An Introduction to the Analysis of Algorithms / Edition 1by Robert Sedgewick, Philippe Flajolet
Pub. Date: 06/15/1996
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
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- New Edition
- Product dimensions:
- 5.80(w) x 8.90(h) x 1.10(d)
Table of Contents1. Analysis of Algorithms.
Analysis of Algorithms.
Example: Analysis of Quicksort.
2. Recurrence Relations.
Nonlinear First-Order Recurrences.
Methods for Solving Recurrences.
Binary Divide-and-Conquer Recurrences and Binary Numbers.
General Divide-and-Conquer Recurrences.
3. 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.
Probability Generating Functions.
Bivariate Generating Functions.
4. Asymptotic Approximations.
Manipulating Asymptotic Expansions.
Asymptotic Approximations of Finite Sums.
“Normal” Examples from the Analysis of Algorithms.
“Poisson” Examples from the Analysis of Algorithms.
Generating Function Asymptotics.
Trees and Forests.
Properties of Trees.
Binary Search Trees.
Average Path Length in Catalan Trees.
Path Length in Binary Search Trees.
Additive Parameters of Random Trees.
Summary of Average-Case Results on Properties of Trees.
Representations of Trees and Binary Trees.
Other Types of Trees.
Algorithms on Permutations.
Representations of Permutations.
Analyzing Properties of Permutations with CGFs.
Inversions and Insertion Sorts.
Left-to-Right Minima and Selection Sort.
Cycles and In Situ Permutation.
7. Strings and Tries.
Combinatorial Properties of Bitstrings.
Finite-State Automata and Knuth-Morris-Pratt Algorithm.
Combinatorial Properties of Tries.
8. Words and Maps.
Basic Properties of Words.
Birthday Paradox and Coupon Collector Problem.
Occupancy Restrictions and Extremal Parameters.
Open Addressing Hashing.
Integer Factorization and Maps.
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