Algorithms and data structures the science of computing do

Algorithmsand
DataStructures:
TheScienceof
Computing
byDouglasBaldwin
andGregW.Scragg
CharlesRiverMedia©
2004(640pages)
ISBN:1584502509

Byfocusingonthe
architectureof
algorithms,
mathematical
modelingand
analysis,and
experimental
confirmationof
theoreticalresults,
thisbookhelps
studentsseecomputer
scienceisabout
problemsolving,not
simplymemorizing
andreciting
languages.
TableofContents
AlgorithmsandDataStructures—TheScienceof
Computing
Preface

PartI-TheScienceofComputing'sThreeMethodsof
Inquiry

Chapter1
Chapter2
Chapter3
Chapter4

- WhatistheScienceofComputing?
- Abstraction:AnIntroductiontoDesign
- Proof:AnIntroductiontoTheory
- Experimentation:AnIntroductiontothe
ScientificMethod

PartII-ProgramDesign

Chapter5 - Conditionals
Chapter6 - DesigningwithRecursion
Chapter7 - AnalysisofRecursion
Chapter8 - CreatingCorrectIterativeAlgorithms
Chapter9 - IterationandEfficiency
Chapter10 - ACaseStudyinDesignandAnalysis:
EfficientSorting
PartIII-IntroductiontoDataStructures

Chapter11 - Lists
Chapter12 - QueuesandStacks
Chapter13 - BinaryTrees
Chapter14 - CaseStudiesinDesign:Abstracting

Indirection
PartIV-TheLimitsofComputerScience

Chapter15 - ExponentialGrowth
Chapter16 - LimitstoPerformance
Chapter17 - TheHaltingProblem
AppendixA - Object-orientedProgramminginJava
AppendixB - AbouttheWebSite
Index
ListofFigures
ListofTables


ListofListings,TheoremsandLemmas
ListofSidebars


AlgorithmsandDataStructures:The
ScienceofComputing
byDouglasBaldwinandGregW.Scragg
CharlesRiverMedia©2004(640pages)
ISBN:1584502509

Byfocusingonthearchitectureofalgorithms,
mathematicalmodelingandanalysis,and
experimentalconfirmationoftheoretical
results,thisbookhelpsstudentsseecomputer
scienceisaboutproblemsolving,notsimply
memorizingandrecitinglanguages.

BackCover
Whilemanycomputersciencetextbooksareconfined
toteachingprogrammingcodeandlanguages,
AlgorithmsandDataStructures:TheScienceof
Computingtakesastepbacktointroduceandexplore
algorithms--thecontentofthecode.Focusingon
threecoretopics:design(thearchitectureof
algorithms),theory(mathematicalmodelingand
analysis),andthescientificmethod(experimental
confirmationoftheoreticalresults),thebookhelps
studentsseethatcomputerscienceisaboutproblem
solving,notsimplythememorizationandrecitationof
languages.Unlikemanyothertexts,themethodsof
inquiryareexplainedinanintegratedmannerso
studentscanseeexplicitlyhowtheyinteract.Recursion
andobjectorientedprogrammingareemphasizedas
themaincontrolstructureandabstractionmechanism,


respectively,inalgorithmdesign.
Features:
Reflectstheprinciplethatcomputerscienceisnot
solelyaboutlearninghowtospeakina
programminglanguages
Coversrecursion,binarytrees,stacks,queues,
hashtables,andobject-orientedalgorithms
WrittenespeciallyforCS2students
AbouttheAuthors
DouglasBaldwinisanAssociateProfessorofComputer
ScienceatSUNYGeneseo.AgraduateofYale

University,hehastaughtcoursesfromCS1to
CompilerConstruction,andfromNetworkingtoTheory
ofProgrammingLanguages.Hehasauthoredmany
journalarticlesandconferencepaperswithinthefield.
GregW.ScraggisProfessorEmeritusfromSUNY
Geneseowithoverthirtyyearsexperienceincomputer
science.SincehisgraduationfromtheUniversityof
California,hehasreceivedseveralgrantsrelatedto
computerscienceeducationandhaswrittenover60
articlesforcomputersciencejournals.



AlgorithmsandDataStructures—TheScienceof
Computing
DouglasBaldwin
GregW.Scragg

CHARLESRIVERMEDIA,INC.
Hingham,Massachusetts
Copyright2004byCHARLESRIVERMEDIA,INC.
Allrightsreserved.
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ISBN:1-58450-250-9
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ACKNOWLEDGMENTS
TheScienceofComputingrepresentstheculminationofaprojectthat
hasbeenindevelopmentforaverylongtime.Inthecourseofthe
project,agreatmanypeopleandorganizationshavecontributedinmany
ways.Whileitisimpossibletolistthemall,wedowishtomentionsome
whosecontributionshavebeenespeciallyimportant.Theresearchinto
themethodologywassupportedbyboththeNationalScienceFoundation
andtheU.S.DepartmentofEducation,andwearegratefulfortheir
support.Duringthefirstseveralyearsoftheproject,HansKoomenwasa
co-investigatorwhoplayedacentralroleinthedevelopmentalwork.We
receivedvaluablefeedbackintheformofreviewsfrommanyincluding
JohnHamer,PeterHenderson,LewHitchner,KrisPowers,OritHazzan,
MarkLeBlanc,AllenTucker,TonyRalston,DanielHyde,StuartHirshfield,
TimGegg-Harrison,NicholasHowe,CatherineMcGeoch,andKen
Slonneger.G.MichaelSchneiderandJimLeisywerealsoparticularly
encouragingofourefforts.HommaFarian,InduTalwar,andNancyJones
alluseddraftsofthetextintheircourses,helpingwiththatcrucialfirst
exposure.WeheldaseriesofworkshopsatSUNYGeneseoatwhich
someoftheideaswerefleshedout.Facultyfromotherinstitutionswho
attendedandcontributedtheirideasincludeElizabethAdams,HansPeterAppelt,LoisBrady,MarcusBrown,JohnCross,NiraHerrmann,
MargaretIwobi,MargaretReek,EthelSchuster,JamesSlack,and
FengmanZhang.Almost1500studentsservedasthefrontlinesoldiers
—theoneswhocontributedastheguineapigsofourefforts—butwe

especiallywishtothankSuzanneSelib,JimDurbin,BruceCowley,Ernie
Johnson,CoralieAshworth,KevinKosieracki,GregArnold,Steve
Batovsky,WendyAbbott,LisaCiferri,NandiniMehta,SteveBender,Mary
Johansen,PeterDenecke,JasonKapusta,MichaelStringer,Jesse
Smith,GarrettBriggs,ElenaKornienko,andGenevieveHerres,allof
whomworkeddirectlywithusonstagesoftheproject.Finally,wecould
nothavecompletedthisprojectwithoutthestaffofCharlesRiverMedia,
especiallyStephenMossberg,DavidPallai,andBryanDavidson.





Preface
AlgorithmsandDataStructures:TheScienceofComputing(whichwe
usuallyrefertosimplyasTheScienceofComputing)isabout
understandingcomputation.Weseeitasadistinctdeparturefrom
previoussecond-coursecomputersciencetexts,whichemphasize
buildingcomputations.TheScienceofComputingdevelops
understandingbycouplingalgorithmdesigntomathematicaland
experimentaltechniquesformodelingandobservingalgorithms'
behavior.Itsattentiontorigorousscientificexperimentationparticularly
distinguishesitfromothercomputingtexts.TheScienceofComputing
introducesstudentstocomputerscience'sthreecoremethodsofinquiry:
design,mathematicaltheory,andthescientificmethod.Itintroduces
thesemethodsearlyinthecurriculum,sothatstudentscanusethem
throughouttheirstudies.Thebookusesastronglyhands-onapproachto
demonstratetheimportanceof,andinteractionsbetween,allthree
methods.

THETARGETAUDIENCE
ThetargetcourseforTheScienceofComputingisthesecondcoursein
acomputersciencecurriculum(CS2).Forbetterorworse,thatcourse
hasbecomemorevariedinrecentyears.TheScienceofComputingis
appropriateformany—butnotall—implementationsofCS2.

TheTargetStudent
TheScienceofComputingisaimedatstudentswhoaremajoringin,or
independentlystudying,computerscience.Itisalsosuitableforstudents
whowanttocombineafirmbackgroundincomputersciencewith
anothermajor.
Theprogramminglanguageforexamplesandexercisesinthisbookis
Java.Weassumethatstudentshavehadanintroductoryprogramming
courseusinganobject-orientedlanguage,althoughnotnecessarilyJava.
Thebookshouldalsobeaccessiblewithjustalittleextraworktothose
whostartedwithaprocedurallanguage.Anappendixhelpsstudents
whosepreviousexperienceiswithalanguageotherthanJavamakethe
transitiontoJava.
ThereisquiteabitofmathinTheScienceofComputing.Weteachallof
theessentialmathematicswithinthetext,assumingonlythatreaders
haveagoodprecollegemathbackground.However,readerswhohave
completedoneormorecollege-levelmathcourses,particularlyin
discretemath,willinevitablyhaveaneasiertimewiththemathinthis
bookthanreaderswithoutsuchabackground.

TheTargetSchoolandDepartment
EverycomputersciencedepartmenthasaCS2course,andmostcould
useTheScienceofComputing.However,thisbookismostsuitedto
thosedepartmentsthat:

Wanttogivestudentsanearlyandfirmfoundationinallthe


methodsofinquirythattheywillneedinlaterstudies,or
Wanttoincreasetheiremphasisonthenonprogramming
aspectsofcomputerscience,or
Wanttocloselyaligntheirprogramswithothermathand/or
scienceprograms.





WHYTHESCIENCEOFCOMPUTING?
Webelievethatanintroductiontocomputerscienceshouldbeanindepthstudyofthebasicfoundationsofthefield.Theappropriate
foundationslienotinwhatcomputersciencestudies,butinhowit
studies.

ThreeMethodsofInquiry
TheScienceofComputingisbasedonthreemethodsofinquirycentral
tocomputerscience(essentially,thethree"paradigms"ofcomputer
sciencedescribedbyDenningetal.in"ComputingasaDiscipline,"
CommunicationsoftheACM,January1989).Inparticular,thebook's
missionistoteach:
Design-thecreationofalgorithms,programs,architectures,etc.
TheScienceofComputingemphasizes:
Abstractionasawayoftreatingcomplexoperationsas
"primitives,"sothatonecanwritealgorithmsintermsappropriate
totheproblemtheysolve.
Recursionasatoolforcontrollingalgorithmsanddefining

problems.
Theory-themathematicalmodelingandanalysisofalgorithms,
programs,problems,etc.
TheScienceofComputingemphasizes:
Theuseofmathematicstopredicttheexecutiontimeof
algorithms.
Theuseofmathematicstoverifythecorrectnessofalgorithms.
EmpiricalAnalysis-theuseofthescientificmethodtostudy
algorithms,programs,etc.


TheScienceofComputingemphasizes:
Therigorousnotionof"experiment"usedinthesciences
Techniquesforcollectingandanalyzingdataontheexecution
timeofprogramsorpartsofprograms.
Advancesincomputersciencedependonallthreeofthesemethodsof
inquiry;therefore,awell-educatedcomputerscientistmustbecome
familiarwitheach—startingearlyinhiseducation.





WHATTHESCIENCEOFCOMPUTINGISNOT
TheScienceofComputingisnotrightforeveryCS2course.In
particular,TheScienceofComputingisnot...
PureTraditional
TheScienceofComputingisnota"standard"CS2withextramaterial.
Tofitasoundintroductiontomethodsofinquiryintoasinglecourse,we
necessarilyreducesomematerialthatistraditionalinCS2.Forinstance,

westudybinarytreesasexamplesofrecursivedefinition,the
constructionofrecursivealgorithms(e.g.,search,insertion,deletion,and
traversal),mathematicalanalysisofdatastructuresandtheiralgorithms,
andexperimentsthatdrivehomethemeaningofmathematicalresults(e.
g.,hownearlyindistinguishable"logarithmic"timeisfrom
"instantaneous");however,wedonottrytocovermultiwaytrees,AVL
trees,Btrees,redblacktrees,andothervariationsontreesthatappearin
manyCS2texts.
TheScienceofComputing'semphasisonmethodsofinquiryratherthan
programmingdoeshaveimplicationsforsubsequentcourses.Students
mayenterthosecourseswithaslightlynarrowerexposuretodata
structuresthanistraditional,andprogramsthatwantCS2toprovidea
foundationinsoftwareengineeringforlatercourseswillfindthatthereis
lessroomtodosoinTheScienceofComputingthaninamore
traditionalCS2.However,theseeffectswillbeoffsetbystudentsleaving
TheScienceofComputingwithstrongerthanusualabilitiesin
mathematicalandexperimentalanalysisofalgorithms.Thismeansthat
intermediatecoursescanquicklyfillinmaterialnotcoveredbyThe
ScienceofComputing.Forexample,intermediateanalysisofalgorithms
coursesshouldbeabletomovemuchfasterafterTheScienceof
ComputingthantheycanafteratraditionalCS2.Bottomline:ifrigid
adherencetoatraditionalmodelisessential,thenthismaynotbethe
righttextforyou.
SoftwareEngineering
SomenewversionsofCS2movethefocusfromdatastructuresto


softwareengineering.Thisalsoisdistinctfromtheapproachhere.Welay
asolidfoundationforlaterstudyofsoftwareengineering,butsoftware
engineeringperseisnotamajorfactorinthisbook.

DataStructures
InspiteofthecoverageinPartIII,TheScienceofComputingisnota
datastructuresbook.Atraditionaldatastructurescoursecouldeasilyuse
TheScienceofComputing,butyouwouldprobablywanttoaddamore
traditionaldatastructurestextorreferencebookasasupplementaltext.
InsteadofanyoftheseotherapproachestoCS2,theaimofThe
ScienceofComputingistopresentamorebalancedtreatmentofdesign,
mathematicalanalysis,andexperimentation,thusmakingitclearto
studentsthatallthreetrulyarefundamentalmethodsforcomputer
scientists.





THESCIENCEOFCOMPUTINGAND
COMPUTINGCURRICULA2001
Ourcentralphilosophyisthatthefoundationsofcomputerscience
extendbeyondprogramstoalgorithmsasabstractionsthatcanand
shouldbethoughtfullydesigned,mathematicallymodeled,and
experimentallyanalyzed.Whileprogrammingisessentialtoputting
algorithmsintoconcreteformforapplieduse,algorithmdesignis
essentialifthereistobeanythingtoprograminthefirstplace,
mathematicalanalysisisessentialtounderstandingwhichalgorithms
leadtocorrectandefficientprograms,andexperimentsareessentialfor
confirmingthepracticalrelevanceoftheoreticalanalyses.Althoughthis
philosophyappearstodifferfromtraditionalapproachestointroductory
computerscience,itisconsistentwiththedirectionsinwhichcomputer
sciencecurriculaareevolving.TheScienceofComputingmatches
nationalandinternationaltrendswell,andisappropriateformostCS2

courses.
OurcentralthemesaligncloselywithmanyofthegoalsintheACM/IEEE
ComputingCurricula2001report,forinstance:[1]
Anintroductorysequencethatexposesstudentstothe
"conceptualfoundations"ofcomputerscience,includingthe
"modesofthoughtandmentaldisciplines"computerscientists
usetosolveproblems.
Introducingdiscretemathearly,andapplyingitthroughoutthe
curriculum.
Anintroductorysequencethatincludesreasoningaboutand
experimentallymeasuringalgorithms'useoftimeandother
resources.
Acurriculuminwhichstudents"havedirecthands-onexperience
withhypothesisformulation,experimentaldesign,hypothesis
testing,anddataanalysis."
Anearlyintroductiontorecursion.


Anintroductorysequencethatincludesabstractionand
encapsulationastoolsfordesigningandunderstanding
programs.
ComputingCurricula2001stronglyrecommendsathree-semester
introductorysequence,andoutlinesseveralpossibleimplementations.
TheScienceofComputingprovidesanappropriateapproachtothe
secondorthirdcoursesinmostoftheseimplementations.

EffectiveThinking
Mostcomputersciencedepartmentsseetheirprimarymissionas
developingstudents'abilitytothinkeffectivelyaboutcomputation.
BecauseTheScienceofComputingisfirstandforemostabouteffective

thinkingincomputerscience,itisanidealCS2bookforsuchschools,
whetherwithinaCC2001-compatiblecurriculumornot.
[1]QuotationsinthislistarefromChapters7and9oftheComputing
Curricula2001ComputerSciencevolume.





DISTINCTIVEFEATURESOFTHISBOOK
Thisbookhasanumberofotherfeaturesthatthestudentandinstructor
shouldconsider.

Abstractvs.Concrete
Abstractionasaproblem-solvinganddesigntechniqueisanimportant
conceptinTheScienceofComputing.Object-orientedprogrammingisa
nearlyidealforminwhichtodiscusssuchabstraction.Earlyinthebook,
studentsuseobject-orientedabstractionbydesigningandanalyzing
algorithmswhoseprimitivesarereallymessagestoobjects.This
abstractionenablesshortalgorithmsthatembodyoneimportantidea
apiecetononethelesssolveinterestingproblems.Classlibrarieslet
studentscodethealgorithmsinworkingprograms,demonstratingthat
theobjectsare"real"evenifstudentsdon'tknowhowtheyare
implemented.Forinstance,manyoftheearlyexamplesofalgorithmsuse
messagestoahypotheticalrobottoperformcertaintasks;studentscan
codeandrunthesealgorithms"forreal"usingasoftwarelibrarythat
providesananimatedsimulationoftherobot.Later,studentslearnto
createtheirownobject-orientedabstractionsastheydesignnewclasses
whosemethodsencapsulatevariousalgorithms.

AlgorithmsandPrograms
Themethodsofinquiry,andthealgorithmsanddatastructurestowhich
weapplythem,arefundamentaltocomputing,regardlessofone's
programminglanguage.However,studentsmustultimatelyapply
fundamentalideasintheformofconcreteprograms.TheScienceof
Computingbalancesthesecompetingrequirementsbydevotingmostof
thetexttoalgorithmsasthingsthataremorethanjustprograms.For
example,wedon'tjustpresentanalgorithmasapieceofcode;we
explainthethinkingthatleadstothatcodeandillustratehow
mathematicalanalysesfocusattentiononpropertiesthatcanbe
observednomatterhowonecodesanalgorithm,abstractingaway
language-specificdetails.Ontheotherhand,theconcreteexamplesin
TheScienceofComputingarewritteninarealprogramminglanguage


(Java).Exercisesandprojectsrequirethatstudentsfollowthealgorithm
throughtothecodedlanguage.Thepresentationhelpsseparate
fundamentalmethodsfromlanguagedetails,helpingstudents
understandthatthefundamentalsarealwaysrelevant,andindependent
oflanguage.Studentsrealizethatthereismuchtolearnaboutthe
fundamentalsthemselves,apartfromsimplyhowtowritesomethingina
particularlanguage.

EarlyCompetence
Design,theory,andempiricalanalysisallrequirelongpracticetomaster.
Wefeelthatstudentsshouldbeginusingeachearlyintheirstudies,and
shouldcontinueusingeachthroughoutthosestudies.TheScienceof
Computinggivesstudentsrudimentarybutrealabilitytouseallthree
methodsofinquiryearlyinthecurriculum.Thiscontrastssharplywith
sometraditionalcurricula,inwhichtheoreticalanalysisisdeferreduntil

intermediateorevenadvancedcourses,andexperimentationmaynever
beexplicitlyaddressedatall.

Integration
Design,theory,andempiricalanalysisarenotindependentmethods,but
rathermutuallysupportingideas.Studentsshouldthereforelearnabout
theminanintegratedmanner,seeingexplicitlyhowthemethodsinteract.
Thisapproachhelpsstudentsunderstandhowallthreemethodsare
relevanttotheirparticularinterestsincomputerscience.Unfortunately,
thetraditionalintroductorysequenceartificiallycompartmentalizes
methodsbyplacingtheminseparatecourses(e.g.,programdesignin
CS1and2,butcorrectnessandperformanceanalysisinananalysisof
algorithmscourse).

ActiveLearning
Webelievethatstudentsshouldactivelyengagecomputersasthey
learn.Readingisonlyapreludetopersonallysolvingproblems,writing
programs,derivingandsolvingequations,conductingexperiments,etc.
Activeengagementisparticularlyvaluableinmakingacoursesuchas