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data structures and algorithm analysis(C++, Edition 3).pdf
Preface
I Preliminaries
1 Data Structures and Algorithms
1.1 A Philosophy of Data Structures
1.1.1 The Need for Data Structures
1.1.2 Costs and Benefits
1.2 Abstract Data Types and Data Structures
1.3 Design Patterns
1.3.1 Flyweight
1.3.2 Visitor
1.3.3 Composite
1.3.4 Strategy
1.4 Problems, Algorithms, and Programs
1.5 Further Reading
1.6 Exercises
2 Mathematical Preliminaries
2.1 Sets and Relations
2.2 Miscellaneous Notation
2.3 Logarithms
2.4 Summations and Recurrences
2.5 Recursion
2.6 Mathematical Proof Techniques
2.6.1 Direct Proof
2.6.2 Proof by Contradiction
2.6.3 Proof by Mathematical Induction
2.7 Estimation
2.8 Further Reading
2.9 Exercises
3 Algorithm Analysis
3.1 Introduction
3.2 Best, Worst, and Average Cases
3.3 A Faster Computer, or a Faster Algorithm?
3.4 Asymptotic Analysis
3.4.1 Upper Bounds
3.4.2 Lower Bounds
3.4.3 Notation
3.4.4 Simplifying Rules
3.4.5 Classifying Functions
3.5 Calculating the Running Time for a Program
3.6 Analyzing Problems
3.7 Common Misunderstandings
3.8 Multiple Parameters
3.9 Space Bounds
3.10 Speeding Up Your Programs
3.11 Empirical Analysis
3.12 Further Reading
3.13 Exercises
3.14 Projects
II Fundamental Data Structures
4 Lists, Stacks, and Queues
4.1 Lists
4.1.1 Array-Based List Implementation
4.1.2 Linked Lists
4.1.3 Comparison of List Implementations
4.1.4 Element Implementations
4.1.5 Doubly Linked Lists
4.2 Stacks
4.2.1 Array-Based Stacks
4.2.2 Linked Stacks
4.2.3 Comparison of Array-Based and Linked Stacks
4.2.4 Implementing Recursion
4.3 Queues
4.3.1 Array-Based Queues
4.3.2 Linked Queues
4.3.3 Comparison of Array-Based and Linked Queues
4.4 Dictionaries
4.5 Further Reading
4.6 Exercises
4.7 Projects
5 Binary Trees
5.1 Definitions and Properties
5.1.1 The Full Binary Tree Theorem
5.1.2 A Binary Tree Node ADT
5.2 Binary Tree Traversals
5.3 Binary Tree Node Implementations
5.3.1 Pointer-Based Node Implementations
5.3.2 Space Requirements
5.3.3 Array Implementation for Complete Binary Trees
5.4 Binary Search Trees
5.5 Heaps and Priority Queues
5.6 Huffman Coding Trees
5.6.1 Building Huffman Coding Trees
5.6.2 Assigning and Using Huffman Codes
5.6.3 Search in Huffman Trees
5.7 Further Reading
5.8 Exercises
5.9 Projects
6 Non-Binary Trees
6.1 General Tree Definitions and Terminology
6.1.1 An ADT for General Tree Nodes
6.1.2 General Tree Traversals
6.2 The Parent Pointer Implementation
6.3 General Tree Implementations
6.3.1 List of Children
6.3.2 The Left-Child/Right-Sibling Implementation
6.3.3 Dynamic Node Implementations
6.3.4 Dynamic ``Left-Child/Right-Sibling'' Implementation
6.4 K-ary Trees
6.5 Sequential Tree Implementations
6.6 Further Reading
6.7 Exercises
6.8 Projects
III Sorting and Searching
7 Internal Sorting
7.1 Sorting Terminology and Notation
7.2 Three (n2) Sorting Algorithms
7.2.1 Insertion Sort
7.2.2 Bubble Sort
7.2.3 Selection Sort
7.2.4 The Cost of Exchange Sorting
7.3 Shellsort
7.4 Mergesort
7.5 Quicksort
7.6 Heapsort
7.7 Binsort and Radix Sort
7.8 An Empirical Comparison of Sorting Algorithms
7.9 Lower Bounds for Sorting
7.10 Further Reading
7.11 Exercises
7.12 Projects
8 File Processing and External Sorting
8.1 Primary versus Secondary Storage
8.2 Disk Drives
8.2.1 Disk Drive Architecture
8.2.2 Disk Access Costs
8.3 Buffers and Buffer Pools
8.4 The Programmer's View of Files
8.5 External Sorting
8.5.1 Simple Approaches to External Sorting
8.5.2 Replacement Selection
8.5.3 Multiway Merging
8.6 Further Reading
8.7 Exercises
8.8 Projects
9 Searching
9.1 Searching Unsorted and Sorted Arrays
9.2 Self-Organizing Lists
9.3 Bit Vectors for Representing Sets
9.4 Hashing
9.4.1 Hash Functions
9.4.2 Open Hashing
9.4.3 Closed Hashing
9.4.4 Analysis of Closed Hashing
9.4.5 Deletion
9.5 Further Reading
9.6 Exercises
9.7 Projects
10 Indexing
10.1 Linear Indexing
10.2 ISAM
10.3 Tree-based Indexing
10.4 2-3 Trees
10.5 B-Trees
10.5.1 B+-Trees
10.5.2 B-Tree Analysis
10.6 Further Reading
10.7 Exercises
10.8 Projects
IV Advanced Data Structures
11 Graphs
11.1 Terminology and Representations
11.2 Graph Implementations
11.3 Graph Traversals
11.3.1 Depth-First Search
11.3.2 Breadth-First Search
11.3.3 Topological Sort
11.4 Shortest-Paths Problems
11.4.1 Single-Source Shortest Paths
11.5 Minimum-Cost Spanning Trees
11.5.1 Prim's Algorithm
11.5.2 Kruskal's Algorithm
11.6 Further Reading
11.7 Exercises
11.8 Projects
12 Lists and Arrays Revisited
12.1 Multilists
12.2 Matrix Representations
12.3 Memory Management
12.3.1 Dynamic Storage Allocation
12.3.2 Failure Policies and Garbage Collection
12.4 Further Reading
12.5 Exercises
12.6 Projects
13 Advanced Tree Structures
13.1 Tries
13.2 Balanced Trees
13.2.1 The AVL Tree
13.2.2 The Splay Tree
13.3 Spatial Data Structures
13.3.1 The K-D Tree
13.3.2 The PR quadtree
13.3.3 Other Point Data Structures
13.3.4 Other Spatial Data Structures
13.4 Further Reading
13.5 Exercises
13.6 Projects
V Theory of Algorithms
14 Analysis Techniques
14.1 Summation Techniques
14.2 Recurrence Relations
14.2.1 Estimating Upper and Lower Bounds
14.2.2 Expanding Recurrences
14.2.3 Divide and Conquer Recurrences
14.2.4 Average-Case Analysis of Quicksort
14.3 Amortized Analysis
14.4 Further Reading
14.5 Exercises
14.6 Projects
15 Lower Bounds
15.1 Introduction to Lower Bounds Proofs
15.2 Lower Bounds on Searching Lists
15.2.1 Searching in Unsorted Lists
15.2.2 Searching in Sorted Lists
15.3 Finding the Maximum Value
15.4 Adversarial Lower Bounds Proofs
15.5 State Space Lower Bounds Proofs
15.6 Finding the ith Best Element
15.7 Optimal Sorting
15.8 Further Reading
15.9 Exercises
15.10 Projects
16 Patterns of Algorithms
16.1 Dynamic Programming
16.1.1 The Knapsack Problem
16.1.2 All-Pairs Shortest Paths
16.2 Randomized Algorithms
16.2.1 Randomized algorithms for finding large values
16.2.2 Skip Lists
16.3 Numerical Algorithms
16.3.1 Exponentiation
16.3.2 Largest Common Factor
16.3.3 Matrix Multiplication
16.3.4 Random Numbers
16.3.5 The Fast Fourier Transform
16.4 Further Reading
16.5 Exercises
16.6 Projects
17 Limits to Computation
17.1 Reductions
17.2 Hard Problems
17.2.1 The Theory of NP-Completeness
17.2.2 NP-Completeness Proofs
17.2.3 Coping with NP-Complete Problems
17.3 Impossible Problems
17.3.1 Uncountability
17.3.2 The Halting Problem Is Unsolvable
17.4 Further Reading
17.5 Exercises
17.6 Projects
VI APPENDIX
A Utility Functions
Bibliography
Index
Data Structures and Algorithm
Analysis
Edition 3.2 (C++ Version)
Clifford A. Shaffer
Department of Computer Science
Virginia Tech
Blacksburg, VA 24061
March 28, 2013
Update 3.2.0.10
For a list of changes, see
http://people.cs.vt.edu/˜shaffer/Book/errata.html
Copyright © 2009-2012 by Clifford A. Shaffer.
This document is made freely available in PDF form for educational and
other non-commercial use. You may make copies of this file and
redistribute in electronic form without charge. You may extract portions of
this document provided that the front page, including the title, author, and
this notice are included. Any commercial use of this document requires the
written consent of the author. The author can be reached at
shaffer@cs.vt.edu.
If you wish to have a printed version of this document, print copies are
published by Dover Publications
(see http://store.doverpublications.com/048648582x.html).
Further information about this text is available at
http://people.cs.vt.edu/˜shaffer/Book/.
Contents
Preface
I Preliminaries
1 Data Structures and Algorithms
1.1 A Philosophy of Data Structures
1.1.1 The Need for Data Structures
1.1.2 Costs and Benefits
1.2 Abstract Data Types and Data Structures
1.3 Design Patterns
Flyweight
1.3.1
1.3.2 Visitor
1.3.3 Composite
1.3.4
Strategy
1.4 Problems, Algorithms, and Programs
1.5 Further Reading
1.6 Exercises
2 Mathematical Preliminaries
2.1 Sets and Relations
2.2 Miscellaneous Notation
2.3 Logarithms
2.4 Summations and Recurrences
2.5 Recursion
2.6 Mathematical Proof Techniques
xiii
1
3
4
4
6
8
12
13
13
14
15
16
18
20
25
25
29
31
32
36
38
iii
iv
Contents
2.6.1 Direct Proof
2.6.2
2.6.3
Proof by Contradiction
Proof by Mathematical Induction
2.7 Estimation
2.8 Further Reading
2.9 Exercises
3 Algorithm Analysis
Introduction
3.1
3.2 Best, Worst, and Average Cases
3.3 A Faster Computer, or a Faster Algorithm?
3.4 Asymptotic Analysis
3.4.1 Upper Bounds
3.4.2 Lower Bounds
3.4.3 Θ Notation
3.4.4
3.4.5 Classifying Functions
Simplifying Rules
3.5 Calculating the Running Time for a Program
3.6 Analyzing Problems
3.7 Common Misunderstandings
3.8 Multiple Parameters
3.9 Space Bounds
3.10 Speeding Up Your Programs
3.11 Empirical Analysis
3.12 Further Reading
3.13 Exercises
3.14 Projects
II Fundamental Data Structures
4 Lists, Stacks, and Queues
4.1 Lists
4.1.1 Array-Based List Implementation
4.1.2 Linked Lists
4.1.3 Comparison of List Implementations
39
39
40
46
47
48
55
55
61
62
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65
67
68
69
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71
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77
79
80
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85
86
86
90
93
95
96
100
103
112
Contents
4.1.4 Element Implementations
4.1.5 Doubly Linked Lists
4.2 Stacks
4.2.1 Array-Based Stacks
4.2.2 Linked Stacks
4.2.3 Comparison of Array-Based and Linked Stacks
4.2.4
Implementing Recursion
4.3 Queues
4.3.1 Array-Based Queues
4.3.2 Linked Queues
4.3.3 Comparison of Array-Based and Linked Queues
4.4 Dictionaries
4.5 Further Reading
4.6 Exercises
4.7 Projects
5 Binary Trees
5.1 Definitions and Properties
5.1.1 The Full Binary Tree Theorem
5.1.2 A Binary Tree Node ADT
5.2 Binary Tree Traversals
5.3 Binary Tree Node Implementations
Pointer-Based Node Implementations
Space Requirements
5.3.1
5.3.2
5.3.3 Array Implementation for Complete Binary Trees
5.4 Binary Search Trees
5.5 Heaps and Priority Queues
5.6 Huffman Coding Trees
5.6.1 Building Huffman Coding Trees
5.6.2 Assigning and Using Huffman Codes
5.6.3
Search in Huffman Trees
5.7 Further Reading
5.8 Exercises
5.9 Projects
6 Non-Binary Trees
v
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115
120
121
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123
125
127
128
133
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151
153
155
155
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160
166
168
168
178
185
186
192
195
196
196
200
203
vi
Contents
6.1 General Tree Definitions and Terminology
6.1.1 An ADT for General Tree Nodes
6.1.2 General Tree Traversals
6.2 The Parent Pointer Implementation
6.3 General Tree Implementations
6.3.1 List of Children
6.3.2 The Left-Child/Right-Sibling Implementation
6.3.3 Dynamic Node Implementations
6.3.4 Dynamic “Left-Child/Right-Sibling” Implementation
6.4 K-ary Trees
6.5 Sequential Tree Implementations
6.6 Further Reading
6.7 Exercises
6.8 Projects
III Sorting and Searching
7 Internal Sorting
7.1 Sorting Terminology and Notation
7.2 Three Θ(n2) Sorting Algorithms
Insertion Sort
7.2.1
7.2.2 Bubble Sort
7.2.3
7.2.4 The Cost of Exchange Sorting
Selection Sort
7.3 Shellsort
7.4 Mergesort
7.5 Quicksort
7.6 Heapsort
7.7 Binsort and Radix Sort
7.8 An Empirical Comparison of Sorting Algorithms
7.9 Lower Bounds for Sorting
7.10 Further Reading
7.11 Exercises
7.12 Projects
203
204
205
207
213
214
215
215
218
218
219
223
223
226
229
231
232
233
233
235
237
238
239
241
244
251
252
259
261
265
265
269
Contents
8 File Processing and External Sorting
8.1 Primary versus Secondary Storage
8.2 Disk Drives
8.2.1 Disk Drive Architecture
8.2.2 Disk Access Costs
8.3 Buffers and Buffer Pools
8.4 The Programmer’s View of Files
8.5 External Sorting
Simple Approaches to External Sorting
8.5.1
8.5.2 Replacement Selection
8.5.3 Multiway Merging
8.6 Further Reading
8.7 Exercises
8.8 Projects
9 Searching
9.1 Searching Unsorted and Sorted Arrays
9.2 Self-Organizing Lists
9.3 Bit Vectors for Representing Sets
9.4 Hashing
9.4.1 Hash Functions
9.4.2 Open Hashing
9.4.3 Closed Hashing
9.4.4 Analysis of Closed Hashing
9.4.5 Deletion
9.5 Further Reading
9.6 Exercises
9.7 Projects
10 Indexing
10.1 Linear Indexing
10.2 ISAM
10.3 Tree-based Indexing
10.4 2-3 Trees
10.5 B-Trees
10.5.1 B+-Trees
vii
273
273
276
276
280
282
290
291
294
296
300
303
304
307
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312
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324
325
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331
339
344
345
345
348
351
353
356
358
360
364
368
viii
Contents
10.5.2 B-Tree Analysis
10.6 Further Reading
10.7 Exercises
10.8 Projects
IV Advanced Data Structures
11 Graphs
11.1 Terminology and Representations
11.2 Graph Implementations
11.3 Graph Traversals
11.3.1 Depth-First Search
11.3.2 Breadth-First Search
11.3.3 Topological Sort
11.4 Shortest-Paths Problems
11.4.1 Single-Source Shortest Paths
11.5 Minimum-Cost Spanning Trees
11.5.1 Prim’s Algorithm
11.5.2 Kruskal’s Algorithm
11.6 Further Reading
11.7 Exercises
11.8 Projects
12 Lists and Arrays Revisited
12.1 Multilists
12.2 Matrix Representations
12.3 Memory Management
12.3.1 Dynamic Storage Allocation
12.3.2 Failure Policies and Garbage Collection
12.4 Further Reading
12.5 Exercises
12.6 Projects
13 Advanced Tree Structures
13.1 Tries
374
375
375
377
379
381
382
386
390
393
394
394
399
400
402
404
407
408
408
412
415
415
418
422
424
431
435
436
437
439
439
Contents
13.2 Balanced Trees
13.2.1 The AVL Tree
13.2.2 The Splay Tree
13.3 Spatial Data Structures
13.3.1 The K-D Tree
13.3.2 The PR quadtree
13.3.3 Other Point Data Structures
13.3.4 Other Spatial Data Structures
13.4 Further Reading
13.5 Exercises
13.6 Projects
V Theory of Algorithms
14 Analysis Techniques
14.1 Summation Techniques
14.2 Recurrence Relations
14.2.1 Estimating Upper and Lower Bounds
14.2.2 Expanding Recurrences
14.2.3 Divide and Conquer Recurrences
14.2.4 Average-Case Analysis of Quicksort
14.3 Amortized Analysis
14.4 Further Reading
14.5 Exercises
14.6 Projects
15 Lower Bounds
15.1 Introduction to Lower Bounds Proofs
15.2 Lower Bounds on Searching Lists
15.2.1 Searching in Unsorted Lists
15.2.2 Searching in Sorted Lists
15.3 Finding the Maximum Value
15.4 Adversarial Lower Bounds Proofs
15.5 State Space Lower Bounds Proofs
15.6 Finding the ith Best Element
ix
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445
447
450
452
457
461
463
463
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