This textbook, for second- or third-year students of computer science, presents insights, notations, and analogies to help them describe and think about algorithms like an expert, without grinding through lots of formal proof. Solutions to many problems are provided to let students check their progress, while class-tested PowerPoint slides are on the web for anyone running the course. By looking at both the big picture and easy step-by-step methods for developing algorithms, the author guides students around the common pitfalls. He stresses paradigms such as loop invariants and recursion to unify a huge range of algorithms into a few meta-algorithms. The book fosters a deeper understanding of how and why each algorithm works. These insights are presented in a careful and clear way, helping students to think abstractly and preparing them for creating their own innovative ways to solve problems.

• Includes lots of exercises, with selected solutions in the text; PowerPoint slides for instructors available from the web • Presents the big picture and step-by-step methods for developing algorithms, while avoiding common pitfalls • Appendices give background on big-O notation, logic, asymptotics, and other mathematical tools

### 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.

### Reviews

'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