Data Structures by MIT(Massachusetts Institute of Technology) Open Courseware. This course has the best lectures which are divided into 2 sessions per week, 1.5 hours per session. You must have a basic knowledge of Data Structures and Algorithms before starting this course. It is one of the oldest courses but as said “Old is Gold”, this course covers all the basic to advanced concepts of DSA . It comes up with lecture videos and hand-written notes, you must have a habit of scribing lectures, and work on given assignments (posted weekly), and projects. This course is mostly recommended for graduate-level students who have got prior knowledge of DSA basics. 

• Time travel
• Dynamic optimality
• Memory hierarchy
• Dynamic graphs
• Succinct, etc.

No certificate is provided in this course. So, if you’re interested more in learning, rather than grabbing certificates, this course is designed for you. You’ll be able to crack coding interviews with top tech companies after learning this course.

• Level: Graduate level
• Price: Free

This course provided by Udemy is the best-known DSA course for beginners . This course covers every topic from concept, and visualization, to the implementation part. You need to have basic knowledge of Python, to begin with, this course. Also, there’s a lifetime accessibility you get with this course. It includes tons of examples and quizzes which you get after learning each topic that’s why it is step-by-step from scratch. Once done with this, you’ll be able to solve questions yourself and work on implementing projects. You improve your problem-solving skills, understand complex topics such as searching, sorting, and traversal, and work on codes for the implementation of each data structure. 

• Basic Concepts (Big O Notation)
• Arrays, Linked List
• Stack and Queue
• Hash and Trees
• Heaps and Tries
• Tree and Graph Traversal
• Problem-Solving, etc. 

Anyone looking to get into product-based companies can enroll in this course and be ready for the interview rounds. No matter whether you’re from a non-tech background, this is purely a beginner-level course. 

• Duration: 20 hours 
• Level: Basic
• Price: Paid

Again, this is a great course for Data Structure and Algorithms provided by Udemy to help you ace coding interviews . Before, you start this course, also know that you should have an idea of JavaScript. It’s completely fine if you don’t have prior knowledge of DSA or computer science, this course covers all. You also get access to a private online chat community with developers to help you along with the course. Learn, implement, and use different data structures and algorithms . You become more confident and prepared for your coding interview rounds. Also, it comes in many languages such as French, Japanese, Spanish, and Turkish, etc. Overall, when you read this course completely, each of the DSA concepts will get clear. 

• Basics (Big O, Coding Problems)
• Arrays and Hash Tables
• Linked Lists
• Stacks and Queues
• Trees and Graphs
• Recursion, Searching (BFS, DFS), and Sorting
• Interview Ready

Want to land a job at the best tech company like Google, Microsft, Netflix, Meta, and Amazon, this course paves the way to get into it. You can easily crack coding interviews using this course. 

• Duration: 19.5 hours 

One of the best courses for learning DSA at Princeton University is provided by Coursera. This course entails all the important topics that every developer must know in order to build efficient software using DSA. It is a six-week designed course. This course is divided into two parts to ease your path in learning DSA.

• Part I mostly focuses on elementary data structures, sorting, and searching algorithms whereas 
• Part II focuses on the graph and string-processing algorithms.

It comes with flexible deadlines, and you can learn at your own pace. You must have a basic knowledge of Java before start learning this DSA course. It significantly focuses on graphs, data compression, data structures, and algorithms. Also, it is free so you can access it anytime, anywhere. 

• Data Structure and Algorithms
• Undirected and directed graphs
• Minimum Spanning Tree
• Radix Sorts
• Substring Search
• Regular Expressions
• Data Compression
• Linear Programming
• Intractability, etc.

This course is designed for those developers who already have an insight into working with DSA. It is recommended to have at least basic knowledge of Data Structures and Algorithms before learning this course. 

• Duration: 54 hours 
• Level: Intermediate

The next best DSA course provided by Coursera is Algorithms Specialization by Stanford University. Through this course, you’ll learn the fundamentals of algorithms and data structure and how it is required in every discipline of computer science. It will help all the programmers/developers to enhance their programming and logical-building skills. In this course, you’ll get to practice and master the fundamentals of algorithms with assessments. Every weekend you’ll get a set of MCQs to test your learning. Along with that, you also attend weekly programming assignments wherein you’ve to implement one algorithm using your desired programming language. In the end, there’s an MCQ-based final exam. 

• Asymptotic “Big-oh” notation
• Sorting and searching algorithms
• Master method 
• Quicksort algorithm
• Heaps and Balanced Search Trees
• Hash Tables and Bloom Filters
• Dijkstra’s algorithm
• Breadth First and Depth First Search 
• Greedy algorithms
• Dynamic programming
• Shortest paths algorithms
• NP problems 
• Local search algorithms

This course acts as a complete package for those who want to crack technical interviews and dive deeper into algorithms concepts. Complete this course with the hands-on project and grab a certificate at the end. 

• Duration: 4 months
• Certificate: Available

Another best DSA course is provided by IIT Bombay (edX) – Algorithms which is a self-paced one. This is a six-week course wherein you’ve to spend only 6-8 hours per week. Also, it is free and there’s an option for upgrading the course in case you need it. In this course, you’ll learn to work with algorithms and also you can create them using sorting techniques like merge sort, quick sort, median finding, and searching algorithms. You need to have basic knowledge of data structures and their implementation. This course teaches you the best techniques to solve problems and how to make them efficient. You’ll learn on working with problems using algorithms and how data structures and algorithms can be used to design scaled-system.

• Sorting algorithms 
• Searching algorithms
• Median finding
• Order statistics
• Geometric algorithms (Polynomial Multiplication)
• String algorithms
• Numerical algorithms
• Matrix Operations, GCD, and Pattern Matching
• Subsequences, Sweep, and Convex Hull
• Graph algorithms, etc.  

Since Algorithms hold the biggest power for all web companies and the most promising startups to function. This course is designed for aspiring developers to crack technical interviews and get placed at big tech companies.

• Duration : 6 weeks

This DSA course offered by NPTEL (National Programme on Technology Enhanced Learning) is again the best course for DSA. Lectured by Prof. Naveen Garg (IIT, Delhi), this course has 36 lectures in which you’ll get to learn well-explained concepts of DSA. The main objective of this course is to clear the basic concepts of DSA and their use in fundamental algorithms. This course is free for learning but if you need a certificate along with learning, you need to sign up with the NPTEL portal and then continue. Also, there’ll be case studies given to explain the concepts clearly. 

• Introduction to DSA
• Stacks, Linked Lists, and Queues
• Dictionaries and Hashing
• Trees and Traversals
• Ordered Dictionaries
• Avial Trees
• Priority Queues
• Binary Heaps
• Breadth-First Search and Depth-First Search
• Dijkstra’s Algorithms
• Single Source Shortest Paths, etc. 

This course provided by NPTEL has great value if you gain a certificate. This course will explain all the concepts of DSA so well that you’ll be able to crack any tech interview in top tech companies. 

• Duration: 12 weeks
• Certificate: Available (For Paid Version)

The next course to learn and master DSA is Data Structures and Algorithms in Java by the University of California San Diego. This course helps you in solving computational problems. Using the programming assignments offered in this course, you’ll learn to implement those in various programming languages. You need to have a basic knowledge of object-oriented programming language and Java before beginning this course. You’ll be able to write scalable code by applying the required DSA in the right scenarios. 

• Dynamic arrays
• Disjoint Sets
• Hash Tables
• Binary Search Tree, etc. 

By learning this course, you’ll be able to answer complex data structures and algorithms problems and with that, you can easily crack programming interviews . Also, in the corporate world, you can implement those DSA concepts in software development domains. 

• Duration: 25 hours (it may take a week, depending on your hours of learning)

The next free DSA course by Udacity, which is Intro to Data Structures and Algorithms comes with immense rich features. It includes rich learning content and self-paced learning which eases your way of learning DSA. This course also comes with interactive quizzes which help you in testing your knowledge in DSA. It is a video-based tutorial and has experienced engineers who review your supplementary examples. Also, you’ll get exercises to solve which makes you ready to solve industry-ready problems. 

• Introduction and Efficiency
• List-Based Collections
• Maps and Hashing
• Case Studies in Algorithms
• Technical Interviewing Questions
• Practice Interviews, etc. 

Through this course, you’ll learn how to explain your solutions to technical problems. Get ready to grab a good job offer through this free course. 

• Duration: 4 Weeks
• Certificate: Available 

**This list is prepared by our internal team after a comprehensive research practice. You can opt for any of the course(s) mentioned in the list (or other than these), based on your own requirements & preferences, to start learning DSA. Though, irrespective of the course you choose, be consistent and dedicated to the learning process to achieve the targeted goals. ** 

When it comes to cracking tech interviews, DSA is the first and foremost topic that hits any software developer’s mind. To help you in learning DSA , the above-mentioned are some of the best courses for Data Structures and Algorithms . All the courses mentioned above have rich content, and well-explained lecture videos, and are also the best ones. Choosing any of the best courses will definitely help you in paving the way to entering into the corporate (or tech) world.

Related Courses: Complete Interview Preparation Mastering System Design Course Complete Data Science Program

Best Data Structures and Algorithms Courses – FAQs

Is there any roadmap for beginners to learn dsa.

Yes, if you’re a beginner, here’s a Complete Roadmap To Learn DSA From Scratch .

Why DSA is important for placement?

Learning DSA increases your chances of getting hired by big tech companies, the reason being – it helps in solving the problem in a more optimized manner and thus makes the program efficient and effective. It gives you an idea of choosing the best algorithm at the right place. 

Is DSA important for web development?

Although it’s nothing like without DSA, you can’t go for web development – learning DSA helps you to come up with more optimized solutions. Since, DSA is the basic building block of software development, having sufficient knowledge of DSA would help you to deliver efficient solutions. For example, while building a website, DSA becomes necessary for efficient storage management to make your website run faster.

Where DSA is actually used?

DSA is used in various modules of software development. Some of the best use cases of DSA are: Linked Lists: can be used in music players while switching the music. Stacks: Messages, and call logs in a cell phone are arranged in stacks Queues: The request is being responded to by the server Graph: GPS navigation system used shortest path APIs Tree: Indexing in databases

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• Assignments

Description. This course surveys the most important algorithms and data structures in use on computers today. Particular emphasis is given to algorithms for sorting, searching, graphs, and strings. The course concentrates on developing implementations, understanding their performance characteristics, and estimating their potential effectiveness in applications.

Prerequisites. COS 126 or approval by the COS placement officer.

Precepts. Precepts meet once per week and cover details pertinent to programming assignments, quizzes, and exams. Come prepared to participate in the discussion, not just ask questions. This includes reading the assignment specification before the corresponding precept.

Faculty Instructor	Faculty Instructor	Faculty Instructor
Graduate Student Preceptor	Graduate Student Preceptor	Graduate Student Preceptor
Graduate Student Preceptor	Graduate Student Preceptor	Graduate Student Preceptor

Review sessions. Review sessions meet at 2:30–3:20pm on Friday afternoons in CS 105. They are intended for students seeking extra help to keep up with the course materials, featuring a weekly recap, Q&A session, and active-learning activities.

Office hours. You are welcome to attend the office hours of any staff member. Office hours are listed on the Help page.

	TIME	LOCATION	PERSON	FACILITATORS
	T Th 11–12:20pm	Friend 101	Kevin Wayne	–
	Th 3–4:20pm	Friend 108	Dan Leyzberg	Kenny Lam Saumya Malik Niva Sivakumar
	Th 7:30–8:50pm	Friend 004	Morgan Nanez	Ty Kay Andrew Tao Dwaipayan Saha
	F 11–12:20pm	Friend 108	Max Tchouambe	Mary Tsahas Aditya Mehta
	F 11–12:20pm	Sherrerd 001	Yingxi Lin	Alex Zhang Emmy Song Harvey Wang
	F 1:30–2:50pm	Julis Romo A12	Dan Leyzberg	Cecilia Zubler Kartik Shah
	F 1:30–2:50pm	Julis Romo A87	Weicong Dong	Bryan Wang Brian Tieu
	F 3–4:20pm	Julis Romo A97	Ryan Torok	Rebecca Zhu Arya Maheshwari Zachary Siegel
	F 3–4:20pm	cancelled	–	–
	F 11–12:20pm	Julis Romo A97	Gabriel Contreras	Samuel Frank Jerry Huang

Need to switch into a full precept? Please contact Colleen Kenny .

ASSESSMENTS

Programming assignments. The programming assignments involve applying the material from lecture to solve problems in science, engineering, and commerce.

Course website. This course website includes links to course content, including lecture slides, precept lessons, programming assignments, quizzes, and old exams.

Discussion forum. The best way to ask a short question about the course materials is via Ed Discussion , an online discussion forum where you can ask (and answer) questions.

• Computer Science and Engineering
• Data Structures And Algorithms (Video) 
• Co-ordinated by : IIT Delhi
• Available from : 2009-12-31
• Introduction to Data Structures and Algorithms
• Queues and Linked Lists
• Dictionaries
• Tree Walks / Traversals
• Ordered Dictionaries
• Red Black Trees
• Insertion in Red Black Trees
• Disk Based Data Structures
• Case Study: Searching for Patterns
• Data Compression
• Priority Queues
• Binary Heaps
• Why Sorting
• More Sorting
• Data Structures for Graphs
• Two Applications of Breadth First Search
• Depth First Search
• Applications of DFS
• DFS in Directed Graphs
• Applications of DFS in Directed Graphs
• Minimum Spanning Trees
• Prims Algorithm for Minimum Spanning Trees
• Single Source Shortest Paths
• Correctness of Dijkstras Algorithm
• Watch on YouTube
• Assignments
• Transcripts

Sl.No	Chapter Name	English
1	Introduction to Data Structures and Algorithms
2	Stacks
3	Queues and Linked Lists
4	Dictionaries
5	Hashing
6	Trees
7	Tree Walks / Traversals
8	Ordered Dictionaries
9	Deletion
10	Quick Sort
11	AVL Trees
12	AVL Trees
13	Trees
14	Red Black Trees
15	Insertion in Red Black Trees
16	Disk Based Data Structures
17	Case Study: Searching for Patterns
18	Tries
19	Data Compression
20	Priority Queues
21	Binary Heaps
22	Why Sorting
23	More Sorting
24	Graphs
25	Data Structures for Graphs
26	Two Applications of Breadth First Search
27	Depth First Search
28	Applications of DFS
29	DFS in Directed Graphs
30	Applications of DFS in Directed Graphs
31	Minimum Spanning Trees
32	The Union
33	Prims Algorithm for Minimum Spanning Trees
34	Single Source Shortest Paths
35	Correctness of Dijkstras Algorithm
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Title: a tighter complexity analysis of sparsegpt.

Abstract: In this work, we improved the analysis of the running time of SparseGPT [Frantar, Alistarh ICML 2023] from $O(d^{3})$ to $O(d^{\omega} + d^{2+a+o(1)} + d^{1+\omega(1,1,a)-a})$ for any $a \in [0, 1]$, where $\omega$ is the exponent of matrix multiplication. In particular, for the current $\omega \approx 2.371$ [Alman, Duan, Williams, Xu, Xu, Zhou 2024], our running times boil down to $O(d^{2.53})$. This running time is due to the analysis of the lazy update behavior in iterative maintenance problems, such as [Deng, Song, Weinstein 2022, Brand, Song, Zhou ICML 2024].

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Knowledge and data fusion-driven dynamical modeling approach for structures with hysteresis-affected uncertain boundaries

• Published: 23 August 2024

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• Chao Chen 1 ,
• Yilong Wang 1 ,
• Shuai Chen 1 ,
• Bo Fang 1 &
• Dengqing Cao 1 , 2  

This paper introduces a novel approach for modeling the dynamics of structural systems, addressing challenges posed by uncertain boundary conditions and hysteresis forces. The methodology integrates low-dimensional dynamical modeling techniques with a blend of traditional knowledge-driven and contemporary data-driven methods. Applied to a flexible beam doubly constrained by uncertain forces containing hysteresis, this hybrid approach demonstrates the effectiveness of combining the knowledge-driven global mode method (GMM) with data-driven technologies. The GMM is employed to model the known components of the structure, while the transformer neural network (TNN) focuses on simulating the hysteresis-affected uncertain boundaries. The differential evolution algorithm is used to identify the parameters that influence the natural characteristics of the system. A comparative study is performed to demonstrate the validity of the developed model and its superior in computation time—99.2% less than that of employing the finite element models. This study establishes a robust theoretical basis for advancing dynamical modeling of systems with complex boundary conditions.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant No. 12202116 and the Natural Science Foundation of Heilongjiang Province under Grant No. LH2023A003.

National Natural Science Foundation of China under Grant Nos.12202116 and Natural Science Foundation of Heilongjiang Province under Grant No.LH2023A003.

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School of Astronautics, Harbin Institute of Technology, Harbin, 150001, China

Chao Chen, Yilong Wang, Shuai Chen, Bo Fang & Dengqing Cao

Center for Dynamics and Intelligent Control, School of Mathematics and Statistics, Shandong University of Technology, ZiBo, 255000, China

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Chao Chen, Yilong Wang, and Dengqing Cao conceived the idea presented. Chao Chen developed the theory and conducted the computations. Yilong Wang guided the visualization of the images. Chen Shuai and Fang Bo assisted Chao Chen in the numerical simulations. All authors discussed the results and contributed to the final manuscript.

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Chen, C., Wang, Y., Chen, S. et al. Knowledge and data fusion-driven dynamical modeling approach for structures with hysteresis-affected uncertain boundaries. Nonlinear Dyn (2024). https://doi.org/10.1007/s11071-024-10096-x

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Received : 27 April 2024

Accepted : 26 July 2024

Published : 23 August 2024

DOI : https://doi.org/10.1007/s11071-024-10096-x

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