An Introduction to the Analysis of Algorithms

Robert Sedgewick, Philippe Flajolet

  • 出版商: Addison Wesley
  • 出版日期: 1995-12-10
  • 定價: $1,300
  • 售價: 9.5$1,235
  • 語言: 英文
  • 頁數: 512
  • 裝訂: Hardcover
  • ISBN: 020140009X
  • ISBN-13: 9780201400090
  • 相關分類: Algorithms-data-structures
  • 立即出貨 (庫存 < 3)




This book is a thorough overview of the primary techniques and models used in the mathematical analysis of algorithms. The first half of the book draws upon classical mathematical material from discrete mathematics, elementary real analysis, and combinatorics; the second half discusses properties of discrete structures and covers the analysis of a variety of classical sorting, searching, and string processing algorithms.

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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.
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.
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.
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.
Integer Factorization and Maps. 020140009XT04062001

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1. 算法分析
2. 循環關係
3. 生成函數
4. 漸進近似
5. 樹
6. 排列
7. 字符串和字典樹
8. 字和映射