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Analysis of Algorithms

Robert Sedgewick

4.4

Based on 986 ratings

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Robert Sedgewick

This course teaches a calculus that enables precise quantitative predictions of large combinatorial structures. In addition, this course covers generating functions and real asymptotics and then introduces the symbolic method in the context of applications in the analysis of algorithms and basic structures such as permutations, trees, strings, words, and mappings.

All the features of this course are available for free. People who are interested in digging deeper into the content may wish to obtain the textbook Analysis of Algorithms, Second Edition (upon which the course is based) or to visit the website aofa.cs.princeton.edu for a wealth of additional material.

This course does not offer a certificate upon completion.

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What's inside

Syllabus

Analysis of Algorithms

We begin by considering historical context and motivation for the scientific study of algorithm performance. Then we consider a classic example that illustrates the key ingredients of the process: the analysis of Quicksort. The lecture concludes with a discussion of some resources that you might find useful during this course.

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Covers core principles of analytic combinatorics

Instructed by Robert Sedgewick, a renowned professor and author in the field of algorithms and data structures

Designed for individuals with a strong foundation in calculus

Incorporates mathematical concepts and techniques to analyze algorithms and combinatorial structures

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Reviews summary

Rigorous theoretical analysis of algorithms

According to learners, this course offers a deeply theoretical and highly rigorous approach to understanding algorithm performance. Students highlight the excellent lectures by Professor Sedgewick, which effectively break down complex concepts. However, many found the course to be very challenging, noting that it requires a strong mathematical background, particularly in calculus and probability. While it provides a strong foundational understanding of the underlying theory, some learners felt it offered less focus on practical coding applications compared to other courses. The difficulty of proofs and assignments was frequently mentioned as a significant hurdle. Overall, it is seen as rewarding for those seeking deep theoretical insight.

Better with the accompanying book.

"While the course is free, I found it almost essential to purchase the textbook to fully understand the material."

"The lectures cover the main points, but the textbook provides crucial details and exercises."

"You really need the book to get the most out of this course; the lectures alone are not sufficient for everyone."

"Accessing the website aofa.cs.princeton.edu is helpful for supplementary materials."

Provides a solid mathematical foundation.

"This course is fantastic if you want a deep dive into the mathematical analysis of algorithms, not just how they work."

"Focused heavily on the mathematical analysis, generating functions, and asymptotics. Great for understanding the 'why' behind algorithm efficiency."

"If you're interested in the rigorous mathematical proofs and theoretical underpinnings, this course is perfect."

"It's less about implementing algorithms and more about the advanced mathematical tools used for their analysis."

Instructor explains complex ideas well.

"Professor Sedgewick's lectures are excellent, very clear and engaging despite the difficult subject matter."

"The lectures were the strongest part of the course. He has a gift for explaining complex ideas."

"His explanations helped me grasp concepts I struggled with in the textbook. Truly a great instructor."

"I appreciate how the lectures structured the material, building logically from one topic to the next."

Focuses on theory, not hands-on coding.

"I was hoping for more hands-on coding examples or projects to solidify the theory."

"This course is much more theoretical than practical. Don't expect to write much code."

"Better for understanding the mathematical theory than for immediate application in coding interviews or development work."

"If you're looking for a course focused on algorithm implementation, this isn't it."

Demanding course, requires strong math skills.

"This course was incredibly difficult for me; I needed a much stronger background in calculus than I had."

"Requires a strong background in calculus, combinatorics, and probability theory. Be prepared for tough proofs."

"The proofs and assignments were quite challenging and time-consuming. Definitely not a walk in the park."

"I found the material conceptually difficult and the pace was sometimes hard to keep up with."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Analysis of Algorithms with these activities:

Review Calculus

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Reacquaint yourself with the principles of calculus and their applications.

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Review your notes or textbooks.
Practice solving basic calculus problems.
Take a practice test or quiz.

Read 'Analytic Combinatorics'

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Supplement your learning with in-depth insights from the leading textbook.

View An Introduction to the Analysis of Algorithms on Amazon

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Obtain a copy of the book.
Read and take notes on the relevant chapters.
Work through the exercises and problems.

Explore Analytic Combinatorics

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Gain a solid foundation in a key topic from the course.

Browse courses on Analytic Combinatorics

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Find online tutorials or courses.
Follow along and take notes.
Practice solving problems and exercises.

Five other activities

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Practice Recurrence Relations

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Improve problem-solving skills and reinforce key concepts.

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Solve practice problems and review examples.
Analyze real-world scenarios.
Use online resources and tools.

Attend a Workshop on Combinatorial Analysis

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Deepen your knowledge and connect with experts in the field.

Browse courses on Combinatorics

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Find and register for a relevant workshop.
Attend the workshop and actively participate.
Network with other attendees and speakers.

Analyze an Algorithm Using Asymptotics

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Gain hands-on experience in evaluating algorithm performance.

Browse courses on Asymptotic Analysis

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Select an algorithm and problem instance.
Implement the algorithm.
Analyze the algorithm's running time.
Compare your findings with theoretical predictions.

Build a Generative Function Model

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Deepen your understanding by applying concepts to a practical project.

Browse courses on Generating Functions

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Choose a specific problem or dataset.
Develop a generative function model.
Test and evaluate your model.
Present your findings.

Develop a Trie Structure

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Reinforce concepts and apply skills by implementing a practical data structure.

Browse courses on Data Structures

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Design and plan the trie structure.
Implement the structure in a programming language.
Test and debug your implementation.
Integrate the trie into a larger project or application.

Career center

Learners who complete Analysis of Algorithms will develop knowledge and skills that may be useful to these careers:

Software Engineer

Software engineers apply the principles of computer science and mathematics to develop software, which is used in a wide variety of industries, including technology, finance, healthcare, and manufacturing. This course can help you develop the analytical and problem-solving skills necessary to be successful in this field. The course covers topics such as algorithm design, data structures, and software design patterns, which are essential for software development. Additionally, the course's emphasis on mathematical analysis can help you develop the critical thinking skills necessary to solve complex software problems.

See salaries and explore the career path for Software Engineer

Data Scientist

Data scientists use their knowledge of mathematics, statistics, and computer science to extract insights from data. This course can help you build a foundation in the mathematical and analytical skills necessary for this field. The course covers topics such as probability, statistics, and machine learning, which are essential for data science. Additionally, the course's emphasis on problem-solving can help you develop the critical thinking skills necessary to solve complex data science problems.

See salaries and explore the career path for Data Scientist

Quantitative Analyst

Quantitative Analysts use mathematical and statistical models to analyze financial data and make investment decisions. This course can help you build a foundation in the mathematical and analytical skills necessary for this field. The course covers topics such as probability, statistics, and financial modeling, which are essential for quantitative analysis. Additionally, the course's emphasis on problem-solving can help you develop the critical thinking skills necessary to solve complex financial problems.

See salaries and explore the career path for Quantitative Analyst

Operations Research Analyst

Operations research analysts use mathematical and analytical techniques to solve problems in a variety of industries, including manufacturing, logistics, and healthcare. This course can help you build a foundation in the mathematical and analytical skills necessary for this field. The course covers topics such as optimization, simulation, and decision analysis, which are essential for operations research. Additionally, the course's emphasis on problem-solving can help you develop the critical thinking skills necessary to solve complex operations research problems.

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Actuary

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Financial Analyst

Financial analysts use mathematical and analytical techniques to evaluate the financial performance of companies. This course can help you build a foundation in the mathematical and analytical skills necessary for this field. The course covers topics such as financial accounting, financial modeling, and investment analysis, which are essential for financial analysis. Additionally, the course's emphasis on problem-solving can help you develop the critical thinking skills necessary to solve complex financial problems.

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Business Analyst

Business analysts use data and analysis to identify and solve problems in businesses. This course can help you build a foundation in the mathematical and analytical skills necessary for this field. The course covers topics such as data analysis, decision analysis, and process improvement, which are essential for business analysis. Additionally, the course's emphasis on problem-solving can help you develop the critical thinking skills necessary to solve complex business problems.

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Market Researcher

Market researchers use data and analysis to understand the needs and wants of consumers. This course can help you build a foundation in the mathematical and analytical skills necessary for this field. The course covers topics such as survey research, data analysis, and market segmentation, which are essential for market research. Additionally, the course's emphasis on problem-solving can help you develop the critical thinking skills necessary to solve complex market research problems.

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Computer Scientist

Computer scientists design, develop, and implement software systems. This course can help you build a foundation in the mathematical and analytical skills necessary for this field. The course covers topics such as algorithm design, data structures, and software design patterns, which are essential for computer science. Additionally, the course's emphasis on problem-solving can help you develop the critical thinking skills necessary to solve complex computer science problems.

See salaries and explore the career path for Computer Scientist

Mathematician

Mathematicians study the properties of numbers, shapes, and other abstract concepts. This course can help you develop the mathematical and analytical skills necessary for this field. The course covers topics such as algebra, calculus, and number theory, which are essential for mathematics. Additionally, the course's emphasis on problem-solving can help you develop the critical thinking skills necessary to solve complex mathematical problems.

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Statistician

Statisticians collect, analyze, and interpret data. This course can help you build a foundation in the mathematical and analytical skills necessary for this field. The course covers topics such as probability, statistics, and data analysis, which are essential for statistics. Additionally, the course's emphasis on problem-solving can help you develop the critical thinking skills necessary to solve complex statistical problems.

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Economist

Economists study the production, distribution, and consumption of goods and services. This course can help you build a foundation in the mathematical and analytical skills necessary for this field. The course covers topics such as microeconomics, macroeconomics, and econometrics, which are essential for economics. Additionally, the course's emphasis on problem-solving can help you develop the critical thinking skills necessary to solve complex economic problems.

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Data Analyst

Data analysts use data and analysis to identify and solve problems in businesses. This course can help you build a foundation in the mathematical and analytical skills necessary for this field. The course covers topics such as data analysis, data visualization, and machine learning, which are essential for data analysis. Additionally, the course's emphasis on problem-solving can help you develop the critical thinking skills necessary to solve complex data analysis problems.

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Operations Manager

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Risk Manager

Risk managers identify, assess, and manage risks. This course can help you build a foundation in the mathematical and analytical skills necessary for this field. The course covers topics such as risk management, risk assessment, and risk mitigation, which are essential for risk management. Additionally, the course's emphasis on problem-solving can help you develop the critical thinking skills necessary to solve complex risk management problems.

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Reading list

We've selected 16 books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Analysis of Algorithms.

Introduction to Algorithms, fourth edition

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Classic textbook on algorithms and valuable resource for anyone interested in learning more about the subject. It covers a wide range of topics, from basic data structures to advanced algorithms. It useful reference for anyone who wants to learn more about the subject.

Analysis of Algorithms

What's inside

Syllabus

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Save this course

Reviews summary

Rigorous theoretical analysis of algorithms

Activities

Career center

Reading list

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