An Introduction to the Analysis of Algorithms

People who analyze algorithms have double happiness. First of all they experience the sheer beauty of elegant mathematical patterns that surround elegant computational procedures. Then they receive a practical payoff when their theories make it possible to get other jobs done more quickly and more economically.... The appearance of this long-awaited book is therefore most welcome. Its authors are not only worldwide leaders of the field, they also are masters of exposition. --D. E. Knuth This book provides a thorough introduction to the primary techniques used in the mathematical analysis of algorithms. The authors draw from classical mathematical material, including discrete mathematics, elementary real analysis, and combinatorics, as well as from classical computer science material, including algorithms and data structures. They focus on average-case or probabilistic analysis, although they also cover the basic mathematical tools required for worst-case or complexity analysis. Topics include recurrences, generating functions, asymptotics, trees, strings, maps, and an analysis of sorting, tree search, string search, and hashing algorithms. Despite the large interest in th