**1. Introduction.**

What's the Book About?

Mathematics Review.

Exponents.

Logarithms.

Series.

Modular Arithmetic.

The P Word.

A Brief Introduction to Recursion

C++ Classes.

Basic class Syntax.

Extra Constructor Syntax and Accessors

Separation of Interface and Implementation.

vector and string.

C++ Details.

Pointers.

Parameter Passing.

Return Passing

Reference Variables.

The Big Three: Destructor, Copy Constructor, operator=.

The World of C.

Templates.

Function Templates.

Class Templates.

Object, Comparable, and an Example.

Using Matrices.

The Data Members, Constructor, and Basic Accessors.

operator [ ].

Destructor, Copy Assignment, Copy Constructor.

Summary.

Exercises.

References.

**2. Algorithm Analysis.**

Mathematical Background.

Model.

What to Analyze.

Running Time Calculations.

A Simple Example.

General Rules.

Solutions for the Maximum Subsequence Sum Problem.

Logarithms in the Running Time.

Checking Your Analysis.

A Grain of Salt.

Summary.

Exercises.

References.

**3. Lists, Stacks, and Queues.**

Abstract Data Types (ADTs).

The List ADT.

Simple Array Implementation of Lists.

Linked Lists.

Programming Details.

Memory Reclamation and the Big Three.

Doubly Linked Lists.

Circular Linked Lists.

Examples.

Cursor Implementation of Linked Lists.

The Stack ADT.

Stack Model.

Implementation of Stacks.

Applications.

The Queue ADT.

Queue Model.

Array Implementation of Queues.

Applications of Queues.

Summary.

Exercises.

**4. Trees.**

Preliminaries.

Implementation of Trees.

Tree Traversals with an Application.

Binary Trees.

Implementation.

An Example: Expression Trees.

The Search Tree ADT-Binary Search Trees.

find.

findMin and findMax.

insert.

remove.

Destructor and Copy Assignment Operator.

Average-Case Analysis.

AVL Trees.

Single Rotation.

Double Rotation.

Splay Trees.

A Simple Idea (That Does Not Work).

Splaying.

Tree Traversals (Revisited).

B-Trees.

Summary.

Exercises.

References.

**5. Hashing.**

General Idea.

Hash Function.

Separate Chaining.

Open Addressing.

Linear Probing.

Quadratic Probing.

Double Hashing.

Rehashing.

Extendible Hashing.

Summary.

Exercises.

References.

**6. Priority Queues (Heaps).**

Model.

Simple Implementations.

Binary Heap.

Structure Property.

Heap-Order Property.

Basic Heap Operations.

Other Heap Operations.

Applications of Priority Queues.

The Selection Problem.

Event Simulation.

d-Heaps.

Leftist Heaps.

Leftist Heap Property.

Leftist Heap Operations.

Skew Heaps.

Binomial Queues.

Binomial Queue Structure.

Binomial Queue Operations.

Implementation of Binomial Queues.

Summary.

Exercises.

References.

**7. Sorting.**

Preliminaries.

Insertion Sort.

The Algorithm.

Analysis of Insertion Sort.

A Lower Bound for Simple Sorting Algorithms.

Shellsort.

Worst-Case Analysis of Shellsort

Heapsort.

Analysis of Heapsort.

Mergesort.

Analysis of Mergesort.

Quicksort.

Picking the Pivot.

Partitioning Strategy.

Small Arrays.

Actual Quicksort Routines.

Analysis of Quicksort

A Linear-Expected-Time Algorithm for Selection.

Indirect Sorting.

vector<Comparable *> Does Not Work.

Smart Pointer Class.

Overloading operator<

Dereferencing a Pointer with *.

Overloading the Type Conversion Operator

Implicit Type Conversions Are Everywhere.

Dual-Direction Implicit Conversions Can Cause Ambiguities.

Pointer Subtraction Is Legal.

A General Lower Bound for Sorting.

Decision Trees.

Bucket Sort.

External Sorting.

Why We Need New Algorithms.

Model for External Sorting.

The Simple Algorithm.

Multiway Merge.

Polyphase Merge.

Replacement Selection.

Summary.

Exercises.

References.

**8. The Disjoint Set ADT.**

Equivalence Relations.

The Dynamic Equivalence Problem.

Basic Data Structure.

Smart Union Algorithms.

Path Compression.

Worst Case for Union-by-Rank and Path Compression.

Analysis of the Union/Find Algorithm.

An Application.

Summary.

Exercises.

References.

**9. Graph Algorithms.**

Definitions.

Representation of Graphs.

Topological Sort.

Shortest-Path Algorithms.

Unweighted Shortest Paths.

Dijkstra's Algorithm.

Graphs with Negative Edge Costs

Acyclic Graphs.

All-Pairs Shortest Path.

Network Flow Problems.

A Simple Maximum-Flow Algorithm.

Minimum Spanning Tree.

Prim's Algorithm.

Kruskal's Algorithm.

Applications of Depth-First Search.

Undirected Graphs.

Biconnectivity.

Euler Circuits.

Directed Graphs.

Finding Strong Components.

Introduction to NP-Completeness.

Easy vs. Hard.

The Class NP.

NP-Complete Problems.

Summary.

Exercises.

References.

**10. Algorithm Design Techniques.**

Greedy Algorithms.

A Simple Scheduling Problem.

Huffman Codes.

Approximate Bin Packing.

Divide and Conquer.

Running Time of Divide and Conquer Algorithms.

Closest-Points Problem.

The Selection Problem.

Theoretical Improvements for Arithmetic Problems.

Dynamic Programming.

Using a Table Instead of Recursion.

Ordering Matrix Multiplications.

Optimal Binary Search Tree.

All-Pairs Shortest Path.

Randomized Algorithms.

Random Number Generators.

Skip Lists.

Primality Testing.

Backtracking Algorithms.

The Turnpike Reconstruction Problem.

Games.

Summary.

Exercises.

References.

**11. Amortized Analysis.**

An Unrelated Puzzle.

Binomial Queues.

Skew Heaps.

Fibonacci Heaps.

Cutting Nodes in Leftist Heaps.

Lazy Merging for Binomial Queues.

The Fibonacci Heap Operations.

Proof of the Time Bound.

Splay Trees.

Summary.

Exercises.

References.

**12. Advanced Data Structures and Implementation.**

Top-Down Splay Trees.

Red-Black Trees.

Bottom-Up Insertion.

Top-Down Red-Black Trees.

Top-Down Deletion.

Deterministic Skip Lists.

AA-Trees.

Treaps.

k-d Trees.

Pairing Heaps.

Summary.

Exercises.

References.

**Appendix A. The Standard Template Library.**

Introduction

Basic STL Concepts.

Header Files and the using Directive

Containers.

iterator.

Pairs.

Function Objects.

Unordered Sequences: vector and list.

vector versus list.

Stacks and Queues.

Sets.

Maps.

Example: Generating a Concordance.

STL Version.

Version without Using the STL

Example: Shortest-Path Calculation.

STL Implementation.

Version without Using the STL.

Other STL Features.

**Appendix B. vector and string Classes.**

First-Class versus Second-Class Objects.

vector Class.

string Class.

**Index. 0201361221T04062001**