Chapter 1 Introduction

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Preface xv Chapter 1 Introduction 1.1 What's the Book About? 1 1.2 Mathematics Review 2 1.2.1 Exponents 3 1.2.2 Logarithms 3 1.2.3 Series 4 1.2.4 Modular Arithmetic 5 1.2.5 The P Word 6 1.

1 Preface xv Chapter 1 Introduction 1.1 What's the Book About? Mathematics Review Exponents Logarithms Series Modular Arithmetic The P Word A Brief Introduction to Recursion C++Classes Basic dass 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= C-style Arrays and Strings Templates Function Templates Class Templates Object, Comparable, and an Example Function Objects Separate Compilation of Class Templates Using Matrices The Data Members, Constructor, and Basic Accessors operator[] Destructor, Copy Assignment, Copy Constructor 39

Summary 39 Exercises 39 References 41 Chapter 2 Algorithm Analysis 2.1 Mathematical Background 43 2.2 Model 46 2.3 What to Analyze 46 2.4 Running Time Calculations 49 2.4.1 A Simple Example 49 2.4.2 General Rules 50 2.

2 Summary 39 Exercises 39 References 41 Chapter 2 Algorithm Analysis 2.1 Mathematical Background Model What to Analyze Running Time Calculations A Simple Example General Rules Solutions for the Maximum Subsequence Sum Logarithms in the Running Time Checking Your Analysis AGrainofSalt 63 Summary 63 Exercises 64 References 69 Chapter 3 Lists, Stacks, and Queues 3.1 Abstract Data Types (ADTs) The List ADT Simple Array Implementation of Lists Simple Linked Lists vector and list in the STL Iterators Example: Using erase on a List const_iterators Implementation of vector Implementation of list The Stack ADT Stack Model Implementation of Stacks Applications The Queue ADT Queue Model Array Implementation of Queues Applications of Queues 106 Summary 107 Exercises 108 Chapter 4 Trees 4.1 Preliminaries Implementation of Trees Tree Traversais with an Application Binary Trees Implementation An Example: Expression Trees The Search Tree ADT Binary Search Trees contains findminandfindmax 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 Traversais (Revisited) B-Trees Sets and Maps in the Standard Library Sets Maps Implementation of set and map An Example That Uses Several Maps 168 Summary 174 Exercises 174 References 181 Chapter 5 Hashing 5.1 General Idea Hash Function Separate Chaining Hash Tables Without Linked Lists Linear Probing Quadratic Probing Double Hashing Rehashing 200

5.6 Hash Tables in the Standard Library 204 5.7 Extendible Hashing 204 Summary 207 Exercises 208 References 211 Chapter 6 Priority Queues (Heaps) 213 6.1 Model 213 6.2 Simple Implementations 214 6.

3 5.6 Hash Tables in the Standard Library Extendible Hashing 204 Summary 207 Exercises 208 References 211 Chapter 6 Priority Queues (Heaps) Model Simple Implementations BinaryHeap 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 Priority Queues in the Standard Library 251 Summary 251 Exercises 251 References 257 Chapter 7 Sorting Preliminaries Insertion Sort The Algorithm STL Implementation of Insertion Sort 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 SmallArrays Actual Quicksort Routines Analysis of Quicksort A Linear-Expected-Time Algorithm for Selection Indirect Sorting vector<comparable*> Does Not Work Smart Potnter 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 Bücket Sort External Sorting Why We Need New Algorithms Model for External Sorting The Simple Algorithm Multiway Merge Polyphase Merge Replacement Selection 304 Summary 305 Exercises 306 References 311 Chapter 8 The Disjoint Set Class Equivalence Relations The Dynamic Equivalence Problem Basic Data Structure 317

8.4 Smart Union Algorithms 321 8.5 Path Compression 324 8.6 Worst Case for Union-by-Rank and Path Compression 325 8.6.1 Analysis of the Union/Find Algorithm 326 8.

4 8.4 Smart Union Algorithms Path Compression Worst Case for Union-by-Rank and Path Compression Analysis of the Union/Find Algorithm An Application 331 Summary 334 Exercises 335 References 336 Chapter 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 Shortest Path Example Network Flow Problems A Simple Maxirnum-Flow Algorithm Minimum Spanning Tree Prim's Algorithm Kruskals Algorithm Applications of Depth-First Search Undirected Graphs Biconnectivity Euler Circuits Directed Graphs Finding Streng Components Introduction to NP-Completeness Easyvs. Hard The Class NP NP-Complete Problems 394 Summary 396 Exercises 396 References 404 Chapter 10 Algorithm Design Techniques 10.1 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 469 Summary 475 Exercises 475 References 485 Chapter 11 Amortized Analysis An Unrelated Puzzle Binomial Queues SkewHeaps Fibonacci Heaps Cutting Nodes in Leftist Heaps Lazy Merging for Binomial Queues The Fibonacci Heap Operations Proof of the Time Bound SplayTrees 509 Summary 513 Exercises 513 References 515

Chapter 12 Advanced Data Structures and Implementation 517 12.1 Top-Down Splay Trees 517 12.2 Red-Black Trees 525 12.2.1 Bottom-Up Insertion 526 12.2.2 Top-Down Red-Black Trees 527 12.2.3 Top-Down Deleüon 531 12.

5 Chapter 12 Advanced Data Structures and Implementation Top-Down Splay Trees Red-Black Trees Bottom-Up Insertion Top-Down Red-Black Trees Top-Down Deleüon Deterministic Skip Lists AA-Trees Treaps fe-d Trees Pairing Heaps 553 Summary 558 Exercises 558 References 563 Appendix A Separate Compilation of Class Templates 567 A. 1 Everything in the Header 568 A.2 Explicit Instantiation 568 A.3 The export Directive 570 Index 571

Data Structures and Algorithm Analysis in C++

INTERNATIONAL EDITION Data Structures and Algorithm Analysis in C++ FOURTH EDITION Mark A. Weiss Data Structures and Algorithm Analysis in C++, International Edition Table of Contents Cover Title Contents