Introduction to the analysis of algorithms.

Chapter 1: Analysis of Algorithms
1.1 Why Analyze an Algorithms
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
Chapter 2: 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
Chapter 3: 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
Chapter 4: 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
Chapter 5: 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
Chapter 6: 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 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
Chapter 7: 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
Chapter 8: 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
Chapter 9: 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
List of Theorems
List of Tables
List of Figures
Index.

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. Authors Robert Sedgewick and the late Philippe Flajolet 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. Improvements and additions in this new edition include upgraded figures and code, an all-new chapter introducing analytic combinatorics, and simplified derivations via analytic combinatorics throughout. The book’s thorough, self-contained coverage will help readers appreciate the field’s challenges and prepare them for advanced study.