Concise Notes on Data Structures and Algorithms Ruby Edition Christopher Fox James Madison University 2011 Contents 1 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 1 Contents 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 2 Contents 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 iii Contents 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 . ..