How to Think About Algorithms

Description

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. 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.