
- 152 pages
- English
- PDF
- Available on iOS & Android
An Introduction to the Analysis of Algorithms
About this book
This textbook covers the mathematical foundations of the analysis of algorithms. The gist of the book is how to argue, without the burden of excessive formalism, that a given algorithm does what it is supposed to do. The two key ideas of the proof of correctness, induction and invariance, are employed in the framework of pre/post-conditions and loop invariants.
The algorithms considered are the basic and traditional algorithms of computer science, such as Greedy, Dynamic and Divide & Conquer. In addition, two classes of algorithms that rarely make it into introductory textbooks are discussed. Randomized algorithms, which are now ubiquitous because of their applications to cryptography; and Online algorithms, which are essential in fields as diverse as operating systems (caching, in particular) and stock-market predictions.
This self-contained book is intended for undergraduate students in computer science and mathematics.
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Information
Table of contents
- Contents
- Preface
- 1. Preliminaries
- 2. Greedy Algorithms
- 3. Divide and Conquer
- 4. Dynamic Programming
- 5. Online Algorithms
- 6. Randomized Algorithms
- Appendix A Number Theory and Group Theory
- Appendix B Relations
- Bibliography
- Index