Lists

CS5010ProgramDesignParadigms“Bootcamp”Lesson4.1

1©MitchellWand,2012-2014ThisworkislicensedunderaCreative Commons Attribution-NonCommercial 4.0 International License.

Howtorepresentinfoofarbitrarysize?

• aphonebookwithmanylistings• aspace-invadersgamewithmanyinvaders• apresentationwithmanyslides

• Eachofthesecanberepresentedasasequenceofinformationitems.

• Theremaybebetterwaysforsomeofthese,butwewillstartwithsequences

• Thisisourfirstexampleofrecursivedata

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Generalization

OverConstants

OverExpressions

OverContexts

OverDataRepresentations

OverMethodImplementations

MixedData

DataRepresentations

Basics

RecursiveData

FunctionalData

Objects&Classes

Stateful Objects

DesignStrategies

Combinesimplerfunctions

Useatemplate

DivideintoCases

Callamoregeneralfunction

CommunicateviaState

Module04

Outlinefortherestofthisweek

• Thearithmeticoflists• Usingthelisttemplate• ListsofStructures

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LearningObjectivesforthisLessonAttheendofthislesson,youshouldbeableto:• Writedownadatadefinitionforinformationrepresentedasalist

• Notatelistsusingconstructor,list,andwritenotations.

• Explainhowlistsarerepresentedassingly-linkeddatastructures,andhowcons,first,andrestworkonthesestructures

• Calculatewiththebasicoperationsonlists:cons,first,andrest .

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Lists:AHandyConstructforSequences

• SequencesofdataitemsarisesooftenthatRackethasastandardwayofrepresentingthem.

• SequenceinformationinRacketisreprestentedbylists.

• We’llseelotsofexamples:– ListOfNumbers– ListOfDigits– ListOfStrings– ListOfBooks

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ListsofNumbers

A List of Numbers (LON) is one of:-- empty-- (cons Number LON)

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Listdataisakindofmixeddata.Justaswedidinourpreviousdatadefinitions, thedatadefinitions forlistsshowstheconstructor foreachcase.Herewehavetwoconstructors:theconstantemptyandthefunction cons.Alistofnumbers (or"LON")iseitherempty orthevaluebuiltbyapplyingcons toanumberandanotherLON.

There’snointerpretationherebecausetheselistsdon’tmeananything(yet).Theydonotrefertoanyreal-worldinformation.

cons isbuilt intoRacket.Wedon’t needadefine-structureforit.

ExamplesofLONsempty

(cons 11 empty)(cons 22 (cons 11 empty))

(cons 33 (cons 22 (cons 11 empty)))(cons 33 empty)

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A List of Numbers (LON) is one of:-- empty-- (cons Number LON)

HerearesomeexamplesofLONs.

empty isaLON bythedatadefinition.

(cons11empty) isaLONbecause11 isanumberandempty isaLON.

(cons22(cons11empty)) isaLONbecause22 isanumberand(cons11empty) isaLON.Andsoon.

ListsofDigits

A Digit is one of"0" | "1" | "2" | ... | "9"

A List of Digits (LOD) is one of:-- empty-- (cons Digit LOD)

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Let'sdoitagain,thistimewithdigits.

WedefineaDigittobeoneofthestrings"0","1",etc.,through"9".

AListofDigits(LOD)iseitheremptyortheconsofaDigitandaListofDigits.

ExamplesofLODsempty

(cons "3" empty)(cons "2" (cons "3" empty))

(cons "4" (cons "2" (cons "3" empty)))• ThesearenotLODs:(cons 4 (cons "2" (cons "3" empty)))

(cons (cons "3" empty) (cons "2" (cons "3" empty)))

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A List of Digits (LOD) is one of:-- empty-- (cons Digit LOD)

Canyouexplainwhyeachofthefirst4examplesareLOD’s,accordingtothe

datadefinition?Canyouexplainwhythelasttwoare

notLODs?

ListsofBooks

A Book is a (make-book ...) .

A List of Books (LOB) is one of:-- empty-- (cons Book LOB)

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Wecanbuild listsofmorecomplicateddataitems.Imaginewehadadatadefinition forBook.ThenwecandefineaListofBooksinthesamewayaswedidforlistsofnumbersorlistsofdigits:aListofBooksiseitheremptyortheconsofaBookandaListofBooks.

ExamplesofLOBs(define book1 (make-book ...))(define book2 (make-book ...))(define book3 (make-book ...))

empty(cons book1 empty)

(cons book2 (cons book1 empty))(cons book2 (cons book2 (cons book1 empty))• NotaLOB:

(cons 4 (cons book2 (cons book1 empty))

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A List of Books (LOB) is one of:-- empty-- (cons Book LOB)

(Why?)

Thisdatadefinitionisself-referential

A List of Numbers (LON) is one of:-- empty-- (cons Number LON)

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Thedatadefinition forLONscontainssomething wehaven'tseenbefore:self-reference.ThesecondconstructorusesLON,eventhough wehaven'tfinished definingLONsyet.That'swhatwemeanbyself-reference.Innormaldefinitions, thiswouldbeaproblem:youwouldn’t likeadictionarythatdidthis.Butself-referencethewaywe'veuseditisOK.We'veseenintheexampleshowthisworks:onceyouhavesomething thatyouknowisaLON,youcandoaconsonittobuildanotherLON.Sincethat'saLON,youcanuseittobuild stillanotherLON.Wealsocallthisarecursive datadefinition.

Thisoneisself-referential,too

A Digit is one of"0" | "1" | "2" | ... | "9"

A List of Digits (LOD) is one of:-- empty-- (cons Digit LOD)

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HowListsRepresentSequences• IfXissomedatadefinition,wedefinealistofX'saseither

emptyortheconsofanXandalistofX's.• Soalistofsardinesiseitherempty orthecons ofasardine

andalistofsardines.• Theinterpretationisalways"asequenceofX's".

– empty representsasequencewithnoelements– (consxlst) representsasequencewhosefirstelementisx and

whoseotherelementsarerepresentedbylst.• Ifwehadsomeinformationthatwewantedtorepresentas

alistofX's(sayalistofpeople),wewouldhavetospecifytheorderinwhichtheX'sappear(say"inincreasingorderofheight"),orelsesay“inanyorder.”

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TheGeneralPatternA ListOfX is one of-- empty

interp: a sequence of X's with no elements-- (cons X ListOfX)

interp: (cons x lst) represents a sequence of X'swhose first element is x and whoseother elements are represented by lst.

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ListNotation• Thereareseveralwaystowritedownlists.• We'vebeenusingtheconstructornotation,sincethatisthemostimportantoneforuseindatadefinitions.

• Thesecondmostimportantnotationwewilluseislistnotation.InRacket,youcangetyouroutputinthisnotationbychoosingthelanguage"BeginningStudentwithListAbbreviations".

• Internally,listsarerepresentedassingly-linkedlists.

• Onoutput,listsmaybenotatedinwritenotation.

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ExamplesofListNotation

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11 22 33

Internalrepresentation:

(list 11 22 33)Listnotation:

(cons 11(cons 22

(cons 33empty))))

Constructornotation:

(11 22 33)write-style(outputonly):

Implementationofcons

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22 33

lst

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(cons 11 lst)

lst = (list 22 33)

(cons 11 lst) = (list 11 22 33)

Nowthatwe'veseentheinternalrepresentationoflists,wecanseehowcons createsanewlist:itsimplyaddsanewnode tothefrontofthelist.Thisoperation takesashort, fixedamountoftime.

OperationsonLists

empty? : ListOfX -> BooleanGiven a list, returns true iff the list is empty

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Racketprovides3functions forinspectinglistsandtakingthemapart.Theseareempty?,first,andrest.

Thepredicateempty?returnstrueifandonlyifthelistisempty.

OperationsonLists

first : ListOfX -> XGIVEN: a listWHERE: the list is non-emptyRETURNS: its first element

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Whenwewritedownthetemplateforlists,wewillseethatwhenwecallfirst, itsargumentwillalwaysbenon-empty.

OperationsonLists

rest : ListOfX -> ListOfXGIVEN: a listWHERE: the list is non-emptyRETURNS: the list of all its elements except the first

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Whenwewritedownthetemplateforlists,wewillseethatwhenwecallrest,itsargumentwillalwaysbenon-empty.

Examples(empty? empty) = true(empty? (cons 11 empty)) = false(empty? (cons 22 (cons 11 empty))) = false

(first (cons 11 empty)) = 11(rest (cons 11 empty)) = empty

(first (cons 22 (cons 11 empty))) = 22(rest (cons 22 (cons 11 empty))) = (cons 11 empty)

(first empty) è Error! (Precondition failed)(rest empty) è Error! (Precondition failed)

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Implementationoffirst and rest

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22 33

lst2

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lst2 = (list 11 22 33)(first lst2) = 11(rest lst2) = (list 22 33)

(first lst2)

(rest lst2)

first andrest simplyfollowapointerinthesingly-linkeddatastructure.

Propertiesofcons,first,andrest

(first (cons v l)) = v

(rest (cons v l)) = lIfl isnon-empty,then(cons (first l) (rest l)) = l

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Herearesomeuseful factsaboutfirst,rest,andcons.Canyouseewhytheyaretrue? Thesefactstellusthatifwewanttobuilda

listwhosefirst isx andwhose rest islst,wecandothisbywriting (consxlst).

SummaryAtthispoint,youshouldbeableto:• Writedownadatadefinitionforinformationrepresentedasalist

• Notatelistsusingconstructor,list,andwritenotations.

• Explainhowlistsarerepresentedassingly-linkeddatastructures,andhowcons,first,andrestworkonthesestructures

• Calculatewiththebasicoperationsonlists:cons,first,andrest .

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NextSteps

• Ifyouhavequestionsaboutthislesson,askthemontheDiscussionBoard

• DoGuidedPractices4.1and4.2• Goontothenextlesson

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