Data Structures and Algorithm Analysis in C++

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1 INTERNATIONAL EDITION Data Structures and Algorithm Analysis in C++ FOURTH EDITION Mark A. Weiss

3 Data Structures and Algorithm Analysis in C++, International Edition Table of Contents Cover Title Contents Preface Chapter 1 Programming: A General Overview 1.1 Whats This Book About? 1.2 Mathematics Review Exponents Logarithms Series Modular Arithmetic The P Word 1.3 A Brief Introduction to Recursion 1.4 C++ Classes Basic class Syntax Extra Constructor Syntax and Accessors Separation of Interface and Implementation vector and string 1.5 C++ Details Pointers Lvalues, Rvalues, and Parameter Passing Return Passing std::swap and std::move The Big-Five: Destructor, Copy Constructor, Move Constructor, CopyAssignment operator=, Move Assignment operator= C-style Arrays and Strings 1.6 Templates Function Templates Class Templates Object, Comparable, and an Example Function Objects Separate Compilation of Class Templates 1.7 Using Matrices The Data Members, Constructor, and Basic Accessors operator[] Big-Five

4 Chapter 2 Algorithm Analysis 2.1 Mathematical Background 2.2 Model 2.3 What to Analyze 2.4 Running-Time Calculations A Simple Example General Rules Solutions for the Maximum SubsequenceSum Problem Logarithms in the Running Time Limitations of Worst-Case Analysis Chapter 3 Lists, Stacks, and Queues 3.1 Abstract Data Types (ADTs) 3.2 The List ADT Simple Array Implementation of Lists Simple Linked Lists 3.3 vector and list in the STL Iterators Example: Using erase on a List const_iterators 3.4 Implementation of vector 3.5 Implementation of list 3.6 The Stack ADT Stack Model Implementation of Stacks Applications 3.7 The Queue ADT Queue Model Array Implementation of Queues Applications of Queues Chapter 4 Trees 4.1 Preliminaries

5 4.1.1 Implementation of Trees Tree Traversals with an Application 4.2 Binary Trees Implementation An Example: Expression Trees 4.3 The Search Tree ADTBinary Search Trees contains findmin and findmax insert remove Destructor and Copy Constructor Average-Case Analysis 4.4 AVL Trees Single Rotation Double Rotation 4.5 Splay Trees A Simple Idea (That Does Not Work) Splaying 4.6 Tree Traversals (Revisited) 4.7 B-Trees 4.8 Sets and Maps in the Standard Library Sets Maps Implementation of set and map An Example That Uses Several Maps Chapter 5 Hashing 5.1 General Idea 5.2 Hash Function 5.3 Separate Chaining 5.4 Hash Tables without Linked Lists Linear Probing Quadratic Probing Double Hashing 5.5 Rehashing 5.6 Hash Tables in the Standard Library 5.7 Hash Tables with Worst-Case O(1) Access Perfect Hashing

6 5.7.2 Cuckoo Hashing Hopscotch Hashing 5.8 Universal Hashing 5.9 Extendible Hashing Chapter 6 Priority Queues (Heaps) 6.1 Model 6.2 Simple Implementations 6.3 Binary Heap Structure Property Heap-Order Property Basic Heap Operations Other Heap Operations 6.4 Applications of Priority Queues The Selection Problem Event Simulation 6.5 d-heaps 6.6 Leftist Heaps Leftist Heap Property Leftist Heap Operations 6.7 Skew Heaps 6.8 Binomial Queues Binomial Queue Structure Binomial Queue Operations Implementation of Binomial Queues 6.9 Priority Queues in the Standard Library Chapter 7 Sorting 7.1 Preliminaries 7.2 Insertion Sort The Algorithm STL Implementation of Insertion Sort Analysis of Insertion Sort 7.3 A Lower Bound for Simple Sorting Algorithms 7.4 Shellsort

7 7.4.1 Worst-Case Analysis of Shellsort 7.5 Heapsort Analysis of Heapsort 7.6 Mergesort Analysis of Mergesort 7.7 Quicksort Picking the Pivot Partitioning Strategy Small Arrays Actual Quicksort Routines Analysis of Quicksort A Linear-Expected-Time Algorithm for Selection 7.8 A General Lower Bound for Sorting Decision Trees 7.9 Decision-Tree Lower Bounds for Selection Problems 7.10 Adversary Lower Bounds 7.11 Linear-Time Sorts: Bucket Sort and Radix Sort 7.12 External Sorting Why We Need New Algorithms Model for External Sorting The Simple Algorithm Multiway Merge Polyphase Merge Replacement Selection Chapter 8 The Disjoint Sets Class 8.1 Equivalence Relations 8.2 The Dynamic Equivalence Problem 8.3 Basic Data Structure 8.4 Smart Union Algorithms 8.5 Path Compression 8.6 Worst Case for Union-by-Rank and Path Compression Slowly Growing Functions An Analysis by Recursive Decomposition An O( M log *N ) Bound An O( M (M, N) ) Bound 8.7 An Application

8 Chapter 9 Graph Algorithms 9.1 Definitions Representation of Graphs 9.2 Topological Sort 9.3 Shortest-Path Algorithms Unweighted Shortest Paths Dijkstras Algorithm Graphs with Negative Edge Costs Acyclic Graphs All-Pairs Shortest Path Shortest Path Example 9.4 Network Flow Problems A Simple Maximum-Flow Algorithm 9.5 Minimum Spanning Tree Prims Algorithm Kruskals Algorithm 9.6 Applications of Depth-First Search Undirected Graphs Biconnectivity Euler Circuits Directed Graphs Finding Strong Components 9.7 Introduction to NP-Completeness Easy vs. Hard The Class NP NP-Complete Problems Chapter 10 Algorithm Design Techniques 10.1 Greedy Algorithms A Simple Scheduling Problem Huffman Codes Approximate Bin Packing 10.2 Divide and Conquer Running Time of Divide-and-Conquer Algorithms Closest-Points Problem

9 The Selection Problem Theoretical Improvements for Arithmetic Problems 10.3 Dynamic Programming Using a Table Instead of Recursion Ordering Matrix Multiplications Optimal Binary Search Tree All-Pairs Shortest Path 10.4 Randomized Algorithms Random-Number Generators Skip Lists Primality Testing 10.5 Backtracking Algorithms The Turnpike Reconstruction Problem Games Chapter 11 Amortized Analysis 11.1 An Unrelated Puzzle 11.2 Binomial Queues 11.3 Skew Heaps 11.4 Fibonacci Heaps Cutting Nodes in Leftist Heaps Lazy Merging for Binomial Queues The Fibonacci Heap Operations Proof of the Time Bound 11.5 Splay Trees Chapter 12 Advanced Data Structuresand Implementation 12.1 Top-Down Splay Trees 12.2 Red-Black Trees Bottom-Up Insertion Top-Down Red-Black Trees Top-Down Deletion 12.3 Treaps 12.4 Suffix Arrays and Suffix Trees Suffix Arrays

10 Suffix Trees Linear-Time Construction of Suffix Arrays and Suffix Trees 12.5 k-d Trees 12.6 Pairing Heaps Appendix A Separate Compilationof Class Templates A.1 Everything in the Header A.2 Explicit Instantiation Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Chapter 1 Introduction

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 1.3 A Brief Introduction