Table Of ContentCambridge University Press
978-1-107-16127-6 — Basic Concepts in Data Structures
Shmuel Tomi Klein
Frontmatter
More Information
BasicConceptsinDataStructures
BasicConceptsinDataStructuresacquaintsthereaderwiththetheoreticalsideofthe
artofwritingcomputerprograms.Insteadofconcentratingonthetechnicalaspectsof
howtoinstructacomputertoperformacertaintask,thebookswitchestothemore
challengingquestionofwhatinfactshouldbedonetosolveagivenproblem.
Thevolumeistheresultofseveraldecadesofteachingexperienceindata
structuresandalgorithms.Itisself-containedanddoesnotassumeanyprior
knowledgeotherthanofsomebasicprogrammingandmathematicaltools.Klein
reproduceshisoralteachingstyleinwriting,withonetopicleadingtoanother,related
one.Mostoftheclassicdatastructuresarecovered,thoughnotinacomprehensive
manner.Alternatively,somemoreadvancedtopics,relatedtopatternmatchingand
coding,arementioned.
shmueltomikleinstartedteachinginhighschool,repeatingtohisclassmates
almostdailythelecturesoftheirmathematicsteacher.Asacomputerscience
undergraduateattheHebrewUniversityofJerusalem,heactedasteachingassistantin
theStatisticsDepartmentandhassincegivencoursesandlecturesondatastructures,
algorithms,andrelatedtopicsinEnglish,French,German,andHebrew.
Klein’sresearchfocusesondatacompressionandtext-processingalgorithms.Heis
afullprofessorandformerchairoftheComputerScienceDepartmentatBar-Ilan
Universityandacoauthorofmorethan100academicpublicationsand10patents.
© in this web service Cambridge University Press www.cambridge.org
Cambridge University Press
978-1-107-16127-6 — Basic Concepts in Data Structures
Shmuel Tomi Klein
Frontmatter
More Information
dedicatedto
myspouse Rina
andourchildren ShoshanitandItay
AvitalandAriel
RaananandYifat
AyalandYahav
© in this web service Cambridge University Press www.cambridge.org
Cambridge University Press
978-1-107-16127-6 — Basic Concepts in Data Structures
Shmuel Tomi Klein
Frontmatter
More Information
Basic Concepts in Data Structures
SHMUEL TOMI KLEIN
Bar-IlanUniversity,Israel
© in this web service Cambridge University Press www.cambridge.org
Cambridge University Press
978-1-107-16127-6 — Basic Concepts in Data Structures
Shmuel Tomi Klein
Frontmatter
More Information
UniversityPrintingHouse,CambridgeCB28BS,UnitedKingdom
OneLibertyPlaza,20thFloor,NewYork,NY10006,USA
477WilliamstownRoad,PortMelbourne,VIC3207,Australia
4843/24,2ndFloor,AnsariRoad,Daryaganj,Delhi110002,India
79AnsonRoad,#06-04/06,Singapore079906
CambridgeUniversityPressispartoftheUniversityofCambridge.
ItfurtherstheUniversity’smissionbydisseminatingknowledgeinthepursuitof
education,learning,andresearchatthehighestinternationallevelsofexcellence.
www.cambridge.org
Informationonthistitle:www.cambridge.org/9781107161276
10.1017/9781316676226
©ShmuelTomiKlein2016
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithoutthewritten
permissionofCambridgeUniversityPress.
Firstpublished2016
PrintedintheUnitedStatesofAmericabySheridanBooks,Inc.
AcataloguerecordforthispublicationisavailablefromtheBritishLibrary.
LibraryofCongressCataloginginPublicationData
Names:Klein,ShmuelT.,author.
Title:Basicconceptsindatastructures/ShmuelTomiKlein,
Bar-IlanUniversity,Israel.
Description:Cambridge,UnitedKingdom;NewYork,NY:CambridgeUniversityPress,
[2016]|Includesbibliographicalreferencesandindex.
Identiiers:LCCN2016026212|ISBN9781107161276(hardback:alk.paper)
Subjects:LCSH:Datastructures(Computerscience)
Classiication:LCCQA76.9.D35K5582016|DDC005.7/3–dc23
LCrecordavailableathttps://lccn.loc.gov/2016026212
ISBN978-1-107-16127-6Hardback
ISBN978-1-316-61384-9Paperback
CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyof
URLsforexternalorthird-partyInternetWebsitesreferredtointhispublication
anddoesnotguaranteethatanycontentonsuchWebsitesis,orwillremain,
accurateorappropriate.
© in this web service Cambridge University Press www.cambridge.org
Cambridge University Press
978-1-107-16127-6 — Basic Concepts in Data Structures
Shmuel Tomi Klein
Frontmatter
More Information
Contents
ListofBackgroundConcepts pageix
Preface xi
1 WhyDataStructures?AMotivatingExample 1
1.1 BoyerandMoore’sAlgorithm 3
1.2 TheBad-CharacterHeuristic 4
1.3 TheGood-SufixHeuristic 7
Exercises 12
2 LinearLists 14
2.1 ManagingDataStorage 14
2.2 Queues 16
2.3 Stacks 21
2.4 OtherLinearLists 28
Exercises 31
3 Graphs 33
3.1 ExtendingtheRelationshipsbetweenRecords 33
3.2 GraphRepresentations 38
3.3 GraphExploration 40
3.4 TheUsefulnessofGraphs 41
Exercises 47
4 Trees 50
4.1 AllowingMultipleSuccessors 50
4.2 GeneralversusBinaryTrees 52
4.3 BinaryTrees:PropertiesandExamples 55
4.4 BinarySearchTrees 58
Exercises 64
v
© in this web service Cambridge University Press www.cambridge.org
Cambridge University Press
978-1-107-16127-6 — Basic Concepts in Data Structures
Shmuel Tomi Klein
Frontmatter
More Information
vi Contents
5 AVLTrees 65
5.1 BoundingtheDepthofTrees 65
5.2 DepthofAVLTrees 66
5.3 InsertionsintoAVLTrees 71
5.4 DeletionsfromAVLTrees 77
5.5 Alternatives 80
Exercises 80
6 B-Trees 83
6.1 Higher-OrderSearchTrees 83
6.2 DeinitionofB-Trees 85
6.3 InsertionintoB-Trees 86
6.4 DeletionsfromB-Trees 90
6.5 Variants 92
Exercises 99
7 Heaps 101
7.1 PriorityQueues 101
7.2 DeinitionandUpdates 102
7.3 ArrayImplementationofHeaps 105
7.4 ConstructionofHeaps 106
7.5 Heapsort 110
Exercises 112
8 Sets 114
8.1 RepresentingaSetbyaBitmap 114
8.2 Union-Find 117
Exercises 125
9 HashTables 127
9.1 CalculatinginsteadofComparing 127
9.2 HashFunctions 129
9.3 HandlingCollisions 134
9.4 AnalysisofUniformHashing 140
9.5 DeletionsfromHashTables 147
9.6 ConcludingRemarks 148
Exercises 150
10 Sorting 152
10.1 ASequenceofSortingAlgorithms 152
10.2 LowerBoundontheWorstCase 156
10.3 LowerBoundontheAverage 160
© in this web service Cambridge University Press www.cambridge.org
Cambridge University Press
978-1-107-16127-6 — Basic Concepts in Data Structures
Shmuel Tomi Klein
Frontmatter
More Information
Contents vii
10.4 Quicksort 166
10.5 FindingthekthLargestElement 170
Exercises 177
11 Codes 178
11.1 RepresentingtheData 178
11.2 CompressionCodes 179
11.3 UniversalCodes 189
11.4 ErrorCorrectingCodes 194
11.5 CryptographicCodes 199
Exercises 202
Appendix SolutionstoSelectedExercises 205
Index 217
© in this web service Cambridge University Press www.cambridge.org
Cambridge University Press
978-1-107-16127-6 — Basic Concepts in Data Structures
Shmuel Tomi Klein
Frontmatter
More Information
List of Background Concepts
BinarySearch page15
SummingthemFirstIntegers 19
AsymptoticNotation 20
Mergesort 26
NumberofBinaryTrees 53
DepthofaTree 65
ProvingPropertiesofTrees 67
FibonacciSequence 70
SwappingTwoElements 108
PrimeNumbers 131
ModularArithmetic 133
BirthdayParadox 135
IniniteandFiniteSummations 142
ApproximatingaSumbyanIntegral 144
AverageComplexityofanAlgorithm 161
RecurrenceRelations 175
ix
© in this web service Cambridge University Press www.cambridge.org
Cambridge University Press
978-1-107-16127-6 — Basic Concepts in Data Structures
Shmuel Tomi Klein
Frontmatter
More Information
Preface
After having mastered some high-level programming language and acquired
knowledge in basic mathematics, it is time for a shift of attention. Instead of
concentratingonthetechnicalaspectsofhowtoinstructacomputertoperform
acertaintask,weswitchtothemorechallengingquestionofwhatinfactshould
bedonetosolveagivenproblem.Theaimofthisbookondatastructuresisto
startacquaintingthereaderwiththetheoreticalsideoftheartofwritingcom-
puterprograms.Thismaybeconsideredasairststepingettingfamiliarwitha
seriesofsimilarields,suchasalgorithms,complexity,andcomputability,that
shouldbelearnedinparalleltoimprovepracticalprogrammingskills.
The book is the result of several decades of teaching experience in data
structuresandalgorithms.Inparticular,IhavetaughtacourseonDataStruc-
turesmorethan30times.Thebookisself-containedanddoesnotassumeany
priorknowledgeofdatastructures,justacomprehensionofbasicprogramming
andmathematicstoolsgenerallylearnedattheverybeginningofcomputersci-
enceorotherrelatedstudies.Inmyuniversity,thecourseisgiven inthesec-
ondsemesteroftheirstyearoftheBScprogram,withaprerequisiteofDis-
creteMathematicsandIntroductiontoProgramming,whichareirst-semester
courses.Theformatistwohoursoflectureplustwohoursofexercises,ledby
ateachingassistant,perweek.
Ihavetriedtoreproducemyoralteachingstyleinwriting.Ibelieveinasso-
ciativelearning,inwhichonetopicleadstoanother,relatedone.Althoughthis
maydivertattentionfromthecentral,currentlytreatedsubject,itisthecumula-
tiveimpactofanentiresectionorchapterthatmatters.Therewasnointention
to produce a comprehensive compendium of all there is to know about data
structuresbutrathertoprovideacollectionofwhatmanycouldagreetobeits
basicingredientsandmajorbuildingblocks,onwhichsubsequentcourseson
algorithmscouldrely.Inaddition,manymoreadvancedtopicsarementioned.
xi
© in this web service Cambridge University Press www.cambridge.org
Cambridge University Press
978-1-107-16127-6 — Basic Concepts in Data Structures
Shmuel Tomi Klein
Frontmatter
More Information
xii Preface
Each chapter comes with its own set of exercises, many of which have
appeared in written exams. Solutions to selected exercises appear in the
appendix.Thereareshortinsertstreatingsomebackgroundconcepts:theyare
slightlyindented,setinanotherfont,andseparatedfromthemaintextbyrules.
Thougheachchaptercouldbeunderstoodonitsown,evenifithaspointersto
earliermaterial,thebookhasbeenwrittenwiththeintentofbeingreadsequen-
tially.
ThereisofcoursealonglistofpeopletowhomIamindebtedforthisproject,
and it is not possible to mention them all. Foremost, I owe all I know to the
continuous efforts of my late father to offer me, from childhood on, the best
possible education in every domain. This included also private lessons, and
I am grateful to my teacher R. Gedalya Stein, who interspersed his Talmud
lessonswithshortlashestonotionsofgrammar,history,andmore,andthereby
plantedtheseedsoftheassociativelearningtechniquesIadoptedlater.There
isnodoubtthatmyhighschoolmathematicsteacherFernandBiendelwasone
ofthebest;hetaughtusrigoranddeepunderstanding,andthefactthatmore
thanhalfofourclassendedupwithaPhDinmathematicsshouldbecredited
tohim.
IwishtothankallmyteachersattheHebrewUniversityofJerusalemandat
theWeizmannInstituteofScienceinRehovotaswellasmycolleaguesatBar-
IlanUniversityandelsewhere.Manyofthemhadanimpactonmyacademic
career,especiallytheadvisorsformytheses,EliShamirandAviezriFraenkel.
AmihoodAmirisdirectlyresponsibleforthisbookbecauseheaskedme,when
hewasdepartmentchair,toteachthecourseonDataStructures.Thanksalso
toFranyaFranekforprovidingacontactatCambridgeUniversityPress.
Last, but not least, I wish to thank my spouse and children, to whom this
bookisdedicated,fortheirongoingencouragementandconstructivecomments
during the whole writing period. As to my grandchildren, they have no idea
whatthisisallabout,soIthankthemforjustbeingthereandlightingupmy
dayswiththeirlove.
© in this web service Cambridge University Press www.cambridge.org
