An Introduction to the Analysis of Algorithms / Edition 1 by Robert Sedgewick, Philippe Flajolet | | 9780201400090 | Paperback | Barnes & Noble
An Introduction to the Analysis of Algorithms / Edition 1

An Introduction to the Analysis of Algorithms / Edition 1

by Robert Sedgewick, Philippe Flajolet
     
 

ISBN-10: 020140009X

ISBN-13: 9780201400090

Pub. Date: 06/15/1996

Publisher: Addison-Wesley

Despite the large interest in the mathematical analysis of algorithms, basic information on methods and models in widespread use has not been directly accessible for work or study in the field. The authors here address this need, combining a body of material that gives the reader both an appreciation for the challenges of the field and the requisite background for

Overview

Despite the large interest in the mathematical analysis of algorithms, basic information on methods and models in widespread use has not been directly accessible for work or study in the field. The authors here address this need, combining a body of material that gives the reader both an appreciation for the challenges of the field and the requisite background for keeping abreast of the new research being done to meet these challenges. Highlights: Thorough, self-contained coverage for students and professionals in computer science and mathematics Focus on mathematical techniques of analysis Basic preparation for the advanced results covered in Knuth's books and the research literature Classical approaches and results in the analysis of algorithms

Product Details

ISBN-13:
9780201400090
Publisher:
Addison-Wesley
Publication date:
06/15/1996
Edition description:
New Edition
Pages:
512
Product dimensions:
5.80(w) x 8.90(h) x 1.10(d)

Table of Contents

1. Analysis of Algorithms.
Why Analyze an Algorithm?
Computational Complexity.
Analysis of Algorithms.
Average-Case Analysis.
Example: Analysis of Quicksort.
Asymptotic Approximations.
Distributions.
Probabilistic Algorithms.

2. Recurrence Relations.
Basic Properties.
First-Order Recurrences.
Nonlinear First-Order Recurrences.
Higher-Order Recurrences.
Methods for Solving Recurrences.
Binary Divide-and-Conquer Recurrences and Binary Numbers.
General Divide-and-Conquer Recurrences.

3. Generating Functions.
Ordinary Generating Functions.
Exponential Generating Functions.
Generating Function Solution of Recurrences.
Expanding Generating Functions.
Transformations with Generating Functions.
Functional Equations on Generating Functions.
Solving the Quicksort Median-of-Three.
Recurrence with OGFs.
Counting with Generating Functions.
The Symbolic Method.
Lagrange Inversion.
Probability Generating Functions.
Bivariate Generating Functions.
Special Functions.

4. Asymptotic Approximations.
Notation for Asymptotic Approximations.
Asymptotic Expansions.
Manipulating Asymptotic Expansions.
Asymptotic Approximations of Finite Sums.
Euler-Maclaurin Summation.
Bivariate Asymptotics.
Laplace Method.
“Normal” Examples from the Analysis of Algorithms.
“Poisson” Examples from the Analysis of Algorithms.
Generating Function Asymptotics.

5. Trees.
Binary Trees.
Trees and Forests.
Properties of Trees.
Tree Algorithms.
Binary Search Trees.
Average Path Length in Catalan Trees.
Path Length in Binary Search Trees.
Additive Parameters of Random Trees.
Height.
Summary of Average-Case Results on Properties of Trees.
Representations of Trees and Binary Trees.
Unordered Trees.
Labelled Trees.
Other Types of Trees.

6. Permutations.
Basic Properties of Permutations.
Algorithms on Permutations.
Representations of Permutations.
Enumeration Problems.
Analyzing Properties of Permutations with CGFs.
Inversions and Insertion Sorts.
Left-to-Right Minima and Selection Sort.
Cycles and In Situ Permutation.
Extremal Parameters.

7. Strings and Tries.
String Searching.
Combinatorial Properties of Bitstrings.
Regular Expressions.
Finite-State Automata and Knuth-Morris-Pratt Algorithm.
Context-Free Grammars.
Tries.
Trie Algorithms.
Combinatorial Properties of Tries.
Larger alphabets.

8. Words and Maps.
Hashing with Separate Chaining.
Basic Properties of Words.
Birthday Paradox and Coupon Collector Problem.
Occupancy Restrictions and Extremal Parameters.
Occupancy Distributions.
Open Addressing Hashing.
Maps.
Integer Factorization and Maps.

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