An Introduction to the Analysis of Algorithms 2nd Edition by Robert Sedgewick, Philippe Flajolet 9780321905758
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Authors:Robert Sedgewick; Philippe Flajolet , Series:IT & Computer [47] , Tags:Computer; Information Technology , Author sort:Flajolet, Robert Sedgewick; Philippe , Identifiers:Identifiers:isbn-13:978-0-321-90575-8 , Languages:Languages:eng , Published:Published:Feb 2013 , Publisher:CRC , Comments:[Sedgewick and Flajolet] are not only worldwide leaders of the field, they also are masters of exposition. I am sure that every serious computer scientist will find this book rewarding in many ways.    —From the Foreword by Donald E. Knuth Despite growing interest, basic information on methods and models for mathematically analyzing algorithms has rarely been directly accessible to practitioners, researchers, or students. An Introduction to the Analysis of Algorithms, Second Edition, organizes and presents that knowledge, fully introducing primary techniques and results in the field.  Robert Sedgewick and the late Philippe Flajolet have drawn from both classical mathematics and computer science, integrating discrete mathematics, elementary real analysis, combinatorics, algorithms, and data structures. They emphasize the mathematics needed to support scientific studies that can serve as the basis for predicting algorithm performance and for comparing different algorithms on the basis of performance.  Techniques covered in the first half of the book include recurrences, generating functions, asymptotics, and analytic combinatorics. Structures studied in the second half of the book include permutations, trees, strings, tries, and mappings. Numerous examples are included throughout to illustrate applications to the analysis of algorithms that are playing a critical role in the evolution of our modern computational infrastructure.  Improvements and additions in this new edition include Upgraded figures and code An all-new chapter introducing analytic combinatorics Simplified derivations via analytic combinatorics throughout The book’s thorough, self-contained coverage will help readers appreciate the field’s challenges, prepare them for advanced results—covered in their monograph Analytic Combinatorics and in Donald Knuth’s Art of Computer Programming books—and provide the background they need to keep abreast of new research.« less; « less
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ISBN 13: 9780321905758
Author: Robert Sedgewick; Philippe Flajolet
Despite growing interest, basic information on methods and models for mathematically analyzing algorithms has rarely been directly accessible to practitioners, researchers, or students. An Introduction to the Analysis of Algorithms, Second Edition, organizes and presents that knowledge, fully introducing primary techniques and results in the field.
An Introduction to the Analysis of Algorithms 2nd Table of contents:
Chapter One. Analysis of Algorithms
1.1. Why Analyze an Algorithm?
1.2. Theory of Algorithms
1.3. Analysis of Algorithms
1.4. Average-Case Analysis
1.5. Example: Analysis of Quicksort
1.6. Asymptotic Approximations
1.7. Distributions
1.8. Randomized Algorithms
References
Chapter Two. Recurrence Relations
2.1. Basic Properties
2.2. First-Order Recurrences
2.3. Nonlinear First-Order Recurrences
2.4. Higher-Order Recurrences
2.5. Methods for Solving Recurrences
2.6. Binary Divide-and-Conquer Recurrences and Binary Numbers
2.7. General Divide-and-Conquer Recurrences
References
Chapter Three. Generating Functions
3.1. Ordinary Generating Functions
3.2. Exponential Generating Functions
3.3. Generating Function Solution of Recurrences
3.4. Expanding Generating Functions
3.5. Transformations with Generating Functions
3.6. Functional Equations on Generating Functions
3.7. Solving the Quicksort Median-of-Three Recurrence with OGFs
3.8. Counting with Generating Functions
3.9. Probability Generating Functions
3.10. Bivariate Generating Functions
3.11. Special Functions
References
Chapter Four. Asymptotic Approximations
4.1. Notation for Asymptotic Approximations
4.2. Asymptotic Expansions
4.3. Manipulating Asymptotic Expansions
4.4. Asymptotic Approximations of Finite Sums
4.5. Euler-Maclaurin Summation
4.6. Bivariate Asymptotics
4.7. Laplace Method
4.8. “Normal” Examples from the Analysis of Algorithms
4.9. “Poisson” Examples from the Analysis of Algorithms
References
Chapter Five. Analytic Combinatorics
5.1. Formal Basis
5.2. Symbolic Method for Unlabelled Classes
5.3. Symbolic Method for Labelled Classes
5.4. Symbolic Method for Parameters
5.5. Generating Function Coefficient Asymptotics
References
Chapter Six. Trees
6.1. Binary Trees
6.2. Forests and Trees
6.3. Combinatorial Equivalences to Trees and Binary Trees
6.4. Properties of Trees
6.5. Examples of Tree Algorithms
6.6. Binary Search Trees
6.7. Average Path Length in Random Catalan Trees
6.8. Path Length in Binary Search Trees
6.9. Additive Parameters of Random Trees
6.10. Height
6.11. Summary of Average-Case Results on Properties of Trees
6.12. Lagrange Inversion
6.13. Rooted Unordered Trees
6.14. Labelled Trees
6.15. Other Types of Trees
References
Chapter Seven. Permutations
7.1. Basic Properties of Permutations
7.2. Algorithms on Permutations
7.3. Representations of Permutations
7.4. Enumeration Problems
7.5. Analyzing Properties of Permutations with CGFs
7.6. Inversions and Insertion Sorts
7.7. Left-to-Right Minima and Selection Sort
7.8. Cycles and In Situ Permutation
7.9. Extremal Parameters
References
Chapter Eight. Strings and Tries
8.1. String Searching
8.2. Combinatorial properties of bitstrings
8.3. Regular Expressions
8.4. Finite-State Automata and the Knuth-Morris-Pratt Algorithm
8.5. Context-Free Grammars
8.6. Tries
8.7. Trie Algorithms
8.8. Combinatorial Properties of Tries
8.9. Larger Alphabets
References
Chapter Nine. Words and Mappings
9.1. Hashing with Separate Chaining
9.2. The Balls-and-Urns Model and Properties of Words
9.3. Birthday Paradox and Coupon Collector Problem
9.4. Occupancy Restrictions and Extremal Parameters
9.5. Occupancy Distributions
9.6. Open Addressing Hashing
9.7. Mappings
9.8. Integer Factorization and Mappings
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