Data Structures and Algorithm Analysis - Computer Science at ...

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1Data Structures and AlgorithmsHow many cities with more than 250,000 people lie within 500 miles of Dallas,Texas? How many people in my company make over $100,000 per year? Can weconnect all of our telephone customers with less than 1,000 miles of cable? Toanswer questions like these, it is not enough to have the necessary information. Wemust organize that information in a way that allows us to find the answers in timeto satisfy our needs.Representing information is fundamental to computer science. The primarypurpose of most computer programs is not to perform calculations, but to store andretrieve information — usually as fast as possible. For this reason, the study ofdata structures and the algorithms that manipulate them is at the heart of computerscience. And that is what this book is about — helping you to understand how tostructure information to support efficient processing.This book has three primary goals. The first is to present the commonly useddata structures. These form a programmer’s basic data structure “toolkit.” Formany problems, some data structure in the toolkit provides a good solution.The second goal is to introduce the idea of tradeoffs and reinforce the conceptthat there are costs and benefits associated with every data structure. This is doneby describing, for each data structure, the amount of space and time required fortypical operations.The third goal is to teach how to measure the effectiveness of a data structure oralgorithm. Only through such measurement can you determine which data structurein your toolkit is most appropriate for a new problem. The techniques presentedalso allow you to judge the merits of new data structures that you or others mightinvent.There are often many approaches to solving a problem. How do we choosebetween them? At the heart of computer program design are two (sometimes conflicting)goals:1. To design an algorithm that is easy to understand, code, and debug.2. To design an algorithm that makes efficient use of the computer’s resources.3
4 Chap. 1 Data Structures and AlgorithmsIdeally, the resulting program is true to both of these goals. We might say thatsuch a program is “elegant.” While the algorithms and program code examples presentedhere attempt to be elegant in this sense, it is not the purpose of this book toexplicitly treat issues related to goal (1). These are primarily concerns of the disciplineof Software Engineering. Rather, this book is mostly about issues relating togoal (2).How do we measure efficiency? Chapter 3 describes a method for evaluatingthe efficiency of an algorithm or computer program, called asymptotic analysis.Asymptotic analysis also allows you to measure the inherent difficulty of a problem.The remaining chapters use asymptotic analysis techniques to estimate the time costfor every algorithm presented. This allows you to see how each algorithm comparesto other algorithms for solving the same problem in terms of its efficiency.This first chapter sets the stage for what is to follow, by presenting some higherorderissues related to the selection and use of data structures. We first examine theprocess by which a designer selects a data structure appropriate to the task at hand.We then consider the role of abstraction in program design. We briefly considerthe concept of a design pattern and see some examples. The chapter ends with anexploration of the relationship between problems, algorithms, and programs.1.1 A Philosophy of Data Structures1.1.1 The Need for Data StructuresYou might think that with ever more powerful computers, program efficiency isbecoming less important. After all, processor speed and memory size still continueto improve. Won’t any efficiency problem we might have today be solved bytomorrow’s hardware?As we develop more powerful computers, our history so far has always been touse that additional computing power to tackle more complex problems, be it in theform of more sophisticated user interfaces, bigger problem sizes, or new problemspreviously deemed computationally infeasible. More complex problems demandmore computation, making the need for efficient programs even greater. Worse yet,as tasks become more complex, they become less like our everyday experience.Today’s computer scientists must be trained to have a thorough understanding of theprinciples behind efficient program design, because their ordinary life experiencesoften do not apply when designing computer programs.In the most general sense, a data structure is any data representation and itsassociated operations. Even an integer or floating point number stored on the computercan be viewed as a simple data structure. More commonly, people use theterm “data structure” to mean an organization or structuring for a collection of dataitems. A sorted list of integers stored in an array is an example of such a structuring.
Page 1 and 2: Data Structures and AlgorithmAnalys
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3Algorithm AnalysisHow long will it
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Sec. 3.1 Introduction 55efficient.
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4Lists, Stacks, and QueuesIf your p
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Sec. 4.1 Lists 95list ADT. Interfac
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Sec. 4.1 Lists 97for (L.moveToStart
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Sec. 4.1 Lists 101/** Singly linked
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Sec. 4.1 Lists 105/** Set curr at l
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Sec. 4.1 Lists 107curr...23 10 12(a
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Sec. 4.1 Lists 111Array-based lists
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Sec. 4.1 Lists 115/** Insert "it" a
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Sec. 4.2 Stacks 117The principle be
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Sec. 4.2 Stacks 121top1top2Figure 4
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Sec. 4.3 Queues 125/** Queue ADT */
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Sec. 4.3 Queues 129/** Array-based
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Sec. 4.4 Dictionaries 133not get at
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Sec. 4.4 Dictionaries 135/** Contai
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Sec. 4.4 Dictionaries 137}/** @retu
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146 Chap. 5 Binary TreesABCDEFGHIFi
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148 Chap. 5 Binary TreesAny number
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150 Chap. 5 Binary Trees/** ADT for
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152 Chap. 5 Binary Treestends to be
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154 Chap. 5 Binary Trees5.3 Binary
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156 Chap. 5 Binary TreesABCDEFGHIFi
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158 Chap. 5 Binary Treesto its call
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160 Chap. 5 Binary Trees5.3.2 Space
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162 Chap. 5 Binary Trees012345 678
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164 Chap. 5 Binary Trees12037422442
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168 Chap. 5 Binary Treessubroot105
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170 Chap. 5 Binary Treesin the case
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172 Chap. 5 Binary Treessynonymous
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174 Chap. 5 Binary Trees/** Heapify
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176 Chap. 5 Binary TreesRH1H2Figure
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178 Chap. 5 Binary Trees5.6 Huffman
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180 Chap. 5 Binary TreesLetter C D
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182 Chap. 5 Binary Trees/** Huffman
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184 Chap. 5 Binary Trees/** Build a
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186 Chap. 5 Binary Treesa reverse p
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188 Chap. 5 Binary Trees18 bits, mo
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190 Chap. 5 Binary Trees5.12 Write
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192 Chap. 5 Binary Trees(c) What is
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194 Chap. 5 Binary Trees5.7 Complet
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196 Chap. 6 Non-Binary TreesRootRAn
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198 Chap. 6 Non-Binary TreesRABCD E
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200 Chap. 6 Non-Binary Trees/** Gen
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204 Chap. 6 Non-Binary Treesditiona
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206 Chap. 6 Non-Binary Treeslence o
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208 Chap. 6 Non-Binary TreesR’RA
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210 Chap. 6 Non-Binary TreesRRABABC
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212 Chap. 6 Non-Binary Trees(a)(b)F
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218 Chap. 6 Non-Binary TreesCAFBEHG
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7Internal SortingWe sort many thing
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Sec. 7.3 Shellsort 231Insertion Bub
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Sec. 7.4 Mergesort 233static
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Sec. 7.5 Quicksort 237Quicksort is
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Sec. 7.5 Quicksort 239static
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Sec. 7.5 Quicksort 241is still unli
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Sec. 7.6 Heapsort 243subarray, only
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Sec. 7.7 Binsort and Radix Sort 245
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Sec. 7.8 An Empirical Comparison of
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Sec. 7.9 Lower Bounds for Sorting 2
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Sec. 7.10 Further Reading 257• Eq
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Sec. 7.11 Exercises 259algorithm to
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Sec. 7.12 Projects 2617.18 Which of
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302 Chap. 9 Searchingintroduced in
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304 Chap. 9 Searchingvalue in L gre
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306 Chap. 9 SearchingWe now show th
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308 Chap. 9 Searchingrecords by exp
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310 Chap. 9 SearchingThis is potent
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312 Chap. 9 Searchingand the total
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314 Chap. 9 SearchingThis method of
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316 Chap. 9 Searchingbirthday is si
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322 Chap. 9 Searching01HashTable100
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324 Chap. 9 Searching/** Insert rec
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328 Chap. 9 SearchingExample 9.9 Co
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330 Chap. 9 Searching/** Dictionary
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332 Chap. 9 SearchingThe cost for a
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334 Chap. 9 Searchingthat is not in
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336 Chap. 9 SearchingA good introdu
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338 Chap. 9 Searching9.16 Assume th
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10IndexingMany large-scale computin
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Sec. 10.1 Linear Indexing 343Linear
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Sec. 10.2 ISAM 347In−memoryTable
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Sec. 10.3 Tree-based Indexing 349Fi
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Sec. 10.4 2-3 Trees 351/** 2-3 tree
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Sec. 10.4 2-3 Trees 35318331223 30
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Sec. 10.5 B-Trees 355private TTNode
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Sec. 10.6 Further Reading 365at mos
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Sec. 10.8 Projects 36710.7 Prove th
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PART IVAdvanced Data Structures369
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372 Chap. 11 Graphs04123147123(a)(b
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374 Chap. 11 Graphs0 1 2 3 40201 11
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376 Chap. 11 Graphstime. This is a
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378 Chap. 11 GraphsIt is reasonably
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380 Chap. 11 Graphs}/** @return an
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382 Chap. 11 Graphs}/** Set the wei
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384 Chap. 11 GraphsABABCCDDFFEE(a)(
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386 Chap. 11 Graphs/** Breadth firs
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388 Chap. 11 Graphs/** Recursive to
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390 Chap. 11 GraphsA103B2205D11C15E
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392 Chap. 11 Graphs/** Dijkstra’s
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394 Chap. 11 GraphsA7 5CB91 26ED 21
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396 Chap. 11 GraphsPrim’s algorit
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398 Chap. 11 GraphsInitialA B C D E
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400 Chap. 11 Graphs(a) IF an undire
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402 Chap. 11 Graphs11.8 Projects11.
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12Lists and Arrays RevisitedSimple
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Sec. 12.1 Multilists 407L1L2L3bcdL4
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Sec. 12.2 Matrix Representations 40
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Sec. 12.3 Memory Management 413/**
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Sec. 12.3 Memory Management 415Smal
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Sec. 12.3 Memory Management 417Tag
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Sec. 12.3 Memory Management 419tend
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Sec. 12.3 Memory Management 421is e
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Sec. 12.3 Memory Management 423AaBc
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Sec. 12.4 Further Reading 4251a3b42
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Sec. 12.6 Projects 42712.7 Write a
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13Advanced Tree StructuresThis chap
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Sec. 13.1 Tries 4310101010120001240
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Sec. 13.2 Balanced Trees 4353737244
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Sec. 13.2 Balanced Trees 437that is
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Sec. 13.2 Balanced Trees 439GPDSASP
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Sec. 13.3 Spatial Data Structures 4
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Sec. 13.4 Further Reading 45313.3.4
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Sec. 13.6 Projects 455(c) Show the
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14Analysis TechniquesOften it is ea
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Sec. 14.1 Summation Techniques 463w
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Sec. 14.1 Summation Techniques 465B
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Sec. 14.2 Recurrence Relations 4671
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Sec. 14.2 Recurrence Relations 469n
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Sec. 14.2 Recurrence Relations 471E
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Sec. 14.2 Recurrence Relations 473N
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Sec. 14.2 Recurrence Relations 475T
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Sec. 14.3 Amortized Analysis 477(ch
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Sec. 14.4 Further Reading 479compar
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Sec. 14.5 Exercises 48114.14 For th
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Sec. 14.6 Projects 48314.24 Use mat
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486 Chap. 15 Lower Boundsthe concep
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488 Chap. 15 Lower Boundsat least o
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490 Chap. 15 Lower BoundsABCGDEFFig
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492 Chap. 15 Lower BoundsProof 1: T
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494 Chap. 15 Lower BoundsFigure 15.
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496 Chap. 15 Lower BoundsTo minimiz
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498 Chap. 15 Lower BoundsThis recur
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500 Chap. 15 Lower BoundsFigure 15.
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502 Chap. 15 Lower Boundsnot only t
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504 Chap. 15 Lower Bounds1234Figure
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506 Chap. 15 Lower Bounds(a) Assume
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16Patterns of AlgorithmsThis chapte
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Sec. 16.1 Dynamic Programming 513on
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Sec. 16.2 Randomized Algorithms 515
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Sec. 16.3 Numerical Algorithms 523
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Sec. 16.3 Numerical Algorithms 525t
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Sec. 16.3 Numerical Algorithms 527B
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Sec. 16.3 Numerical Algorithms 529o
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Sec. 16.3 Numerical Algorithms 531o
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Sec. 16.6 Projects 533value depth5
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536 Chap. 17 Limits to ComputationT
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540 Chap. 17 Limits to ComputationS
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542 Chap. 17 Limits to Computationa
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544 Chap. 17 Limits to Computation3
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548 Chap. 17 Limits to Computationp
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550 Chap. 17 Limits to ComputationE
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552 Chap. 17 Limits to Computation1
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554 Chap. 17 Limits to ComputationM
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556 Chap. 17 Limits to Computationw
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560 Chap. 17 Limits to Computationt
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562 Chap. 17 Limits to Computationm
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564 Chap. 17 Limits to Computation(
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Bibliography[AG06] Ken Arnold and J
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BIBLIOGRAPHY 569[GI91] Zvi Galil an
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BIBLIOGRAPHY 571[SJH93] Clifford A.
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Index80/20 rule, 309, 333abstract d
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INDEX 575image space, 430key space,
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INDEX 577building, 172-177for memor
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INDEX 579octree, 451Ω notation, 65
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INDEX 581comparing algorithms, 224-
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