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Trees and Graphs

Basics

Sriram Sankaranarayanan

Basic algorithms on tree data structures, binary search trees, self-balancing trees, graph data structures and basic traversal algorithms on graphs. This course also covers advanced topics such as kd-trees for spatial data and algorithms for spatial data.

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Basic algorithms on tree data structures, binary search trees, self-balancing trees, graph data structures and basic traversal algorithms on graphs. This course also covers advanced topics such as kd-trees for spatial data and algorithms for spatial data.

Trees and Graphs: Basics can be taken for academic credit as part of CU Boulder’s Master of Science in Data Science (MS-DS) degree offered on the Coursera platform. The MS-DS is an interdisciplinary degree that brings together faculty from CU Boulder’s departments of Applied Mathematics, Computer Science, Information Science, and others. With performance-based admissions and no application process, the MS-DS is ideal for individuals with a broad range of undergraduate education and/or professional experience in computer science, information science, mathematics, and statistics. Learn more about the MS-DS program at https://www.coursera.org/degrees/master-of-science-data-science-boulder.

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What's inside

Syllabus

Binary Search Trees and Algorithms on Trees
In this module, you will learn about binary search trees and basic algorithms on binary search trees. We will also become familiar with the problem of balancing in binary search trees and study some solutions for balanced binary search trees such as Red-Black Trees.
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Traffic lights

Read about what's good
what should give you pause
and possible dealbreakers
Provides a comprehensive overview of advanced data structures and algorithms essential for data scientists and computer scientists
Suitable for students with experience in basic data structures and algorithm concepts
Taught by an experienced and recognized instructor in the field of computer science
Emphasizes practical applications of data structures and algorithms in the real world
Aligned with the requirements of the MS in Data Science from CU Boulder, a reputable university
May require additional prerequisite knowledge for students with limited exposure to data structures and algorithms

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Reviews summary

Foundational algorithms for data science

According to learners, this course provides a solid foundation in core data structures and algorithms, including trees and graphs. Many students praise the instructor's clear explanations, finding complex topics like Bellman-Ford and Dijkstra's algorithms easier to grasp. While the content is comprehensive for basics, some note a strong theoretical focus, with fewer hands-on coding exercises than desired. Quizzes and assignments are often described as challenging, sometimes requiring external resources. This course is considered a valuable prerequisite for advanced studies in data science and computer science.
Emphasizes conceptual understanding over practical coding implementation.
"I wished for more hands-on coding exercises. It's very strong on theory, which is good, but applying it directly would have been even better."
"I found the course lacks practical application. There are very few coding exercises, and the focus is almost entirely on theoretical proofs and concepts."
"It's a good theoretical course but don't expect much coding practice."
Provides a thorough introduction to essential data structures.
"This course was exactly what I needed to solidify my understanding of fundamental algorithms."
"A very comprehensive introduction to trees and graphs."
"It sets you up perfectly for more advanced algorithm courses. This is a must-take for any aspiring data scientist."
Instructor excels at simplifying complex algorithmic concepts.
"The instructor's explanations for Red-Black Trees and Dijkstra's algorithm were incredibly clear, making complex topics digestible."
"Fantastic course! The way the instructor explained Union-Find and spanning tree algorithms was superb."
"I found the lectures very clear and concise, making topics like Red-Black Trees much more understandable."
Pacing can be fast for beginners; assumes some prior CS knowledge.
"The pace felt just right for someone with a basic CS background."
"The pacing was a bit fast for me as a beginner coming from a non-CS background."
"Completely overwhelmed. The course claims to be 'basics' but moves at an extremely fast pace with dense theoretical concepts. I felt lost without a strong prior background in discrete math and data structures. Not for true beginners."
Quizzes and assignments are demanding and require extra effort.
"The quizzes and assignments are quite challenging and sometimes felt like a significant leap from the lecture material. I had to spend a lot of time searching external resources."
"The assignments are tough but fair, they really make you think."
"I struggled with some of the homework assignments; they definitely push you beyond the lecture material."

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 Trees and Graphs: Basics with these activities:
Refresher: Asymptotic Analysis
This will help you prepare for the mathematical rigor of this course
Browse courses on Asymptotic Analysis
Show steps
  • Review time complexity concepts
  • Practice analyzing time complexity of common algorithms
Review of Introduction to Algorithms, 3rd Edition by Cormen, Leiserson, Rivest, and Stein
Reinforce your understanding of the fundamental concepts of algorithms and data structures
View Algorithms Unlocked (Mit Press) on Amazon
Show steps
  • Read the book
  • Summarize key concepts
  • Solve practice problems
Visualize a binary search tree
Will help you understand the insertion, deletion, and searching in a BST
Browse courses on Binary Search Trees
Show steps
  • Draw a binary search tree with a given set of values
  • Perform insert, delete, and search operations on the tree
Four other activities
Expand to see all activities and additional details
Show all seven activities
Study group for graph theory
Group study can clarify confusing material and improve understanding of concepts.
Browse courses on Graph Theory
Show steps
  • Set up a study group meeting
  • Review course material together
  • Work on practice problems together
Graph Algorithms Problem Solving
Will help familiarize you with common graph algorithms and their applications.
Browse courses on Graph Algorithms
Show steps
  • Solve a variety of graph problems using depth first search
  • Solve a variety of graph problems using breadth first search
  • Solve a variety of graph problems using Dijkstra's algorithm
Write a blog post about a graph algorithm
Create rich content that will help you master both the content and your writing abilities
Browse courses on Graph Algorithms
Show steps
  • Research a graph algorithm
  • Write a outline
  • Write a draft
  • Edit and publish your blog post
Annotated Bibliography on graph algorithms
Gain a deeper understanding of a specific graph algorithm by researching and summarizing findings.
Browse courses on Graph Algorithms
Show steps
  • Research graph algorithms
  • Select relevant articles or papers
  • Read and annotate the selected resources

Career center

Learners who complete Trees and Graphs: Basics will develop knowledge and skills that may be useful to these careers:
Data Scientist
Data Scientists are responsible for collecting, analyzing, and interpreting data to help businesses make informed decisions. This course provides a strong foundation in the algorithms and data structures used in data science, which are essential for success in this role. Specifically, the modules on binary search trees, graph traversal algorithms, and shortest path algorithms are particularly relevant to the work of a Data Scientist.
See salaries and explore the career path for Data Scientist
Software Engineer
Software Engineers design, develop, and maintain software systems. This course provides a strong foundation in the algorithms and data structures used in software engineering, which are essential for success in this role. Specifically, the modules on binary search trees, graph traversal algorithms, and shortest path algorithms are particularly relevant to the work of a Software Engineer.
See salaries and explore the career path for Software Engineer
Database Administrator
Database Administrators are responsible for managing and maintaining databases. This course provides a strong foundation in the algorithms and data structures used in database management, which are essential for success in this role. Specifically, the modules on binary search trees, graph traversal algorithms, and shortest path algorithms are particularly relevant to the work of a Database Administrator.
See salaries and explore the career path for Database Administrator
Data Analyst
Data Analysts collect, analyze, and interpret data to help businesses make informed decisions. This course provides a strong foundation in the algorithms and data structures used in data analysis, which are essential for success in this role. Specifically, the modules on binary search trees, graph traversal algorithms, and shortest path algorithms are particularly relevant to the work of a Data Analyst.
See salaries and explore the career path for Data Analyst
Business Analyst
Business Analysts help businesses understand their data and make better decisions. This course provides a strong foundation in the algorithms and data structures used in business analysis, which are essential for success in this role. Specifically, the modules on binary search trees, graph traversal algorithms, and shortest path algorithms are particularly relevant to the work of a Business Analyst.
See salaries and explore the career path for Business Analyst
Quantitative Analyst
Quantitative Analysts use mathematical and statistical methods to analyze data and make predictions. This course provides a strong foundation in the algorithms and data structures used in quantitative analysis, which are essential for success in this role. Specifically, the modules on binary search trees, graph traversal algorithms, and shortest path algorithms are particularly relevant to the work of a Quantitative Analyst.
See salaries and explore the career path for Quantitative Analyst
Operations Research Analyst
Operations Research Analysts use mathematical and statistical methods to solve business problems. This course provides a strong foundation in the algorithms and data structures used in operations research, which are essential for success in this role. Specifically, the modules on binary search trees, graph traversal algorithms, and shortest path algorithms are particularly relevant to the work of an Operations Research Analyst.
See salaries and explore the career path for Operations Research Analyst
Computer Scientist
Computer Scientists design, develop, and analyze algorithms and data structures. This course provides a strong foundation in the algorithms and data structures used in computer science, which are essential for success in this role. Specifically, the modules on binary search trees, graph traversal algorithms, and shortest path algorithms are particularly relevant to the work of a Computer Scientist.
See salaries and explore the career path for Computer Scientist
Machine Learning Engineer
Machine Learning Engineers design and develop machine learning models. This course provides a strong foundation in the algorithms and data structures used in machine learning, which are essential for success in this role. Specifically, the modules on binary search trees, graph traversal algorithms, and shortest path algorithms are particularly relevant to the work of a Machine Learning Engineer.
See salaries and explore the career path for Machine Learning Engineer
Data Engineer
Data Engineers design and build data pipelines. This course provides a strong foundation in the algorithms and data structures used in data engineering, which are essential for success in this role. Specifically, the modules on binary search trees, graph traversal algorithms, and shortest path algorithms are particularly relevant to the work of a Data Engineer.
See salaries and explore the career path for Data Engineer
Statistician
Statisticians collect, analyze, and interpret data. This course provides a strong foundation in the algorithms and data structures used in statistics, which are essential for success in this role. Specifically, the modules on binary search trees, graph traversal algorithms, and shortest path algorithms are particularly relevant to the work of a Statistician.
See salaries and explore the career path for Statistician
Actuary
Actuaries use mathematical and statistical methods to assess risk and uncertainty. This course provides a strong foundation in the algorithms and data structures used in actuarial science, which are essential for success in this role. Specifically, the modules on binary search trees, graph traversal algorithms, and shortest path algorithms are particularly relevant to the work of an Actuary.
See salaries and explore the career path for Actuary
Financial Analyst
Financial Analysts use mathematical and statistical methods to analyze financial data and make investment recommendations. This course provides a strong foundation in the algorithms and data structures used in financial analysis, which are essential for success in this role. Specifically, the modules on binary search trees, graph traversal algorithms, and shortest path algorithms are particularly relevant to the work of a Financial Analyst.
See salaries and explore the career path for Financial Analyst
Market Researcher
Market Researchers collect, analyze, and interpret data to understand consumer behavior and market trends. This course provides a strong foundation in the algorithms and data structures used in market research, which are essential for success in this role. Specifically, the modules on binary search trees, graph traversal algorithms, and shortest path algorithms are particularly relevant to the work of a Market Researcher.
See salaries and explore the career path for Market Researcher
User Experience Researcher
User Experience Researchers conduct research to understand how users interact with products and services. This course provides a strong foundation in the algorithms and data structures used in user experience research, which are essential for success in this role. Specifically, the modules on binary search trees, graph traversal algorithms, and shortest path algorithms are particularly relevant to the work of a User Experience Researcher.
See salaries and explore the career path for User Experience Researcher

Reading list

We've selected 12 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 Trees and Graphs: Basics.
Cover image
Introduction to Algorithms, fourth edition
Save
Is commonly used as a textbook for undergraduate and graduate courses in algorithms. It covers algorithms commonly taught in computer science programs and their analyses.
Introduction to Algorithms, fourth edition
Paperback
Check
Introduction to Algorithms, fourth edition
Kindle Edition
Check
Cover image
Data Structures and Algorithms in Java
Save
Is commonly used as a textbook for undergraduate courses in data structures and algorithms. It covers data structures commonly implemented in Java and their algorithms.
Data Structures and Algorithms in Java
Paperback
$$$$
Data Structures and Algorithms in Java, 6th Edition
Kindle Edition
$$$
Cover image
Introduction to Programming in Java
Save
Is commonly used as a textbook for undergraduate courses in algorithms. It covers algorithms commonly taught in computer science programs and their analyses. Also includes exercises and challenges for further learning and practice.
Introduction to Programming in Java: An...
Paperback
$$$
Introduction to Programming in Java: An...
Paperback
$$$
Introduction to Programming in Java: An...
Kindle Edition
$$
Cover image
The New Turing Omnibus
Save
Provides simple and entertaining introductions to graph theory and tree theory. Can be used as a supplementary reading for the course.
New Turing Omnibus (New Turning Omnibus : 66...
Paperback
$$
New Turing Omnibus by A. K. Dewdney (1-Aug-2003)...
Paperback
$$
Cover image
Data Structures and Algorithms in Java, 6th Edition
Save
Is commonly used as a textbook for undergraduate courses in data structures and algorithms. It covers data structures commonly implemented in Python and their algorithms.
Data Structures and Algorithms in Java 6th Edition...
Paperback
$$$
Data Structures and Algorithms in Java, 6th Edition
Kindle Edition
$$$
Cover image
Algorithms, Part II
Save
Covers algorithms commonly taught in computer science programs and their analyses. It also includes exercises and challenges for further learning and practice.
Algorithms, Part II
Kindle Edition
$$
Cover image
Graph Theory with Applications to Engineering and...
Save
Provides a comprehensive introduction to graph theory with applications to engineering and computer science. It covers a wide range of graph theoretical concepts.
Graph Theory with Applications to Engineering and...
Paperback
Check
Graph Theory with Applications to Engineering and...
Kindle Edition
Check
Discrete Mathematics and Its Applications (Eighth...
Save
Provides a comprehensive introduction to discrete mathematics with applications to computer science. It covers a wide range of topics, including graph theory, trees, and algorithms.
(中文) Discrete Mathematics and Its Applications (in...
Paperback
$$
Algorithms and Data Structures
Save
Provides a concise and clear introduction to algorithms and data structures. It covers a wide range of topics, including trees, graphs, and sorting algorithms.
Algorithms and Data Structures
Paperback
Check
Algorithms and Data Structures
Kindle Edition
Check
Cover image
An Introduction to Data Structures and Algorithms
Save
Provides a comprehensive introduction to graph theory with a focus on computer science applications. It covers a wide range of graph theoretical concepts.
An Introduction to Data Structures and Algorithms
Hardcover
$$
An Introduction to Data Structures and Algorithms...
Kindle Edition
$$
Cover image
Handbook of Graph Theory, Second Edition
Save
Provides a comprehensive reference for graph theory. It covers a wide range of graph theoretical concepts, including trees, graphs, and algorithms.
Handbook of Graph Theory, Second Edition
Paperback
Check
Handbook of Graph Theory, Second Edition
Kindle Edition
Check
Exchange in Oceania
Save
Provides a comprehensive introduction to graph theory. It covers a wide range of graph theoretical concepts, including trees, graphs, and algorithms.
Exchange in Oceania: A Graph Theoretic Analysis...
Hardcover
$$$$

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Effort
8-15 hours a week for 4 weeks
Level
Advanced
Via
Coursera
Institution
University of Colorado Boulder
Instructor
Sriram Sankaranarayanan
Language
English
Transcripts
Español Français Português Deutsch Italiano 中文 العربية 한국어 日本語 हिंदी Nederlands Svenska Pусский Türkçe Polski Ελληνικά українська мова magyar nyelv Bahasa Indonesia ไทย қазақша اُردُو, فارسی বাংলা پښتو آذربایجان دیلی
Trees and Graphs: Basics belongs to the following collections:
  1. Data Science Foundations: Data Structures and Algorithms
  2. Foundations of Data Structures and Algorithms
Traffic lights
Read about what's good
what should give you pause
and possible dealbreakers
Provides a comprehensive overview of advanced data structures and algorithms essential for data scientists and computer scientists
Suitable for students with experience in basic data structures and algorithm concepts
Taught by an experienced and recognized instructor in the field of computer science
Emphasizes practical applications of data structures and algorithms in the real world
Aligned with the requirements of the MS in Data Science from CU Boulder, a reputable university
May require additional prerequisite knowledge for students with limited exposure to data structures and algorithms
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