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How to Think about Algorithms


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Table of Contents

Part I. Iterative Algorithms and Loop Invariants: 1. 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; Part II. Recursion: 8. Abstractions, techniques, and theory; 9. Some simple examples of recursive algorithms; 10. Recursion on trees; 11. Recursive images; 12. Parsing with context-free grammars; Part III. Optimization Problems: 13. Definition of optimization problems; 14. Graph search algorithms; 15. Network flows and linear programming; 16. Greedy algorithms; 17. Recursive backtracking; 18. Dynamic programming algorithms; 19. Examples of dynamic programming; 20. Reductions and NP-completeness; 21. Randomized algorithms; Part IV. Appendix: 22. Existential and universal quantifiers; 23. Time complexity; 24. Logarithms and exponentials; 25. Asymptotic growth; 26. Adding made easy approximations; 27. Recurrence relations; 28. A formal proof of correctness; Part V. Exercise Solutions.

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Textbook that teaches students how to think about algorithms like an expert, without getting bogged down in formal proof.

About the Author

Jeff Edmonds received his Ph.D. in 1992 at University of Toronto in theoretical computer science. His thesis proved that certain computation problems require a given amount of time and space. He did his postdoctorate work at the ICSI in Berkeley on secure multi-media data transmission and in 1995 became an Associate Professor in the Department of Computer Science at York University, Canada. He has taught their algorithms course thirteen times to date. He has worked extensively at IIT Mumbai, India, and University of California San Diego. He is well published in the top theoretical computer science journals in topics including complexity theory, scheduling, proof systems, probability theory, combinatorics, and, of course, algorithms.


'Reading this is like sitting at the feet of the master: it leads an apprentice from knowing how to program to understanding deep principles of algorithms.' Harold Thimbleby, The Times Higher Education Supplement
'... a great book to learn how to design and create new algorithms ... a good book that the reader will appreciate in the first and subsequent reads, and it will make better developers and programmers.' Journal of Functional Programming
"Edmonds intends this text for use in advanced undergraduate courses in algorithms. The author encourages abstract thinking through exercises informed by real-world scenarios to help students access and master algorithm concepts, including proofs of correctness, with greater ease. Twenty-one chapters under the main themes of iterative algorithms and loop invariants (section one), recursion (section two), and optimization problems (section three) cover topics that include: measures of progress and loop invariants, abstract data types, binary search, iterative sorting algorithms, abstractions and theory, recursion on trees, recursive images, graph search algorithms, network flows and linear programming, greedy algorithms, and dynamic programming algorithms. Seven additional chapters in the appendix consider specific algorithms such as those measuring time complexity and asymptomatic growth." Book News, Inc.
"Reading this is like sitting at the feet of the master: it leads an apprentice from knowing how to program to understanding deep principles of algorithms. Presentation [is] informed and friendly." Harold Thimbleby, Times Higher Education
"I believe this book could be considered a must-read for every teacher of algorithms. Even if he reads things he already knows, he will be able to view them from different angles and in the process get some very useful ideas on how to explain algorithms in class. The book would also be invaluable to researchers who wish to gain a deeper understanding on how algorithms work, and to undergraduate students who wish to develop their algorithmic thought... it has the potential to be considered a classic." Kyriakos N. Sgarbas for SIGACT News
"All in all this is a great book to learn how to design and create new algorithms. The author teaches you how to think about algorithms step by step, building the necessary knowledge and illustrating the process with common algorithms. This is a good book that the reader will appreciate in the first and subsequent reads, it will make better developers and programmers." Journal of Fuctional Programming

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