Foundations of Algorithms

Foundations of Algorithms, Fifth Edition offers a well-balanced presentation of algorithm design, complexity analysis of algorithms, and computational complexity. Ideal for any computer science student with a background in college algebra and discrete structures, the text presents mathematical concepts using standard English and simple notation to maximize accessibility and user-friendliness. Concrete examples, appendices reviewing essential mathematical concepts, and a student-focused approach reinforce theoretical explanations and promote learning and retention. C++ and Java pseudocode help students better understand complex algorithms. A chapter on numerical algorithms includes a review of basic number theory, Euclid’s Algorithm for finding the greatest common divisor, a review of modular arithmetic, an algorithm for solving modular linear equations, an algorithm for computing modular powers, and the new polynomial-time algorithm for determining whether a number is prime.

The revised and updated Fifth Edition features an all-new chapter on genetic algorithms and genetic programming, including approximate solutions to the traveling salesperson problem, an algorithm for an artificial ant that navigates along a trail of food, and an application to financial trading. With fully updated exercises and examples, Foundations of Algorithms is an essential text for undergraduate and graduate courses in the design and analysis of algorithms.

Contents: Preface. 1. Algorithms: Efficiency, Analysis, and Order. 2. Divide-and-Conquer. 3. Dynamic Programming. 4. The Greedy Approach. 5. Backtracking. 6. Branch-and-Bound. 7. Introduction to Computational Complexity. 8. More Computational Complexity. 9. Computational Complexity and Intractability. 10. Genetic Algorithms and Genetic Programming. 11. Number-Theoretic Algorithms. 12. Introduction to Parallel Algorithms.Appendices. References. Index.