How to Think about Algorithms

by Jeff Edmonds

Overview

Understand algorithms and their design with this revised student-friendly textbook. Unlike other algorithms books, this one is approachable, the methods it explains are straightforward, and the insights it provides are numerous and valuable. Without grinding through lots of formal proof, students will benefit from step-by-step methods for developing algorithms, expert guidance on common pitfalls, and an appreciation of the bigger picture. Revised and updated, this second edition includes a new chapter on machine learning algorithms, and concise key concept summaries at the end of each part for quick reference. Also new to this edition are more than 150 new exercises: selected solutions are included to let students check their progress, while a full solutions manual is available online for instructors. No other text explains complex topics such as loop invariants as clearly, helping students to think abstractly and preparing them for creating their own innovative ways to solve problems.

Product Details

ISBN-13:	9781009302135
Publisher:	Cambridge University Press
Publication date:	03/07/2024
Edition description:	2nd ed.
Pages:	464
Product dimensions:	6.73(w) x 9.53(h) x 1.06(d)

About the Author

Jeff Edmonds is Professor in the Department of Electrical Engineering and Computer Science at York University, Canada.

Table of Contents

Preface; Introduction; Part I. Iterative Algorithms and Loop Invariants: 1. Iterative algorithms: measures of progress and loop invariants; 2. Examples using more-of-the-input loop invariant; 3. Abstract data types; 4. Narrowing the search space: binary search; 5. Iterative sorting algorithms; 6. Euclid's GCD algorithm; 7. The loop invariant for lower bounds; 8. Key concepts summary: loop invariants and iterative algorithms; 9. Additional exercises: Part I; 10. Partial solutions to additional exercises: Part I; Part II. Recursion: 11. Abstractions, techniques, and theory; 12. Some simple examples of recursive algorithms; 13. Recursion on trees; 14. Recursive images; 15. Parsing with context-free grammars; 16. Key concepts summary: recursion; 17. Additional exercises: Part II; 18. Partial solutions to additional exercises: Part II; Part III. Optimization Problems: 19. Definition of optimization problems; 20. Graph search algorithms; 21. Network flows and linear programming; 22. Greedy algorithms; 23. Recursive backtracking; 24. Dynamic programming algorithms; 25. Examples of dynamic programming; 26. Reductions and NP-completeness; 27. Randomized algorithms; 28. Key concepts summary: greedy algorithms and dynamic programmings; 29. Additional exercises: Part III; 30. Partial solutions to additional exercises: Part III; Part IV. Additional Topics: 31. Existential and universal quantifiers; 32. Time complexity; 33. Logarithms and exponentials; 34. Asymptotic growth; 35. Adding-made-easy approximations; 36. Recurrence relations; 37. A formal proof of correctness; 38. Additional exercises: Part IV; 39. Partial solutions to additional exercises: Part IV; Exercise Solutions; Conclusion; Index.

Editorial Reviews

‘Jeff Edmonds’ How to Think about Algorithms offers a fresh perspective, placing methodical but intuitive design principles (pre- and post-conditions, invariants, ‘transparent’ correctness) as the bedrock on which to build and practice algorithmic thinking. The book reads like an epic guided meditation on the vast universe of algorithms, directing the reader’s attention to the core of each insight, while stimulating the mind through well-paced examples, playful but concise analogies, and thought-provoking exercises.’ Nathan Chenette, Rose-Hulman Institute of Technology

‘With a good book like this in your hands, learning about algorithms and getting programs to work well will be fun and empowering. Anybody who wants to be a good programmer will get a great deal from this surprisingly readable book. Its approach makes it perfect for reading on your own if you want to enjoy learning about algorithms without being distracted by heavy maths. It has lots of exercises that are worth doing. Most importantly, How to Think about Algorithms does just that: it shows you how to think about algorithms and become a better programmer. Knowing how to think about algorithms gives you the insights and skills to make computers do anything more reliably and faster. The book is also ideal for any taught university course, because it is self-contained and systematically sets out the essential material, but most importantly because it empowers students to think for themselves.’ Harold Thimbleby, Swansea University

From the Publisher