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Class notes SCO204 Data Structures and Algorithms
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C ontents1 INTRODUCTION 1
What Are Data Structures and Algorithms?....................................................................1
Structure of the Book.......................................................................................................3
The Ruby Programming Language..................................................................................3
Review Questions............................................................................................................3
Exercises..........................................................................................................................4
Review Question Answers...............................................................................................4
2 BUILT-IN TYPES 5
Simple and Structured Types...........................................................................................5
Types in Ruby..................................................................................................................5
Symbol: A Simple Type in Ruby.....................................................................................5
Review Questions............................................................................................................9
Exercises..........................................................................................................................9
Review Question Answers...............................................................................................9
3 ARRAYS 10
Introduction....................................................................................................................10
Varieties of Arrays.........................................................................................................10
Arrays in Ruby...............................................................................................................11
Review Questions..........................................................................................................12
Exercises........................................................................................................................12
Review Question Answers.............................................................................................13
4 ASSERTIONS 14
Introduction....................................................................................................................14
Types of Assertions.......................................................................................................14
Assertions and Abstract Data Types..............................................................................15
Using Assertions............................................................................................................15
Assertions in Ruby.........................................................................................................16
Review Questions..........................................................................................................17
Exercises........................................................................................................................17
Review Question Answers.............................................................................................19
5 CONTAINERS 20
Introduction....................................................................................................................20
Varieties of Containers..................................................................................................20
A Container Taxonomy.................................................................................................20
, Interfaces in Ruby..........................................................................................................21
Exercises........................................................................................................................22
Review Question Answers.............................................................................................23
6 STACKS 24
Introduction....................................................................................................................24
The Stack ADT..............................................................................................................24
The Stack Interface........................................................................................................25
Using Stacks—An Example..........................................................................................25
Contiguous Implementation of the Stack ADT.............................................................26
Linked Implementation of the Stack ADT.....................................................................27
Summary and Conclusion..............................................................................................28
Review Questions..........................................................................................................28
Exercises........................................................................................................................29
Review Question Answers.............................................................................................29
7 QUEUES 31
Introduction....................................................................................................................31
The Queue ADT.............................................................................................................31
The Queue Interface.......................................................................................................31
Using Queues—An Example.........................................................................................32
Contiguous Implementation of the Queue ADT............................................................32
Linked Implementation of the Queue ADT...................................................................34
Summary and Conclusion..............................................................................................35
Review Questions..........................................................................................................35
Exercises........................................................................................................................35
Review Question Answers.............................................................................................36
8 STACKS AND RECURSION 37
Introduction....................................................................................................................37
Balanced Brackets..........................................................................................................38
Infix, Prefix, and Postfix Expressions...........................................................................39
Tail Recursive Algorithms.............................................................................................44
Summary and Conclusion..............................................................................................44
Review Questions..........................................................................................................45
Exercises........................................................................................................................45
Review Question Answers.............................................................................................45
9 COLLECTIONS 47
Introduction....................................................................................................................47
Iteration Design Alternatives.........................................................................................47
The Iterator Design Pattern............................................................................................48
Iteration in Ruby............................................................................................................49
, Collections, Iterators, and Containers............................................................................50
Summary and Conclusion..............................................................................................51
Review Questions..........................................................................................................52
Exercises........................................................................................................................52
Review Question Answers.............................................................................................52
10 LISTS 54
Introduction....................................................................................................................54
The List ADT.................................................................................................................54
The List Interface...........................................................................................................55
Using Lists—An Example.............................................................................................55
Contiguous Implementation of the List ADT................................................................56
Linked Implementation of the List ADT.......................................................................56
Implementing Lists in Ruby..........................................................................................58
Summary and Conclusion..............................................................................................58
Review Questions..........................................................................................................58
Exercises........................................................................................................................58
Review Question Answers.............................................................................................59
11 ANALYZING ALGORITHMS 61
Introduction....................................................................................................................61
Measuring the Amount of Work Done..........................................................................61
Which Operations to Count...........................................................................................62
Best, Worst, and Average Case Complexity..................................................................63
Review Questions..........................................................................................................65
Exercises........................................................................................................................66
Review Question Answers.............................................................................................66
12 FUNCTION GROWTH RATES 68
Introduction....................................................................................................................68
Definitions and Notation................................................................................................68
Establishing the Order of Growth of a Function............................................................69
Applying Orders of Growth...........................................................................................70
Summary and Conclusion..............................................................................................70
Review Questions..........................................................................................................70
Exercises........................................................................................................................70
Review Question Answers.............................................................................................71
13 BASIC SORTING ALGORITHMS 72
Introduction....................................................................................................................72
Bubble Sort....................................................................................................................72
Selection Sort.................................................................................................................73
, Insertion Sort..................................................................................................................74
Shell Sort........................................................................................................................76
Summary and Conclusion..............................................................................................77
Review Questions..........................................................................................................78
Exercises........................................................................................................................78
Review Question Answers.............................................................................................78
14 RECURRENCES 80
Introduction....................................................................................................................80
Setting Up Recurrences..................................................................................................80
Review Questions..........................................................................................................83
Exercises........................................................................................................................83
Review Question Answers.............................................................................................84
15: MERGE SORT AND QUICKSORT 85
Introduction....................................................................................................................85
Merge Sort.....................................................................................................................85
Quicksort........................................................................................................................87
Summary and Conclusion..............................................................................................91
Review Questions..........................................................................................................91
Exercises........................................................................................................................91
Review Question Answers.............................................................................................92
16 TREES, HEAPS, AND HEAPSORT 93
Introduction....................................................................................................................93
Basic Terminology.........................................................................................................93
Binary Trees...................................................................................................................94
Heaps.............................................................................................................................94
Heapsort.........................................................................................................................95
Summary and Conclusion..............................................................................................97
Review Questions..........................................................................................................97
Exercises........................................................................................................................97
Review Question Answers.............................................................................................98
17 BINARY TREES 99
Introduction....................................................................................................................99
The Binary Tree ADT....................................................................................................99
The Binary Tree Class.................................................................................................100
Contiguous Implementation of Binary Trees...............................................................102
Linked Implementation of Binary Trees......................................................................102
Summary and Conclusion............................................................................................103
Review Questions........................................................................................................103
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