Chapter 1 Programming： A General Overview 1
1.1 What’s This 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 to Recursion 8
1.4 C++ Classes 12
1.4.1 Basic class Syntax 12
1.4.2 Extra Constructor Syntax and Accessors 13
1.4.3 Separation of Interface and Implementation 16
1.4.4 vector and string 19
1.5 C++ Details 21
1.5.1 Pointers 21
1.5.2 Lvalues， Rvalues， and References 23
1.5.3 Parameter Passing 25
1.5.4 Return Passing 27
1.5.5 std：：swap and std：：move 29
1.5.6 The Big—Five： Destructor， Copy Constructor， Move Constructor， Copy
Assignment operator=， Move Assignment operator= 30
1.5.7 C—style Arrays and Strings 35
1.6 Templates 36
1.6.1 Function Templates 37
1.6.2 Class Templates 38
1.6.3 Object， Comparable， and an Example 39
1.6.4 Function Objects 41
1.6.5 Separate Compilation of Class Templates 44
1.7 Using Matrices 44
1.7.1 The Data Members， Constructor， and Basic Accessors 44
1.7.2 operator（） 45
1.7.3 Big—Five 46
Summary 46
Exercises 46
References 48
Chapter 2 Algorithm Analysis 51
2.1 Mathematical Background 51
2.2 Model 54
2.3 What to Analyze 54
2.4 Running—Time Calculations 57
2.4.1 A Simple Example 58
2.4.2 General Rules 58
2.4.3 Solutions for the Maximum Subsequence
Sum Problem 60
2.4.4 Logarithms in the Running Time 66
2.4.5 Limitations of Worst—Case Analysis 70
Summary 70
Exercises 71
References 76
Chapter 3 Lists， Stacks， and Queues 77
3.1 Abstract Data Types （ADTs） 77
3.2 The List ADT 78
3.2.1 Simple Array Implementation of Lists 78
3.2.2 Simple Linked Lists 79
3.3 vector and list in the STL 80
3.3.1 Iterators 82
3.3.2 Example： Using erase on a List 83
3.3.3 const_iterators 84
3.4 Implementation of vector 86
3.5 Implementation of list 91
3.6 The Stack ADT 103
3.6.1 Stack Model 103
3.6.2 Implementation of Stacks 104
3.6.3 Applications 104
3.7 The Queue ADT 112
3.7.1 Queue Model 113
3.7.2 Array Implementation of Queues 113
3.7.3 Applications of Queues 115
Summary 116
Exercises 116
Chapter 4 Trees 121
4.1 Preliminaries 121
4.1.1 Implementation of Trees 122
4.1.2 Tree Traversals with an Application 123
4.2 Binary Trees 126
4.2.1 Implementation 128
4.2.2 An Example： Expression Trees 128
4.3 The Search Tree ADT？aBinary Search Trees 132
4.3.1 contains 134
4.3.2 findMin and findMax 135
4.3.3 insert 136
4.3.4 remove 139
4.3.5 Destructor and Copy Constructor 141
4.3.6 Average—Case Analysis 141
4.4 AVL Trees 144
4.4.1 Single Rotation 147
4.4.2 Double Rotation 149
4.5 Splay Trees 158
4.5.1 A Simple Idea （That Does Not Work） 158
4.5.2 Splaying 160
4.6 Tree Traversals （Revisited） 166
4.7 B—Trees 168
4.8 Sets and Maps in the Standard Library 173
4.8.1 Sets 173
4.8.2 Maps 174
4.8.3 Implementation of set and map 175
4.8.4 An Example That Uses Several Maps 176
Summary 181
Exercises 182
References 189
Chapter 5 Hashing 193
5.1 General Idea 193
5.2 Hash Function 194
5.3 Separate Chaining 196
5.4 Hash Tables without Linked Lists 201
5.4.1 Linear Probing 201
5.4.2 Quadratic Probing 202
5.4.3 Double Hashing 207
5.5 Rehashing 208
5.6 Hash Tables in the Standard Library 210
5.7 Hash Tables with Worst—Case O（1） Access 212
5.7.1 Perfect Hashing 213
5.7.2 Cuckoo Hashing 215
5.7.3 Hopscotch Hashing 227
5.8 Universal Hashing 230
5.9 Extendible Hashing 233
Summary 236
Exercises 237
References 241
Chapter 6 Priority Queues （Heaps） 245
6.1 Model 245
6.2 Simple Implementations 246
6.3 Binary Heap 247
6.3.1 Structure Property 247
6.3.2 Heap—Order Property 248
6.3.3 Basic Heap Operations 249
6.3.4 Other Heap Operations 252
6.4 Applications of Priority Queues 257
6.4.1 The Selection Problem 258
6.4.2 Event Simulation 259
6.5 d—Heaps 260
6.6 Leftist Heaps 261
6.6.1 Leftist Heap Property 261
6.6.2 Leftist Heap Operations 262
6.7 Skew Heaps 269
6.8 Binomial Queues 271
6.8.1 Binomial Queue Structure 271
6.8.2 Binomial Queue Operations 271
6.8.3 Implementation of Binomial Queues 276
6.9 Priority Queues in the Standard Library 282
Summary 283
Exercises 283
References 288
Chapter 7 Sorting 291
7.1 Preliminaries 291
7.2 Insertion Sort 292
7.2.1 The Algorithm 292
7.2.2 STL Implementation of Insertion Sort 293
7.2.3 Analysis of Insertion Sort 294
7.3 A Lower Bound for Simple Sorting Algorithms 295
7.4 Shellsort 296
7.4.1 Worst—Case Analysis of Shellsort 297
7.5 Heapsort 300
7.5.1 Analysis of Heapsort 301
7.6 Mergesort 304
7.6.1 Analysis of Mergesort 306
7.7 Quicksort 309
7.7.1 Picking the Pivot 311
7.7.2 Partitioning Strategy 313
7.7.3 Small Arrays 315
7.7.4 Actual Quicksort Routines 315
7.7.5 Analysis of Quicksort 318
7.7.6 A Linear—Expected—Time Algorithm for Selection 321
7.8 A General Lower Bound for Sorting 323
7.8.1 Decision Trees 323
7.9 Decision—Tree Lower Bounds for Selection Problems 325
7.10 Adversary Lower Bounds 328
7.11 Linear—Time Sorts： Bucket Sort and Radix Sort 331
7.12 External Sorting 336
7.12.1 Why We Need New Algorithms 336
7.12.2 Model for External Sorting 336
7.12.3 The Simple Algorithm 337
7.12.4 Multiway Merge 338
7.12.5 Polyphase Merge 339
7.12.6 Replacement Selection 340
Summary 341
Exercises 341
References 347
……
Chapter 8 The Disjoint Sets Class 351
Chapter 9 Graph Algorithms 379
Chapter 10 Algorithm Design Techniques 449
Chapter 11 Amortized Analysis 533
Chapter 12 Advanced Data Structures
Appendix A Separate Compilation of Class Templates 615
Index 619