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Tim Roughgarden
The primary topics in this part of the specialization are: asymptotic ("Big-oh") notation, sorting and searching, divide and conquer (master method, integer and matrix multiplication, closest pair), and randomized algorithms (QuickSort, contraction algorithm for min cuts).
Register for this course and see more details by visiting:
OpenCourser.com/course/gajyy5/divide
What's inside
Syllabus
Week 1
Introduction; "big-oh" notation and asymptotic analysis.
Week 2
Divide-and-conquer basics; the master method for analyzing divide and conquer algorithms.
Read more
Syllabus
Week 1
Introduction; "big-oh" notation and asymptotic analysis.
Week 2
Divide-and-conquer basics; the master method for analyzing divide and conquer algorithms.
Read more
Week 3
The QuickSort algorithm and its analysis; probability review.
Week 4
Linear-time selection; graphs, cuts, and the contraction algorithm.
Good to know
Good to know
Know what's good ,
what to watch for , and
possible dealbreakers
Explores algorithmic analysis and design, which is standard in software engineering, data science, and programming
Taught by Tim Roughgarden, who is a renowned computer scientist and author of popular textbooks on algorithms
Develops skills in algorithmic analysis and design, which are essential for building efficient and effective software systems
Examines asymptotic notation, sorting, searching, divide and conquer, and randomization, which are core concepts in algorithmic theory
Provides a solid foundation for advanced courses in algorithms and data structures
Requires some background in mathematics and programming, which may limit accessibility for beginners
Save this course
Save Divide and Conquer, Sorting and Searching, and Randomized Algorithms to your list so you can find it easily later:
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Reviews summary
Intelligent algorithms: conquer and divide
Learners say this course provides a mathematically rigorous introduction to algorithms and algorithm analysis, with a focus on divide and conquer strategies. Students gain a detailed understanding of merge sort, quicksort, and randomized algorithms, and how to prove their asymptotic runtime. The course is challenging but rewarding, featuring engaging assignments that allow learners to implement algorithms in their preferred programming language. Instructor Tim Roughgarden's clear explanations and enthusiasm for the subject enhance the learning experience.
This course emphasizes the practical implementation of algorithms, allowing learners to apply their knowledge in real-world scenarios.
"Students gain a detailed understanding of merge sort, quicksort, and randomized algorithms, and how to prove their asymptotic runtime."
"The course is challenging but rewarding, featuring engaging assignments that allow learners to implement algorithms in their preferred programming language."
Professor Roughgarden's passion for the subject shines through in his clear explanations and engaging delivery.
"Instructor Tim Roughgarden's clear explanations and enthusiasm for the subject enhance the learning experience."
The programming assignments in this course are challenging and help learners apply the concepts they learn.
"The course is challenging but rewarding, featuring engaging assignments that allow learners to implement algorithms in their preferred programming language."
This course provides crystal clear explanations of various concepts in algorithms. These include divide and conquer strategies, merge sort, quicksort, and randomized algorithms.
"Learners say this course provides a mathematically rigorous introduction to algorithms and algorithm analysis, with a focus on divide and conquer strategies."
"Students gain a detailed understanding of merge sort, quicksort, and randomized algorithms, and how to prove their asymptotic runtime."
This course is considered mathematically complex and may not be suitable for learners without a strong math foundation.
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 Divide and Conquer, Sorting and Searching, and Randomized Algorithms with these
activities:
Identify a Mentor in Algorithm Analysis
Show steps
Connect with an experienced professional or academic who can provide guidance and support in your journey to master algorithm analysis.
Show steps
-
Attend industry events or online forums to network with potential mentors
-
Reach out to professors or professionals in your field
-
Clearly articulate your learning goals and seek guidance
Review Asymptotic Notation Concepts
Show steps
Reinforce your understanding of asymptotic notation and complexity analysis, which are foundational concepts in algorithm analysis.
Browse courses on
Asymptotic Notation
Show steps
-
Review the definition of asymptotic notation and its variants (e.g., O(), Ω(), Θ())
-
Practice applying asymptotic notation to analyze the running time of simple algorithms
Write an Explanation of QuickSort
Show steps
Enhance your understanding of QuickSort by explaining its concept and implementation in your own words, consolidating your grasp of the algorithm.
Browse courses on
Sorting Algorithms
Show steps
-
Review the QuickSort algorithm
-
Write a clear and concise explanation of how QuickSort works
-
Illustrate your explanation with examples
-
Share your explanation with a classmate or online forum
Four other activities
Expand to see all activities and additional details
Show all seven activities
Solve Algorithmic Challenges on LeetCode
Show steps
Strengthen your problem-solving skills and deepen your understanding of sorting, searching, and other fundamental algorithms.
Browse courses on
Sorting Algorithms
Show steps
-
Select a problem on LeetCode related to the course topics
-
Analyze the problem statement and design an algorithm
-
Implement the algorithm in your preferred programming language
-
Test and debug your solution
Participate in a Coding Club or Competition
Show steps
Engage in collaborative problem-solving and get hands-on experience, enhancing your algorithmic skills and teamwork abilities.
Show steps
-
Identify a coding club or competition relevant to algorithm analysis
-
Join the club or register for the competition
-
Actively participate in discussions and challenges
-
Collaborate with other participants and share knowledge
Implement a Divide-and-Conquer Algorithm
Show steps
Gain practical experience by implementing a divide-and-conquer algorithm from scratch, allowing you to fully grasp its mechanics and efficiency.
Show steps
-
Choose a divide-and-conquer algorithm to implement (e.g., merge sort, quick sort, binary search)
-
Design the algorithm's recursive structure
-
Implement the algorithm in your preferred programming language
-
Test and debug your implementation
-
Analyze the running time of your implementation
Design an Algorithm for a Real-World Problem
Show steps
Apply your knowledge to a practical problem, showcasing your ability to analyze, design, and implement algorithmic solutions in a real-world context.
Show steps
-
Identify a problem that can benefit from an algorithmic solution
-
Analyze the problem and determine suitable algorithms
-
Design and implement the algorithm in a programming language
-
Evaluate the performance and efficiency of your algorithm
-
Present your solution to a technical audience
Identify a Mentor in Algorithm Analysis
Show steps
Connect with an experienced professional or academic who can provide guidance and support in your journey to master algorithm analysis.
Show steps
Show steps
Show steps
- Attend industry events or online forums to network with potential mentors
- Reach out to professors or professionals in your field
- Clearly articulate your learning goals and seek guidance
Review Asymptotic Notation Concepts
Show steps
Reinforce your understanding of asymptotic notation and complexity analysis, which are foundational concepts in algorithm analysis.
Browse courses on
Asymptotic Notation
Show steps
Show steps
Show steps
- Review the definition of asymptotic notation and its variants (e.g., O(), Ω(), Θ())
- Practice applying asymptotic notation to analyze the running time of simple algorithms
Write an Explanation of QuickSort
Show steps
Enhance your understanding of QuickSort by explaining its concept and implementation in your own words, consolidating your grasp of the algorithm.
Browse courses on
Sorting Algorithms
Show steps
Show steps
Show steps
- Review the QuickSort algorithm
- Write a clear and concise explanation of how QuickSort works
- Illustrate your explanation with examples
- Share your explanation with a classmate or online forum
Four other activities
Expand to see all activities and additional details
Show all seven activities
Solve Algorithmic Challenges on LeetCode
Show steps
Strengthen your problem-solving skills and deepen your understanding of sorting, searching, and other fundamental algorithms.
Browse courses on
Sorting Algorithms
Show steps
Show steps
Show steps
- Select a problem on LeetCode related to the course topics
- Analyze the problem statement and design an algorithm
- Implement the algorithm in your preferred programming language
- Test and debug your solution
Participate in a Coding Club or Competition
Show steps
Engage in collaborative problem-solving and get hands-on experience, enhancing your algorithmic skills and teamwork abilities.
Show steps
Show steps
Show steps
- Identify a coding club or competition relevant to algorithm analysis
- Join the club or register for the competition
- Actively participate in discussions and challenges
- Collaborate with other participants and share knowledge
Implement a Divide-and-Conquer Algorithm
Show steps
Gain practical experience by implementing a divide-and-conquer algorithm from scratch, allowing you to fully grasp its mechanics and efficiency.
Show steps
Show steps
Show steps
- Choose a divide-and-conquer algorithm to implement (e.g., merge sort, quick sort, binary search)
- Design the algorithm's recursive structure
- Implement the algorithm in your preferred programming language
- Test and debug your implementation
- Analyze the running time of your implementation
Design an Algorithm for a Real-World Problem
Show steps
Apply your knowledge to a practical problem, showcasing your ability to analyze, design, and implement algorithmic solutions in a real-world context.
Show steps
Show steps
Show steps
- Identify a problem that can benefit from an algorithmic solution
- Analyze the problem and determine suitable algorithms
- Design and implement the algorithm in a programming language
- Evaluate the performance and efficiency of your algorithm
- Present your solution to a technical audience
Career center
Learners who complete Divide and Conquer, Sorting and Searching, and Randomized Algorithms will develop knowledge and skills
that may be useful to these careers:
Machine Learning Engineer
Machine Learning Engineer
As a Machine Learning Engineer, you will gather and analyze data to build predictive models that solve real-world problems. The techniques covered in this course, such as divide and conquer algorithms and randomized algorithms, are foundational to building these models. For example, divide and conquer algorithms can be used to split data into smaller subsets, making it easier to identify patterns and build more accurate models. Randomized algorithms can be used to improve the efficiency of machine learning algorithms. By taking this course, you will lay a solid foundation for a successful career as a Machine Learning Engineer.
Software Engineer
Software Engineer
Software Engineers design, develop, and maintain software systems. The techniques covered in this course, such as divide and conquer algorithms and randomized algorithms, are essential for developing efficient and reliable software. For example, divide and conquer algorithms can be used to break down complex problems into smaller, more manageable subproblems, while randomized algorithms can be used to improve the performance of algorithms. By taking this course, you will gain the skills you need to succeed as a Software Engineer.
Data Scientist
Data Scientist
Data Scientists collect, analyze, and interpret data to help organizations make informed decisions. The techniques covered in this course, such as divide and conquer algorithms and randomized algorithms, are essential for working with large datasets. For example, divide and conquer algorithms can be used to efficiently process large datasets, while randomized algorithms can be used to improve the accuracy of data analysis. By taking this course, you will gain the skills you need to succeed as a Data Scientist.
Statistician
Statistician
Statisticians collect, analyze, and interpret data to help organizations make informed decisions. The techniques covered in this course, such as divide and conquer algorithms and randomized algorithms, are essential for working with large datasets. For example, divide and conquer algorithms can be used to efficiently process large datasets, while randomized algorithms can be used to improve the accuracy of statistical analysis. By taking this course, you will gain the skills you need to succeed as a Statistician.
Data Analyst
Data Analyst
Data Analysts collect, analyze, and interpret data to help organizations make informed decisions. The techniques covered in this course, such as divide and conquer algorithms and randomized algorithms, are essential for working with large datasets. For example, divide and conquer algorithms can be used to efficiently process large datasets, while randomized algorithms can be used to improve the accuracy of data analysis. By taking this course, you will gain the skills you need to succeed as a Data Analyst.
Financial Analyst
Financial Analyst
Financial Analysts use mathematical and statistical techniques to analyze financial data. The techniques covered in this course, such as divide and conquer algorithms and randomized algorithms, are essential for developing accurate and reliable financial models. For example, divide and conquer algorithms can be used to efficiently process large financial datasets, while randomized algorithms can be used to improve the accuracy of financial models. By taking this course, you will gain the skills you need to succeed as a Financial Analyst.
Quantitative Analyst
Quantitative Analyst
Quantitative Analysts use mathematical and statistical techniques to analyze financial data. The techniques covered in this course, such as divide and conquer algorithms and randomized algorithms, are essential for developing accurate and reliable financial models. For example, divide and conquer algorithms can be used to efficiently process large financial datasets, while randomized algorithms can be used to improve the accuracy of financial models. By taking this course, you will gain the skills you need to succeed as a Quantitative Analyst.
Actuary
Actuary
Actuaries use mathematical and statistical techniques to assess risk and uncertainty. The techniques covered in this course, such as divide and conquer algorithms and randomized algorithms, are essential for developing accurate and reliable risk models. For example, divide and conquer algorithms can be used to efficiently process large insurance datasets, while randomized algorithms can be used to improve the accuracy of risk models. By taking this course, you will gain the skills you need to succeed as an Actuary.
Computer Scientist
Computer Scientist
Computer Scientists research and develop new computing technologies. The techniques covered in this course, such as divide and conquer algorithms and randomized algorithms, are fundamental to computer science research. For example, divide and conquer algorithms can be used to design efficient algorithms for solving complex problems, while randomized algorithms can be used to improve the performance of algorithms. By taking this course, you will gain the skills you need to succeed as a Computer Scientist.
Risk Manager
Risk Manager
Risk Managers use mathematical and statistical techniques to assess risk and uncertainty. The techniques covered in this course, such as divide and conquer algorithms and randomized algorithms, are essential for developing accurate and reliable risk models. For example, divide and conquer algorithms can be used to efficiently process large insurance datasets, while randomized algorithms can be used to improve the accuracy of risk models. By taking this course, you will gain the skills you need to succeed as a Risk Manager.
Software Developer
Software Developer
Software Developers design, develop, and maintain software systems. The techniques covered in this course, such as divide and conquer algorithms and randomized algorithms, are essential for developing efficient and reliable software. For example, divide and conquer algorithms can be used to break down complex problems into smaller, more manageable subproblems, while randomized algorithms can be used to improve the performance of algorithms. By taking this course, you will gain the skills you need to succeed as a Software Developer.
Quantitative Researcher
Quantitative Researcher
Quantitative Researchers use mathematical and statistical techniques to analyze financial data. The techniques covered in this course, such as divide and conquer algorithms and randomized algorithms, are essential for developing accurate and reliable financial models. For example, divide and conquer algorithms can be used to efficiently process large financial datasets, while randomized algorithms can be used to improve the accuracy of financial models. By taking this course, you will gain the skills you need to succeed as a Quantitative Researcher.
Algorithm Engineer
Algorithm Engineer
Algorithm Engineers design, develop, and analyze algorithms to solve complex problems. The techniques covered in this course, such as divide and conquer algorithms and randomized algorithms, are essential for developing efficient and effective algorithms. For example, divide and conquer algorithms can be used to efficiently solve large-scale optimization problems, while randomized algorithms can be used to improve the performance of simulation models. By taking this course, you will gain the skills you need to succeed as an Algorithm Engineer.
Business Analyst
Business Analyst
Business Analysts use data and analysis to help organizations make better decisions. The techniques covered in this course, such as divide and conquer algorithms and randomized algorithms, are essential for working with large datasets. For example, divide and conquer algorithms can be used to efficiently process large datasets, while randomized algorithms can be used to improve the accuracy of data analysis. By taking this course, you will gain the skills you need to succeed as a Business Analyst.
Operations Research Analyst
Operations Research Analyst
Operations Research Analysts use mathematical and statistical techniques to solve complex business problems. The techniques covered in this course, such as divide and conquer algorithms and randomized algorithms, are essential for developing efficient and effective solutions to business problems. For example, divide and conquer algorithms can be used to efficiently solve large-scale optimization problems, while randomized algorithms can be used to improve the performance of simulation models. By taking this course, you will gain the skills you need to succeed as an Operations Research Analyst.
For more career information including salaries, visit:
OpenCourser.com/course/gajyy5/divide
Reading list
We've selected 37 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
Divide and Conquer, Sorting and Searching, and Randomized Algorithms.
Provides a comprehensive treatment of graph algorithms. It covers a wide range of topics, including depth-first search, breadth-first search, and randomized algorithms.
Provides a comprehensive overview of algorithms and data structures, including topics covered in the course such as divide-and-conquer and randomized algorithms.
Save
Provides a comprehensive treatment of network flows. It covers a wide range of topics, including the max-flow min-cut theorem, the Ford-Fulkerson algorithm, and randomized algorithms.
Provides a comprehensive treatment of computational complexity. It covers a wide range of topics, including Turing machines, NP-completeness, and randomized algorithms.
This classic textbook provides a comprehensive overview of algorithms and data structures, including topics such as divide and conquer, sorting, and searching.
This classic book provides a comprehensive treatment of sorting and searching algorithms. It good resource for students who want to learn more about the history and development of these algorithms.
Provides a comprehensive treatment of online algorithms. It covers a wide range of topics, including the competitive ratio, the adversary model, and randomized algorithms.
Provides a comprehensive treatment of approximation algorithms. It covers a wide range of topics, including the greedy algorithm, the approximation ratio, and randomized algorithms.
Offers practical guidance on designing algorithms, covering techniques such as divide-and-conquer and randomization.
Comprehensive guide to algorithm design and analysis. It valuable reference for students who want to learn more about the theory behind the algorithms covered in this course.
This textbook covers a similar range of topics as Introduction to Algorithms, but with a focus on Java implementations. It includes interactive visualizations and exercises that can be helpful for understanding the concepts.
Save
Covers a variety of algorithm design techniques, including divide-and-conquer, dynamic programming, and greedy algorithms. It good resource for students who want to learn more about how to design efficient algorithms.
Provides a comprehensive treatment of algorithmics and complexity. It covers a wide range of topics, including sorting, searching, divide-and-conquer, and randomized algorithms.
Covers a wide range of algorithms and data structures, including topics relevant to the course such as sorting and searching.
Save
Collection of essays on programming techniques and algorithms. It covers a wide range of topics, including sorting, searching, divide-and-conquer, and randomized algorithms.
Provides a comprehensive treatment of algorithms and data structures. It covers a wide range of topics, including sorting, searching, divide-and-conquer, and randomized algorithms.
This advanced textbook covers randomized algorithms, including topics such as QuickSort and the contraction algorithm for min cuts.
Presents algorithms and data structures in Python, which can be useful for implementing and experimenting with concepts covered in the course.
Save
Provides a comprehensive treatment of sorting and searching algorithms in Java. It good resource for students who want to learn more about these topics in the context of a specific programming language.
Save
Less technical introduction to algorithms than Introduction to Algorithms. It good choice for students who want to learn about the basics of algorithms without getting too bogged down in the details.
Save
Provides a practical guide to algorithm design and implementation in C++. It covers a variety of techniques, including divide-and-conquer, dynamic programming, and greedy algorithms.
Provides a solid foundation in probability theory, which is essential for understanding randomized algorithms covered in the course.
Provides a practical guide to algorithm design and analysis. It covers a variety of techniques, including divide-and-conquer, dynamic programming, and greedy algorithms.
Classic introduction to algorithms. It good choice for students who want to learn about the history of algorithms and the different techniques used to design them.
Covers the theory and applications of randomized algorithms. It good resource for students who want to learn more about this topic.
Save
Provides a mathematical foundation for computer science. It good resource for students who want to learn more about the mathematical concepts that underlie algorithms and data structures.
Provides a comprehensive treatment of data structures and algorithms in C++. It good resource for students who want to learn more about these topics in the context of a specific programming language.
Provides a comprehensive treatment of data structures in Java. It good resource for students who want to learn more about these topics in the context of a specific programming language.
This monumental series of books provides an in-depth treatment of algorithms and data structures, with a focus on mathematical foundations.
This textbook provides a concise and accessible introduction to divide-and-conquer algorithms.
Provides a concise and clear overview of algorithms and data structures. It good resource for students who want to learn the basics of these topics.
Gentle introduction to algorithms. It good choice for students who are new to the subject.
This textbook provides a review of probability theory, which is essential for understanding randomized algorithms.
Comprehensive guide to the art of computer programming. It valuable reference for students who want to learn more about the design and analysis of algorithms.
Good introduction to probability. It good choice for students who want to learn more about the mathematical foundations of randomized algorithms.
Save
Good introduction to data mining. It good choice for students who want to learn more about the theory and applications of data mining.
Good introduction to machine learning. It good choice for students who want to learn more about the theory and applications of machine learning.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/gajyy5/divide
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Effort
4 weeks of study, 4-8 hours/week
Level
Intermediate
Via
Coursera
Institution
Stanford University
Instructor
Tim Roughgarden
Language
English
Transcripts
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آذربایجان دیلی
This course belongs to a
collection
called
Algorithms. It's comprised of four courses:
- Shortest Paths Revisited, NP-Complete Problems and What To Do About Them
- Graph Search, Shortest Paths, and Data Structures
- Divide and Conquer, Sorting and Searching, and Randomized Algorithms (viewing)
- Greedy Algorithms, Minimum Spanning Trees, and Dynamic Programming
Good to know
Explores algorithmic analysis and design, which is standard in software engineering, data science, and programming
Taught by Tim Roughgarden, who is a renowned computer scientist and author of popular textbooks on algorithms
Develops skills in algorithmic analysis and design, which are essential for building efficient and effective software systems
Examines asymptotic notation, sorting, searching, divide and conquer, and randomization, which are core concepts in algorithmic theory
Provides a solid foundation for advanced courses in algorithms and data structures
Requires some background in mathematics and programming, which may limit accessibility for beginners
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