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Complexity Theory - Running Time Analysis of Algorithms

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Based on 2,407 ratings
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Holczer Balazs

This course is about algorithms running time analysis and complexity theory. In order to be able to classify algorithms we have to define limiting behaviors for functions describing the given algorithm.

We will understand running times such as O(N*logN), O(N), O(logN) and O(1) - as well as exponential and factorial running time complexities.

Thats why big O, big Ω and big θ notations came to be. We are going to talk about the theory behind complexity theory as well as we are going to see some concrete examples.

Read more

This course is about algorithms running time analysis and complexity theory. In order to be able to classify algorithms we have to define limiting behaviors for functions describing the given algorithm.

We will understand running times such as O(N*logN), O(N), O(logN) and O(1) - as well as exponential and factorial running time complexities.

Thats why big O, big Ω and big θ notations came to be. We are going to talk about the theory behind complexity theory as well as we are going to see some concrete examples.

Then we will consider complexity classes including P (polynomial) as well as NP (non-deterministic polynomial), NP-complete and NP-hard complexity classes.

Section 1 - Algorithms Analysis

  • how to measure the running time of algorithms

  • running time analysis with big O (ordo), big Ω (omega) and big θ (theta) notations

  • complexity classes

  • polynomial (P) and non-deterministic polynomial (NP) algorithms

Section 2 - Algorithms Analysis (Case Studies)

  • constant running time O(1)

  • linear running time O(N)

  • logarithmic running time O(logN)

  • quadratic running time complexity O(N*N)

These concepts are fundamental if we want to have a good grasp on data structures and graph algorithms - so these topics are definitely worth considering. Hope you will like it. Thanks for joining my course, let's get started.

These concepts are fundamental if we want to have a good grasp on data structures and graph algorithms - so these topics are definitely worth considering. Hope you will like it. Thanks for joining my course, let's get started.

Enroll now

What's inside

Syllabus

Complexity notations - big (O) ordo
Introduction
Algorithms (Running Time) Analysis
How to measure the running times of algorithms?
Read more

Traffic lights

Read about what's good
what should give you pause
and possible dealbreakers
Explores big O, big Ω, and big θ notations, which are essential for understanding algorithm efficiency and performance in computer science
Covers complexity classes such as P, NP, NP-complete, and NP-hard, which are fundamental concepts in theoretical computer science
Examines running times like O(N*logN), O(N), O(logN), and O(1), providing a practical understanding of how algorithms scale with input size
Requires a grasp of data structures and graph algorithms, suggesting prior coursework or experience in these areas may be beneficial
Includes case studies of different running times, such as O(1), O(logN), O(N), and O(N*N), offering practical examples to solidify theoretical concepts
Features Algorhyme, an algorithms visualizer app, which may require learners to download and install software on their personal devices

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Reviews summary

Introduction to algorithms complexity and analysis

According to learners, this course provides a solid introduction to algorithms running time analysis and complexity theory, covering fundamental concepts like Big O, Omega, and Theta notations. Many students find it helpful for understanding the basics, especially if they are new to the topic or need a refresher. However, some reviewers mention that the course lacks depth for those seeking more advanced knowledge or extensive practical coding examples, focusing more heavily on theoretical aspects. Opinions vary on the clarity of explanations in certain sections.
Strong on concepts, light on coding.
"It is purely theory based course which is not bad but just good to mention."
"Could use more coding examples to demonstrate the concepts practically."
"Focuses heavily on the mathematical side of analysis rather than implementation."
Clearly explains Big O, Omega, Theta.
"I really understood Big O, Big Omega and Big Theta after this course."
"The explanation of asymptotic notations was particularly clear and helpful."
"Good breakdown of the different complexity notations."
Excellent starting point for core concepts.
"This course is a good introduction to the complexities of algorithms."
"Provided a solid foundation in understanding Big O notation and running time."
"As a beginner, I found the explanations clear and easy to follow for the basics."
Some parts clear, others potentially confusing.
"Some sections were very clear, others were a bit hard to grasp without external resources."
"While overall informative, the explanations in certain lectures felt rushed or unclear."
"I had to rewatch a few videos to fully understand the concepts being presented."
May be too basic for experienced learners.
"The course is too introductory, needs more advanced topics and examples."
"Felt it didn't go deep enough into practical application or complex cases."
"If you already know the basics, this course might not offer much new information."

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 Complexity Theory - Running Time Analysis of Algorithms with these activities:
Review Data Structures
Reviewing data structures will help you understand the practical implications of different time complexities.
Browse courses on Data Structures
Show steps
  • Review the definitions of common data structures.
  • Practice implementing basic operations on each data structure.
  • Analyze the time complexity of these operations.
Review Introduction to Algorithms
Reviewing this book will provide a solid theoretical foundation for understanding time complexity analysis.
View Introduction to Algorithms, fourth edition on Amazon
Show steps
  • Read the chapters on algorithm analysis and time complexity.
  • Work through the examples and exercises.
  • Relate the concepts to the material covered in the course.
LeetCode Time Complexity Problems
Practicing LeetCode problems will help you apply your knowledge of time complexity analysis to real-world scenarios.
Show steps
  • Select LeetCode problems focused on time complexity.
  • Solve the problems and analyze the time complexity of your solutions.
  • Compare your solutions with others and identify areas for improvement.
Four other activities
Expand to see all activities and additional details
Show all seven activities
Create a Time Complexity Cheat Sheet
Creating a cheat sheet will help you consolidate your understanding of different time complexities and their characteristics.
Show steps
  • List common time complexities (O(1), O(log n), O(n), etc.).
  • Provide examples of algorithms that exhibit each time complexity.
  • Explain the characteristics of each time complexity.
Review Algorithm Design
Reviewing this book will provide insights into algorithm design and its relationship to time complexity.
View Algorithm Design on Amazon
Show steps
  • Read the chapters on algorithm design paradigms.
  • Study the examples and case studies.
  • Apply the techniques to solve new problems.
Analyze Sorting Algorithm Performance
Analyzing sorting algorithms will provide hands-on experience with time complexity analysis and algorithm comparison.
Show steps
  • Implement several sorting algorithms (e.g., bubble sort, merge sort, quicksort).
  • Measure the running time of each algorithm for different input sizes.
  • Plot the running times and compare them to the theoretical time complexities.
Tutor other students
Tutoring others will reinforce your understanding of time complexity analysis and help you identify areas where you need more practice.
Show steps
  • Offer to tutor other students in the course.
  • Explain the concepts of time complexity analysis.
  • Help students solve problems and analyze their solutions.

Career center

Learners who complete Complexity Theory - Running Time Analysis of Algorithms will develop knowledge and skills that may be useful to these careers:
Algorithm Developer
An algorithm developer designs and implements algorithms for various applications. This course is directly relevant to their work because it focuses on algorithms running time analysis and complexity theory. Understanding the material on measuring the running time of algorithms helps an algorithm developer ensure the feasibility of their code. The course's in-depth look at complexity classes, along with concrete examples are directly beneficial to an algorithm developer. An algorithm developer should take this course to enhance their skills in designing and analyzing efficient algorithms.
See salaries and explore the career path for Algorithm Developer
Performance Engineer
A performance engineer analyzes and optimizes the performance of software systems. This course is directly relevant because it focuses on the analysis of algorithms running time and complexity theory. Studying big O, big Ω, and big θ notations, which the course covers and are used for specifying such performance requirements, may be beneficial to a performance engineer. A performance engineer should take this course to improve their ability to optimize the performance of software systems.
See salaries and explore the career path for Performance Engineer
Software Engineer
A software engineer designs, develops, and tests software applications. This course helps a software engineer understand the time and space complexity of algorithms, crucial for writing efficient and scalable code. Understanding running times such as O(N*logN), O(N), and O(logN) is essential for optimizing software performance. The course's exploration of complexity classes like P and NP provides a theoretical foundation for tackling computationally challenging problems. A software engineer should take this course to sharpen their ability to analyze algorithms and write high-performance software.
See salaries and explore the career path for Software Engineer
Systems Architect
A systems architect designs and oversees the implementation of computer systems. This course helps a systems architect understand the performance characteristics of different components within a system. The course's lessons on measuring the running time of algorithms and understanding complexity classes aid in selecting efficient algorithms for system components. A systems architect should consider taking this course to enhance their ability to design high-performance computer systems.
See salaries and explore the career path for Systems Architect
Quantitative Analyst
A quantitative analyst develops mathematical models for financial analysis. This course helps a quantitative analyst understand the computational complexity of the algorithms used in quantitative finance such as those used for high frequency trading. The course's exploration of complexity classes becomes valuable when evaluating the feasibility of complex financial models. A quantitative analyst should take this course to enhance their ability to develop and analyze computationally efficient financial algorithms.
See salaries and explore the career path for Quantitative Analyst
Game Developer
A game developer designs and develops video games. The performance of the code is very important for the success of these interactive applications. This course helps a game developer understand the performance implications of different algorithms used in game development. The course's case studies, which explore exponential and factorial running time complexities, become valuable when writing efficient code. A game developer should take this course to improve their ability to write high-performance code.
See salaries and explore the career path for Game Developer
Cryptographer
A cryptographer designs and analyzes encryption algorithms. This course may be useful to a cryptographer because understanding algorithms running time analysis and complexity theory is necessary for designing secure encryption methods. The course's in-depth look at complexity classes such as NP-complete and NP-hard, becomes valuable when assessing the security of cryptographic algorithms. A cryptographer should take this course to improve their knowledge of the computational complexity of cryptographic operations.
See salaries and explore the career path for Cryptographer
Bioinformatician
A bioinformatician analyzes biological data using computational techniques. This course is helpful for a bioinformatician because it shows how to classify algorithms, which is useful for dealing with DNA sequencing and analysis. Understanding big O, big Ω, and big θ notations, helps with algorithm choice. A bioinformatician should take this course to improve their ability to analyze biological algorithms.
See salaries and explore the career path for Bioinformatician
Research Scientist
A research scientist conducts research in computer science or related fields, often requiring a graduate degree. This course may be useful for this role since it covers algorithms running time analysis and complexity theory. Understanding how to measure the running time of algorithms is important for assessing the feasibility of novel algorithms. A research scientist would take this course to enhance their ability to design and analyze algorithms.
See salaries and explore the career path for Research Scientist
Data Scientist
A data scientist analyzes large datasets to extract meaningful insights and build predictive models. This course provides a foundation for understanding the computational complexity of data analysis algorithms, which is important when working with large datasets. Understanding big O, big Ω, and big θ notations, which the course covers, is fundamental for selecting appropriate algorithms for different data analysis tasks. Studying polynomial and non-deterministic polynomial algorithms may be insightful for some Data Scientists. A data scientist should take this course to improve their ability to choose and implement efficient data analysis techniques.
See salaries and explore the career path for Data Scientist
Robotics Engineer
A robotics engineer designs and develops robots and robotic systems. This course may be useful as it provides insights into the computational complexity of algorithms used in robotics, such as path planning and motion control. Understanding big O notation, which the course covers, aids in writing code that runs in real time. A robotics engineer may find this course useful to better understand how to write robust and efficient control software.
See salaries and explore the career path for Robotics Engineer
Data Engineer
A data engineer builds and maintains data pipelines and infrastructure. This course may be useful for a data engineer as it provides insights into the complexity and scalability of data processing algorithms. The course's exploration of polynomial and non-deterministic polynomial algorithms may be insightful when working with large-scale data processing frameworks. A data engineer may find this course useful to better understand how to optimize data pipelines.
See salaries and explore the career path for Data Engineer
Machine Learning Engineer
A machine learning engineer develops and deploys machine learning models. Machine learning engineers benefit from understanding the time and space complexity of the algorithms they use. This course on algorithms running time analysis may be useful to a machine learning engineer. The course's coverage of big O notation and complexity classes may help with the selection and optimization of machine learning algorithms. A machine learning engineer should take this course to gain insights into the performance of machine learning algorithms.
See salaries and explore the career path for Machine Learning Engineer
Technology Consultant
A technology consultant advises clients on technology solutions. This course may be useful for understanding the performance implications of different technologies and algorithms when recommending solutions to clients. The course's exploration of complexity classes along with examples becomes valuable when matching the right technologies with specific client needs. A technology consultant should take this course to enhance their ability to make informed technology recommendations.
See salaries and explore the career path for Technology Consultant
Database Administrator
A database administrator maintains and optimizes database systems. This course may be useful as it provides insights into the performance characteristics of different algorithms used within database systems. Understanding the practical implications of algorithmic complexity, as demonstrated in the case studies of constant, linear, logarithmic, and quadratic running times, may help with the maintenance of databases. A database administrator may find this course useful to better understand how to optimize database performance.
See salaries and explore the career path for Database Administrator

Reading list

We've selected two 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 Complexity Theory - Running Time Analysis of Algorithms.
Cover image
Introduction to Algorithms, fourth edition
Save
This is the French translation of "Introduction to Algorithms" by Cormen et al. It provides a comprehensive and rigorous introduction to algorithms, covering a wide range of topics including sorting, searching, graph algorithms, and dynamic programming. It provides rigorous analysis of algorithm running times using big O, big Ω, and big θ notations, which are central to the course. offers much more depth than the course, and useful reference.
Introduction to Algorithms, fourth edition
Hardcover
$$$$
Introduction to Algorithms, fourth edition
Kindle Edition
$$$
Algorithm Design
Save
Focuses on algorithm design techniques, such as greedy algorithms, dynamic programming, and network flow. It provides a rigorous analysis of algorithm correctness and running time, with an emphasis on problem-solving. While the course focuses on running time analysis, this book provides the necessary background on algorithm design to understand the context of these analyses. This book is more valuable as additional reading than as a current reference.
Algorithm Design
Hardcover
$$$$
Algorithm Design
Mass Market Paperback
$$
Algorithm Design
Kindle Edition
$$$

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4.3 Filled star Filled star Filled star Filled star Empty star
Effort
2 total hours
Via
Udemy
Instructor
Holczer Balazs
Language
English
Traffic lights
Read about what's good
what should give you pause
and possible dealbreakers
Explores big O, big Ω, and big θ notations, which are essential for understanding algorithm efficiency and performance in computer science
Covers complexity classes such as P, NP, NP-complete, and NP-hard, which are fundamental concepts in theoretical computer science
Examines running times like O(N*logN), O(N), O(logN), and O(1), providing a practical understanding of how algorithms scale with input size
Requires a grasp of data structures and graph algorithms, suggesting prior coursework or experience in these areas may be beneficial
Includes case studies of different running times, such as O(1), O(logN), O(N), and O(N*N), offering practical examples to solidify theoretical concepts
Features Algorhyme, an algorithms visualizer app, which may require learners to download and install software on their personal devices
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