vce algorithmics (hess) 2015–2016 · during the 2015–2016 accreditation period for vce...

VCE Algorithmics (HESS) 2015–2016

Written examination – End of year

Examination specifications

Overall conditionsThe examination will be sat at a time and date to be set annually by the Victorian Curriculum and Assessment Authority (VCAA). VCAA examination rules will apply. Details of these rules are published annually in the VCE and VCAL Administrative Handbook.There will be 15 minutes reading time and 2 hours writing time.The examination will be marked by a panel appointed by the VCAA.The examination will contribute 60 per cent to the study score.

ContentThe VCE Algorithmics (HESS) Study Design 2015–2016 is the document for the development of the examination. All outcomes in Units 3 and 4 will be examined. All of the key knowledge and skills that underpin the outcomes in Units 3 and 4 are examinable.Students will not be required to use information and communications technology (ICT) in the examination.

FormatThe examination will be in the form of a question and answer book.The examination will consist of two sections.Section A will consist of 20 multiple-choice questions worth 1 mark each and will be worth a total of 20 marks.Section B will consist of a number of short- and extended-answer questions worth a total of 80 marks. Questions may include short scenarios, case studies, multiple parts and the use of stimulus material.All questions will be compulsory. The total marks for the examination will be 100.Answers to Section A are to be recorded on the answer sheet provided for multiple-choice questions.Answers to Section B are to be recorded in the spaces provided in the question and answer book.

Approved materials and equipment• Normalstationeryrequirements(pens,pencils,highlighters,erasers,sharpenersandrulers)• Onescientificcalculator

Relevant referencesThe following publications should be referred to in relation to the VCE Algorithmics (HESS) examination:• VCEAlgorithmics(HESS)StudyDesign2015–2016• VCAABulletin

©VICTORIANCURRICULUMANDASSESSMENTAUTHORITY2015

Version 2 – September 2015

VCEAlgorithmics(HESS)(Specificationsandsample)–Version2–September2015 2

AdviceDuring the 2015–2016 accreditation period for VCE Algorithmics (HESS), examinations will be prepared accordingtotheexaminationspecificationsabove.Eachexaminationwillconformtothesespecificationsandwill test a representative sample of the key knowledge and skills from all outcomes in Units 3 and 4.The following sample examination provides an indication of the types of questions teachers and students can expect until the current accreditation period is over.Answers to multiple-choice questions are provided on page 25.Answers to other questions are not provided.

ALGORITHMICS (HESS)Written examination

Day Date Reading time: *.** to *.** (15 minutes) Writing time: *.** to *.** (2 hours)

QUESTION AND ANSWER BOOK

Structure of bookSection Number of

questionsNumber of questions

to be answeredNumber of

marks

A 20 20 20B 14 14 80

Total 100

• Studentsarepermittedtobringintotheexaminationroom:pens,pencils,highlighters,erasers,sharpeners,rulersandonescientificcalculator.

• StudentsareNOTpermittedtobringintotheexaminationroom:blanksheetsofpaperand/orcorrectionfluid/tape.

Materials supplied• Questionandanswerbookof24pages.• Answersheetformultiple-choicequestions.

Instructions• Writeyourstudent numberinthespaceprovidedaboveonthispage.• Checkthatyournameandstudent numberasprintedonyouranswersheetformultiple-choice

questionsarecorrect,andsignyournameinthespaceprovidedtoverifythis.

• AllwrittenresponsesmustbeinEnglish.

At the end of the examination• Placetheanswersheetformultiple-choicequestionsinsidethefrontcoverofthisbook.

Students are NOT permitted to bring mobile phones and/or any other unauthorised electronic devices into the examination room.

©VICTORIANCURRICULUMANDASSESSMENTAUTHORITY2015

Version2–September2015

SUPERVISOR TO ATTACH PROCESSING LABEL HEREVictorian Certificate of Education Year

STUDENT NUMBER

Letter

ALGORITHMICS(SAMPLE) 2 Version2–September2015

SECTION A – continued

Question 1AheuristicisatechniquethatwillattempttofindA. aprecisesolutiontoaproblem.B. anoptimalsolutiontoaproblem.C. allofthepossiblesolutionstoaproblem.D. asolutiontoaprobleminareasonabletimeframe.

Question 2Whichoneofthefollowingtypesofalgorithmiscommonlyusedtodeterminetheminimumspanningtreeofagraph?A. PrimB. PageRankC. Bellman-FordD. Floyd-Warshall

Question 3

T(n)=T(n/2)+O(1)

WhichoneofthefollowingisthesolutiontotheaboverecurrencerelationusingtheMasterTheorem?A. Ө(n)B. Ө(n2)C. Ө(logn)D. Ө(nlogn)

Question 4Depth-firstsearchisanalgorithmthatcanbeusedtosearchgraphdatastructures.ThetimecomplexityofsearchingagraphwithVverticesandEedgesintheworstcaseisA. O(log|E |+log|V |)B. O(|E |+|V |)C. O(log|E |)D. O(log|V |)

SECTION A – Multiple-choice questions

Instructions for Section AAnswerallquestionsinpencilontheanswersheetprovidedformultiple-choicequestions.Choosetheresponsethatiscorrectorthatbest answersthequestion.Acorrectanswerscores1,anincorrectanswerscores0.Markswillnotbedeductedforincorrectanswers.Nomarkswillbegivenifmorethanoneansweriscompletedforanyquestion.

Version2–September2015 3 ALGORITHMICS(SAMPLE)

SECTION A – continuedTURN OVER

Question 5WhichoneofthefollowingisabenefitofDNAcomputing,whenimplementingalgorithms,incomparisonwithdigitalmethodsofcomputation?A. DNAcomputingsolvesallalgorithmsmuchfasterthandigitalmethodsofcomputation.B. DNAcomputingprovidesnewcapabilitiesofcomputabilitytheorythatdigitalmethodsofcomputation

donothave.C. EfficiencyisgreateranderrorsarefarfewerwithDNAcomputingthanwithdigitalmethodsof

computation.D. DNAcomputingcanprovidemassiveparallelismthatcanbeusedtospeedupasearchcomparedto

digitalmethodsofcomputation.

Use the following information to answer Questions 6 and 7.

A

B C

D E

H I

F G

Question 6Startingatnode(vertex)A,thefirstfournodesvisitedinadepth-firstsearchareA. A B D EB. A B D CC. A B C DD. A C F G

Question 7Startingatnode(vertex)A,thefirstfournodesvisitedinabreadth-firstsearchareA. A B D EB. A B D CC. A B C DD. A C F G



Question 8Dynamicprogramminginvolvesusingarecurrencerelationtoidentifyandsolvesub-problemsandthenA. removingduplicatecomputationofsub-problems.B. minimisingthedifferencebetweensub-problemresults.C. backtrackingifthesub-problemhasalreadybeensolved.D. usinganiterativecomputationthatavoidstherepeatedcomputationofsharedsub-problems.

Question 9Themanagerofaverylargerestauranthasdetectedaproblemwiththetimetakentowashallofthedirtydishesthatareinasinglepilenearthesinksinthekitchen.Thebestabstractdatatype(ADT)torepresenttheprocessingofthedishesisaA. tree.B. stack.C. graph.D. queue.

Question 10Analgorithmcontainsaloopinvariant.Ifthealgorithmiscorrect,theloopinvariantmustbeA. trueatalltimes.B. trueonlyattheendofthebodyoftheloop.C. trueonlyatthestartofthebodyoftheloop.D. truebeforetheloopisexecutedandaftertheloophasfinished.

Question 11WhatisaTuringmachineusefulfor?A. analysingthelogicofcomputeralgorithmsasatheoreticaltoolB. theprocessingofalgorithmsusingpracticalcomputingtechnologyC. themodellingofthestrengthsofparticularalgorithms,includingoptimisationD. effectivelymodellingconcurrency,inparticularwithalways-haltingconcurrentsystems

Question 12

…isanalgorithmdesignpatternwhereinaproblemissolvedbysplittingitintosmaller,non-overlappingsub-problems,thenindividuallysolvingthesub-problemsandcombiningtheirsolutionstoformasolutiontotheoriginalproblem.

Whichoneofthefollowingdesignpatternsisdefinedabove?A. minimaxB. backtrackingC. divideandconquerD. dynamicprogramming


SECTION A – continuedTURN OVER

Question 13WhichoneofthefollowingoperationsistypicallyassociatedwiththegraphADT?A. popB. pushC. indexD. traverse

Question 14Eachofthediagramsbelowdepictsthesameweightedgraph.Assumingboldededgesshowasolution,whichdiagramalsoshowsasolutiontothetravellingsalesmanproblem?

16

43

17

56

32

27

W

XZ

Y

16

43

17

56

32

27

W

XZ

Y

16

43

17

56

32

27

W

XZ

Y

16

43

17

56

32

27

W

XZ

Y

A. B.

C. D.

Question 15An‘undecidable’decisionproblemisonewhereA. itcannotbedecidedhowaTuringmachinecansolvetheproblem.B. itcannotbedecidedbyaTuringmachineiftheproblemhasasolution.C. analgorithmforaTuringmachinetosolvetheproblemcannoteverbefound.D. analgorithmforaTuringmachinetosolvetheproblemcannotpresentlybefound.



Use the following information to answer Questions 16 and 17.ATuringmachineissetupwiththeinstructionsshowninthefollowingtable,whereeachrowrepresentsonestepofthemachineandHisthehaltingstate.Itbeginsinstate1.

Current state

Tape symbol

Print operation

Head motion

Next state

1 blank 0 left H

1 0 none right 1

1 1 none none 2

2 blank 1 none H

2 0 1 left H

2 1 none right 2

H

Themachineisgiventhefollowingtape.Forthismachine,thetaperemainsstationarywhiletheheadmoves.Thearrowshowsthestartingpositionofthehead.

0 1 1

Question 16AftertheTuringmachine’sfirststep,itwillbeinA. state1andtheheadwillbeonepositiontotheright.B. state2andtheheadwillstillbeatthestartingposition.C. state1andtheheadwillstillbeatthestartingposition.D. thehaltingstateandtheheadwillbeonepositiontotheleft.

Question 17Whichoneofthefollowingbestrepresentsthetape’sappearanceandthepositionoftheheadwhentheTuringmachinehalts?

0 1 1 00 1 1

0 1 1

1

1 0 1 1

A. B.

C. D.


END OF SECTION ATURN OVER

Question 18Atablecomparingtwoadvancedalgorithmdesignpatternshasbeenprepared.Theleft-handcolumn’sheadingis‘characteristic’.Theremainingtwocolumnsarecurrentlylabelled 1 and 2 .

Characteristic 1 2

canmakeuseofrecursion yes yes

dividesproblemsintosub-problems no yes

equivalenttodepth-firstsearch yes no

Whichoneofthefollowingstatementsiscorrect?A. Label 1 shouldread‘divideandconquer’andlabel 2 shouldread‘backtracking’.B. Label 1 shouldread‘backtracking’andlabel 2 shouldread‘divideandconquer’.C. Label 1 shouldread‘dynamicprogramming’andlabel 2 shouldread‘divideandconquer’.D. Label 1 shouldread‘divideandconquer’andlabel 2 shouldread‘dynamicprogramming’.

Question 19AlimitationoftheChurch-TuringthesisisthatitdoesnotconsiderA. Turingmachines.B. analogcomputing.C. thelambdacalculus.D. algorithmsforcomputingmathematicalfunctions.

Question 20Intheearly1900s,DavidHilbertproposedaprogramtoformalisethefoundationofmathematicsbyestablishingaformalsystemforarithmeticthatwasconsistent,completeanddecidable.ChurchandTuringindependentlyshowedthattheredidnotexistaproceduretocomputetheanswertoanarbitrarystatementinfirst-orderlogicthatwasA. complete.B. decidable.C. completeordecidable.D. completeanddecidableatthesametime.


SECTION B – continued

Question 1 (5marks)Consideranalgorithmthathasthreeinputvariables,A,BandC,andaselectionoftestdatawheretwopossiblevaluesforeachoftheinputvariablesissuchthat

A={3,5} B={X,Y} C={7,9}

a. Whatisthetotalnumberofpossibletestcasesrequiredtotestthegivendata? 1mark

b. Describetheprocessthatwouldbeundertakentopair-wisetestthealgorithmwiththegivendata.Inyouranswer,giveallofthepossiblepair-wisetestcases. 4marks

SECTION B

Instructions for Section BAnswerallquestionsinthespacesprovided.


SECTION B – continuedTURN OVER

Question 2 (6marks)Considerthefollowingtypesofblack-boxtesting:

pair-wise boundaryvalue edgecase errorguessing

Describeandjustifythemostappropriateorderfortestinganalgorithmsolutionifalltypesoftestingweretobecarriedoutonanalgorithm.



Question 3 (3marks)

A

B C

DE

G

H

I

F

a. Whatisthepathcoverageoftheabovegraph?Stateallpathsaspartofyoursolution. 2marks

b. Howmanypathsneedtobefollowedtoensurebranchcoverageoftheabovegraph? 1mark



Question 4 (4marks)ExplaintheprocessinvolvedwhenDNAcomputingisusedtosolveNon-deterministicPolynomial-time(NP)-hardproblems,suchasthetravellingsalesmanproblem.



Question 5 (4marks)Considerthefollowingpseudocode.

AlgorithmsearchGraph(start,target) variables:Q,node //Qisaqueue setQtostart repeatuntilQisempty setnodetofirstnodeinqueue setQtoeverynodeexceptfirstnodeinqueue setnode.visitedtotrue foreachsuccessorofnode.neighbours ifsuccessor.visited=falsethen setsuccessor.predecessortonode Q.enqueue(successor) endif endfor endrepeat ifnode=targetthen variables:next setnexttotarget repeatuntilnext=start setnext.tracedtotrue setnexttonext.predecessor endrepeat endif setstart.tracedtotrue

Thepseudocodeaboverepresentsasearchingalgorithmthattakestwoinputs:asetofnodes(start)andthetargetthatisbeingsearchedfor(target).

UsingBig-Onotation,statethetimecomplexityofthealgorithmintheworstcase,wherethenumberofnodesinthesetofnodesisn.Showallworkingandcalculationsinyouranswer.



Question 6 (5marks)Compareaqueueandapriorityqueue.Useexamplesaspartofyourexplanation.



Question 7 (6marks)

2 3

2

5

6

2

4

8

Stateandexplaintwopropertiesofthegraphabove.Foreachproperty,annotatethegraphtoshowwhereanexampleofthatpropertyislocated.

Property1

Property2



Question 8 (8marks)a. Sketchagraphthatcouldbeusedtomodelthefriendshipnetworkofagroupofsixpeople. 4marks

b. Selecttwoofthepropertiesyouincludedinthegraphabove.Justifytheuseofbothofthesepropertiesinthegraph. 4marks

Property1

Property2



Question 9 (2marks)Tworesearchersuseequivalentgraphstorepresentthesocialstructureofpeoplewhobelongtoasmallgroup.Oneresearcherusedletterstolabelhergraph,theotherusednumbers.

1

2 3

4

5

6

7

a

b c

d

e

f

g

Inthespacebelow,drawanewgraphthatcombinesthetworesearchers’graphs.Labeleachnodewithtwo labels(letter,number)showingtheconnectionsbetweenthelettersandnumbersinthetwographs.



Question 10 (6marks)

A B C D E F

road ramp ferry

side road

Thediagramaboveshowsvehicleslineduponaroad,readytoboardaferry.Thevehiclesvaryinsizeandweight,andsotheyneedtoberearrangedtobalancetheferry’sloadbeforetheycanbedrivenontotheferry.ThecarsneedtoendupontherampintheorderACEBDF.Thevehiclescanonlybemovedaccordingtothefollowingrules:• oneormorevehiclesmovedfromtheroadtotheramp• oneormorevehiclesmovedfromtheroadtothesideroad• oneormorevehiclesmovedfromthesideroadtotheroad• vehiclesmaynotjumpinfrontoforpassothervehicles

Writeanalgorithminpseudocodethatproducesanend-stateofvehiclesintheorderACEBDFontherampleadingtotheferry.


SECTION B – Question 11–continued

Question 11 (5marks)Considerthegraphbelowrepresentingthecomputers(A–H)inasmalllocalareanetwork.Thenumbersontheconnectionsrepresentthelengths(inmetres)ofcablerequiredtoconnecteachcomputertotheonesnexttoit.

A

BC

E

H

D

G

F

6

4

3

4

5

3

2

6

3

2

5

2

2



a. Usingthetemplatebelow,drawtheconnectionsbetweencomputerstoshowtheminimumspanningtree.Labelthecablelengthsbetweeneachcomputer. 4marks

A

BC

E

H

D

G

F

b. State,inmetres,theminimumamountofcablerequiredtoconnectallofthecomputersasaminimumspanningtree. 1mark



Question 12 (8marks)SusanhaswrittenasimplerecursivefunctionforgeneratingthenthFibonaccinumber.Forexample, ifn=20,the20thFibonaccinumber,6765,isreturned.

functionfibonacci(n) if n<=1return n returnfibonacci(n−1)+fibonacci(n−2)

Aspartofhertestingofthealgorithm,Susanmeasuredthetimeittooktoreturnavalue.Forn=10,thefunctionreturnedthecorrectresultalmostinstantaneously,butforn=50ittookmorethananhour.Inordertotrytoworkoutwhyitwastakingsolong,Susanconstructedatreeshowingeachcalculationmadebythefunctionforn=5.

fibonacci(5)

fibonacci(4)

fibonacci(3)

fibonacci(2)

fibonacci(1) fibonacci(0)

fibonacci(1) fibonacci(1) fibonacci(0) fibonacci(1) fibonacci(0)

fibonacci(2) fibonacci(2) fibonacci(1)

fibonacci(3)

(5 – 1) (5 – 2)

(4 – 1)

(3 – 1)

(2 – 1) (2 – 2)

(3 – 2) (2 – 1) (2 – 2) (2 – 1) (2 – 2)

(4 – 2) (3 – 1) (3 – 2)



a. i. Whenlookingatherdiagram,whatshouldSusannoticeasthemostlylikelyreasonforherfunction’spoorperformance? 1mark

ii. Explainhowthisreasonaccountsforthefunction’sincreasinglypoorperformanceforincreasingvaluesofn. 2marks

b. i. Outlinehowyouwouldapplydynamicprogrammingtothisproblemtoimprovethefunction’sperformance. 3marks

ii. Explainhowyoursolutionismoreefficientthantheoriginalsolution. 2marks



Question 13 (10marks)Rodneyisdevelopingapattern-matchingalgorithm.Itmustsearchatextstring,T,foragivenstring,G,andstopifitfindsit.IfGisfoundinT,thealgorithmmustoutputthepositionofGinT,otherwiseitmustoutputzero(0).Tohelphimunderstandhowthealgorithmshouldwork,Rodneydecidestosolveasmallerproblemfirstbydrawingastategraphforfindingtheword‘cat’inT.ThediagrambelowshowswhatRodneyhasdrawnsofar.Theupper-caselettersAtoFarelabelsforthepartsofthediagramthatRodneyhasnotyetcompleted.EachtransitioninhisstategraphistriggeredbythereadingofthenextcharacterinT.

char is not ‘c’

char is ‘c’

charis ‘c’

CF

AD E

B

2. Found ‘c’3. Found ‘ca’+ record position

in T1. Searching

no more chars

5. End of T

char is not ‘a’and not ‘c’

char is not ‘t’



a. Forthetransitionfromstate2tostate5,whatlabelshouldRodneywriteatA? 1mark

b. Ifstate5isreached,Rodneyexpectssomeactiontotakeplace.

WhatactionshouldbewrittenatB? 1mark

c. Forthetransitionfromstate2tostate3,whatlabelshouldbewrittenatC? 1mark

d. Rodneyhasstartedtodrawatransitionfromstate3labelled‘charisnot“t”(D)’.

Towhichstate(1,2,3or5)shouldthistransitiongo? 1mark

e. Rodneyhasalsostartedanothertransition(E).

Whatshouldthistransitionbelabelled,andtowhichstate(1,2,3or5)shoulditgo? 2marks

f. State4hasnotyetbeendrawnonthediagram.Itisarrivedatviaatransitionfromstate3(F). i. Whatshouldthetransitionfromstate3tostate4belabelled? 1mark

ii. Whatshouldstate4belabelled? 1mark

iii. Whenstate4hasbeenreached,whataction(s),ifany,shouldbecarriedout?Ifyouexpectnoactiontobeundertaken,write‘none’andexplainwhynot. 2marks


END OF QUESTION AND ANSWER BOOK

Question 14 (8marks)OneargumentagainstSearle’sChineseRoomArgumentisthatacomputerwiththeabilitytointeractwiththeworldthewayahumandoes(forexample,arobot)couldlearnabouttheworldinthesamewayachilddoes.Thecomputercould,therefore,attachmeaningtosymbolsand,indoingso,understandnaturallanguage.

Discussthestrengthsandweaknessesofthisargument.Inyourresponse,provideanoutlineofSearle’sChineseRoomArgumentanditsconnectiontotheTuringtest.


Answers to multiple-choice questions

Question Answer

1 D

2 A

3 C

4 B

5 D

6 A

7 C

8 D

9 B

10 D

11 A

12 C

13 D

14 D

15 C

16 A

17 A

18 B

19 B

20 B

vce algorithmics (hess) 2015–2016 · during the 2015–2016 accreditation period for vce...

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