PREFACE
Synopsis
Changes in the Second Edition
Course Structure
Book Production
Acknowledgments
CHAFTEltl
Programming Principles
1.1 Introduction
1.2 The Game of Life
1.2.1 Rules for the Game of Life
1.2.2 Examples
1.2.3 The Solution
1.2.4 Life: The Main Program
1.3 Programming Style
1.3.1 Names
1.3.2 Documentation and Fonnat
1.3.3 Refinement and Modularity
1.4 Coding, Testing, andFurther Refinement
1.4.1 Stubs
1.4.2 Counting Neighbors
1.4.3 Input and Output
1.4.4 Drivers
1.4.5 Program Tracing
1.4.6 Principles of Program Testing
Pointers and Pitfalls
Review Questions
References for Further Study
C
Programming Principles
The Game of Life
CHAPTER 2
Introduction to
Software Engineering
2.1 Program Maintenance
2.1.1 Review of the Life Program
2.1.2 A Fresh Start and a New Method for Life
2.2 Algorithm Development: A Second Version of Life
2.2.1 Lists: Specifications for a Data Structure
2.2.2 The Main Program
2.2.3 Information Hiding
2.2.4 Refinement: Development of the Subprograms
2.2.5 Verification of Algorithms
2.3 Coding
2.3.1 The List Functions
2.3.2 Error Processing
2.3.3 Demonstration and Testing
2.4 Ceding the Life Functions
2.5 Program Analysis and Comparison
2.6 Conclusions and Preview
2.6.1 The Game of Life
2.6.2 Program Design
2.6.3 C
Pointers ahd Pitfalls
Review Questions
References for Further Study
Contents
CHAFTER 3
Stacks and Recursion
3.1 Stacks
3.1.1 Introduction
3.1.2 First Example: Reversing a Line
3.1.3 Information Hiding
3.1.4 Specifications for a Stac-
3.1.5 Implementation of Stacks
3.1.6 Linked Stacks
3.2 Introduction to Recursion
3.2.1 Stack Frames for Subprograms
3.2.2 Tree of Subprogram Calls
3.2.3 Factorials: A Recursive Definition
3.2.4 Divide and Conquer:
The Towers of Hanoi
3.3 Backtracking: Postponing the Work
3.3.1 Solving the Eight-Queens Puzzle
3.3.2 Example: Four Queens
3.3.3 Backtracking
3.3.4 Refinement:
Choosing the Data Structures
3.3.5 Analysis of Backtracking
3.4 Principles of Recursion
3.4.1 Designing Recursive Algorithms
3.4.2 How Recursion Works
3.4.3 Tail Recursion
3.4.4 When Not to Use Recursion
3.4.5 Guidelines and Condusions
Pointers and Pitfalls
Review Questions
References for Further Study
CHAPTER 4
Queues and Linked Lists
4.1 Definitions
4.2 Implementations of Queues
4.3 Circular Queues in C
4.4 Application of Queues: Simulation
4.4.1 Introduction
4.4.2 Simulation of an Airport
4.4.3 The Main Program
4.4.4 Steps of the Simulation
4.4.5 Pseudo-Random Numbers
4.4.6 Sampie Results
4.5 Pointers and Linked Lists
4.5.1 Introduction and Survey
4.5.2 Pointers and Dynamic Memory in C
4.5.3 The Basics of Linked Lists
4.6 Linked Queues
4.7 Application: Polynomial Arithmetic
4.7.1 Purpose of the Project
4.7.2 The Main Program
4.7.3 Data Structures and Their Implementation
4.7.4 Reading and Writing Polynomials
4.7.5 Addition of Polynomials
4.7.6 Completing the Project
4.8 Abstract Data Types and
Their Implementations
4.8.1 Introduction
4.8.2 General Definitions '
4.8.3 Refinement of Data Specification
Pointers and Pitfalls
Review Questions
References for Further Study
CHAPTER 5
General Lists -
5.1 List Specifications
5.2 Implementation of Lists
5.2.1 Contiguous Implementation
5.2.2 Simply Linked Implementation
5.2.3 Variation: Keeping the Current Position
5.2.4 Doubly Linked Lists
5.2.5 Comparison of Implementations
5.3 Strings
5.4 Application: A Text Editor
5.4.1 Specifications
5.4.2 Implementation
5.5 Linked Lists in Arrays
5.6 Generating Permutations
Pointers and Pitfalls
Review Questions
References for Further Study
CHAPTER 6
Searching
6.1 Searching:
Introduction and Notation
6.2 Sequential Search
6.3 Coatrooms: A Project
6.3.1 Introduction and Specification
6.3.2 Demonstration and Testing
Programs
6.4 Binary Search
6.4.1 Algorithm Development
6.4.2 The Forgetful Version
6.4.3 Recognizing Equality
6.5 Comparison Trees
6.5.1 Analysis for n = 10
6.5.2 Generalization
6.5.3 Comparison of Methods
6.5.4 A General Relationship
6.6 Lower Bounds
6.7 Asymptotics
6.7.1 Introduction
6.7.2 The Big-O Notation
6.7.3 Imprecision of the Big-O Notation
6.7.4 Ordering of Common Functions
Pointers and Pitfalls
Review Questions
References for Further Study
CHAPTER 7
Sorting
7.1 Introduction and Notation
7.2 Insertion Sort
7.2.1 Ordered Lists
7.2.2 Sorting by Insertin.
7.2.3 Linked Version
7.2.4 Analysis
7.3 SelectionSort
7.3.1 TheAlgorithm
7.3.2 Contiguous Implementation
7.3.3 Analysis
7.3.4 Comparisons
7.4 Shell Sort
7.5 Lower Bounds
7.6 Divide-and-Conquer Sorting
7.6.1 TheMainldeas
7.6.2 An Example
7.7 Mergesort for Linked Lists
7.7.1 TheFunctions
7.7.2 Analysis of Mergesort
7.8 Quicksort for Contiguous Lists
7.8.1 The Main Function
7.8.2 Partitioning the List
7.8.3 Analysis of Quicksort
7.8.4 Average-Case Analysis of Quicksort
7.8.5 Comparison with Mergesort
7.9 Heaps and Heapsort
7.9.1 Two-Way Trees as Lists
7.9.2 Heapsort
7.9.3 Analysis of Heapsort
7.9.4 PriorityQueues
7.10 Review: Comparison of Methods
Pointers and Pitfalls
Review Questions
References for Further Study
CHAPTER 8
Tables and Information Retrieval
8.1 Introduction:
Breaking the Ig n Barrier
8.2 Rectangular Arrays
8.3 Tables of Various Shapes
8.3.1 Triangular Tables
8.3.2 Jagged Tables
8.3.3 Inverted Tables
8.4 Tables: A New Abstract Data Type
8.5 Application: Radix Sort
8.5.1 Theldea
8.5.2 Implementation
8.5.3 Analysis
8.6 Hashing
8.6.1 Sparse Tables
8.6.2 Choosing a Hash Function
8.6.3 Collision Resolution with
Open Addressing
8.6.4 Collision Resolution by Chaining
8.7 Analysis of Hashing
8.8 Conclusions:
Comparison of Methods
8.9 Application:
The Life Game Revisited
8.9.1 Choice of Algorithm
8.9.2 Specfication of Data Structures
8.9.3 The Main Program
8.9.4 Functions
Pointers and Pitfalls
Review Questions
References for Further Study
CHAPTER 9
Binary Trees
9.1 Introduction to Binarv Trees
9.1.1 Definitions
9.1.2 Traversal of Binary Trees
9.1.3 Linked Implementation of
BmaryTrees
9.2 Binary Search Trees
9.2.1 Ordered Lists and Implementations
9.2.2 Treesearch
9.2.3 Insertion into a Binary Search Tree
9.2.4 Treesort
9.2.5 Deletion from a Binary Search Tree
9.3 Building a Binary Search Tree
9.3.1 Getting Started
9.3.2 Declarations and the Main Function
9.3.3 Inserting a Node
9.3.4 Finishing the Task
9.3.5 Evaluation
9.3.6 Random Search Trees and
Optimality
9.4 Height Balance: AVL Trees
9.4.1 Definition
9.4.2 Insertion of a Node
9.4.3 Deletion of aNode
9.4.4 The Height of an AVL Tree
9.5 SplayTrees:
A Self-Adjusting Data Structure
9.5.1 Introduction
9.5.2 Splaying Steps
9.5.3 Splaying Algorithm
9.5.4 Amortized Algorithm Analysis:
Introduction
9.5.5 Amortized Analysis of Splaying
Pointers and Pitfalls
Review Questions
References for Further Study
CHAPTER 10
Multiway Trees
10.1 Orchards, Trees, and Binary Trees
10.1.1 OntheClassification of Spedes
10.1.2 Ordered Trees
10.1.3 Forests and Orehards
10.1.4 The Formal Correspondence
10.1.5 Rotations
10.1.6 Summary
10.2 Lexicographic Search Trees: Tries
10.2.1 Tries
10.2.2 Searching for a Key
10.2.3 CAlgorithm
10.2.4 Insertion into a Trie
10.2.5 Deletion from a Trie
10.2.6 AssessmentofTries
10.3 Extemal Searching: B-Trees
10.3.1 AccessTime
10.3.2 Multiway Search Trees
10.3.3 Balanced Multiway Trees
10.3.4 Insertion into a B-tree
10.3.5 CAlgorithms:
Searching and Insertion
10.3.6 Deletion from a B-tree
10.4 Red-Black Trees
10.4.1 Introduction
10.4.2 Definition and Analysis
10.4.3 Insertion
10.4.4 C Insertion
10.5 Tree-Structured Programs:
Look-Ahead in Games
10.5.1 GameTrees
10.5.2 The Minimax Method
10.5.3 Algorithm Development
10.5.4 Refinement
Pointers and Pitfalls
Review Questions
References for Further Study
CHAPTER 11
Graphs
11.1 Mathematical Background
11.1.1 Definitions and Examples
11.1.2 Undirected Graphs
11.1.3 Directed Graphs
11.2 Computer Representation
11.3 Graph Traversal
11.3.1 Methods
11.3.2 Depth-First Algorithm
11.3.3 Breadth-First Algorithm
11.4 Topological Sorting
11.4.1 TheProblem
11.4.2 Depth-First Algorithm
11.4.3 Breadth-First Algorithm
11.5 A Greedy Algorithm:
Shortest Paths
11.6 Graphs as Data Structures
Pointers and Pitfalls
Review Questions
References for Further Shudy
CHAPTER 12
Case Study: The Polish Notation
12.1 The Problem
12.1.1 The Quadratic Formula
12.2 The Idea
12.2.1 Expression Trees
12.2.2 Polish Notation
12.2.3 C Method
12.3 Evaluation of Polish Expressions
12.3.1 Evaluation of an Expression in
Prefix Form
12.3.2 C Conventions
12.3.3 C Function for Prefix Evaluation
12.3.4 Evaluation of Postfix Expressions
12.3.5 Proof of the Program:
Counting Stack Entries
12.3.6 Recursive Evaluation of
Postfix Expressions
12.4 Translation from Infix From to Polish
Fonn
12.5 An Interactive Expression
Evaluator
12.5.1 Overall Structure
12.5.2 Representation of the Data
12.5.3 Initialization and Auxiliary Tasks
12.5.4 Translation of the Expression
12.5.5 Evaluating the Expression
12.5.6 Graphing the Expression
References for Further Study
APPENDIX A
Mathematical Methods
A.l Sums of Powers of Integers
A.2 Logarithms
A.2.l Definition of Logarithms
A.2.2 Simple Properties
A.2.3 ChoiceofBase
A.2.4 Natural Logarithms
A.2.5 Notation
A.2.6 ChangeofBase
A.2.7 Logarithmic Graphs
A.2.8 Hannonic Numbers
A.3 Permutations, Combinations,
Factorials
A.3.l Permutations
A.3.2 Combinations
A.3.3 Factorials
A.4 Fibonacci Numbers
A.5 Catalan Numbers
A.5.1 ThevMain Result
A.5.2 The Proof by One-to-One
Correspondences
A.5.3 History
A.5.4 Numerical Results
References for Further Study
APPENDIX B
Removal of Recursion
B.l General Methods for Removing
Recursion
B.l.l Preliminary Assumptions
B.l.2 GeneralRules
B.1.3 Indirect Recursion
B.1.4 Towers of Hanoi
B.1.5 Further Simplifications
B.2 Recursion Removal by Folding
B.2.1 Program Schemata
B.2.2 Proof of the Transformation
B.2.3 Towers of Hanoi:
The Final Version
B.3 Nonrecursive Quicksort
B.4 Stackless Recursion Removal:
Mergesort
B.5 Threaded Binary Trees
B.5.1 Introduction
B.5.2 Threads
8.5.3 Inorder and Preorder Traversal
B.5.4 Insertion in a Threaded Tree
B.5.5 Postorder Traversal
References for Further Study
APPENDIX C
An Introduction to C
C.l Introduction
C.l.l Overview of a C Program
C.2 CElements
C.2.1 Reserved Words
C.2.2 Constants
C.3 Types and Declarations
C.3.1 Basic Types
C.3.2 Arrays
C.3-3 Enumerations
C.3 4 Structures
C.3.5 Unions
C.3.6 Type Definitions with typedef
C.4 Operators
C.5 Control Flow Statements
C.5.1 K-Else
C.5.2 Switch
C.5.3 Loops
C.5.4 Break and Continue
C.5.5 Goto
C.6 Pointers
C.6.1 Pointer to a Simple Variable
C.6.2 Pointer to an Array
C.6.3 Array of Pointers
C.6.4 Pointer to Structures
C.7 Functions
C.7.1 Arguments to Functions:
CallbyValue
C.7.2 Arguments to FUNctions:
Call by Reference
C.7.3 Function Prototypes and Include
Files
C.8 Pointers and Functions
C.8.1 Pointer to a FuCnction
C.8.2 Functions that Retum a Pointe
C.8.3 Pointer to a Pointer as an
Argument
References for Further Study
INDEX
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