403:AlgorithmsandDataStructures

Prof.PetkoBogdanov

Introduction

Fall2016UAlbany

ComputerScience

Whatisthiscourseabout?

• Designandanalysisofalgorithms.• Whatisanalgorithm?• Algorithm:awell-defined(computational)proceduretosolveaproblem

Input:DirtyHands

Output:CleanHands

Beforewedelveintoalgorithms…

• Instructor:PetkoBogdanov,• Forthisweekonly:Prof.Mariya Zheleva– mzheleva@albany.edu

• OfficeHours:Tue,Thu:1pmto3pm,orbyappointment

• Office:UAB416->Administrativebuildingnotonthepodium(1215WesternAve)

• Email:pbogdanov@albany.edu

UAB

TAs

• Ashish Jadhav– ajadhav2@albany.edu– Officehours:Tue,Thu 10:30am-11:30am.

• Zumrut Akcam– zakcam@albany.edu– Officehours:Tue3-4pmandWed11am-12pm

• TAofficehoursroomsTBD(lookforanannouncementfromBlackboard)

Prerequisites

• Prerequisites:– CSI210(DiscreteStructures)and– CSI213(DataStructures)

• Istheresomeonewhohasnottakenthoseclasses?– DoHW1and…– Ifyougetmorethan80pointsyoucanstayintheclass

– Else,please,take210and213first

Book• RequiredText:– ThomasH.Cormen,CharlesE.Leiserson,RonaldL.Rivest,Cliord Stein,“IntroductiontoAlgorithms:Ed.3”,MITPress

• Wewillmostlyfollowthebook• Someassignmentfromthebook

Grading

Midterm- 20%

Final- 30%

Programs- 20%

Homework- 30%

Policies:exams

• Twoexams– openbook–Midterm– inclasson10/17/2016– Final– earlyDecember2016(dateTBD)

• Make-upexams– Onlyformajoremergencies(validandverifiable)– Contacttheinstructorassoonasyouknowyouwillbemissinganexamtore-schedule

Policies:programming

• Twoprogrammingassignments– Implementationandcomparisonofalgorithms– InJavaonthedepartmentLinuxcluster• Besuretochecktheycompileontheclusterbeforesubmitting!0pointsforprogramsthatdon’tcompile.

– Testinput/outputprovided• Willnotbethesameforgrading

Policies:homework

• Sixhomeworkassignments– Aboutaweektocompleteeach– Equally-graded– Best-5-of-6policy• Nomake-uphomeworks

• AssignmentsubmissionthroughBlackboard– Programmingasasinglearchivefile– HomeworkasascannedPDFofyoursolution• Onlyifyouarenotabletoscanbeforeclass:youcanbringahardcopy

Policies:cheating

• Cheatingonexams– YouwillreceiveanE-gradeandwillbereported

• Cheatingonassignments– Allassignmentsaretobecompletedindividually– Firstattempt:allstudentsinvolvedwillget0pointsfortheassignment

– FollowingattemptswillresultinE-grade;studentswillbereportedfordisciplinaryaction

Policies:I grades(incomplete)

• OnlygivenforcircumstancesbeyondyourcontrolIF:– Yourworkisingoodstandingasofthemidtermpoint(10/17/2016)• Homeworkscore>=50%• Programmingcompletedatleastat50%• MidtermgradeequivalentofC

– Youareabletoprovidewrittendocumentationtoproveyouareunabletocompletethecourse

Policies:attendance

• Notmandatorybutwilldetermineyourclassperformance– Itisyourresponsibilitytofindoutthematerialandnotescoveredinclassesyoumissed

• Thisisahybridslide/boardcourse– Alwayscomepreparedtotakenotes

Reading ahead

• Readmaterialaheadinthebook– makemoreoutofthelectures– letideas“sink”longer– donotworryifsomedetailsunclear

• Forthisweek:ReadChapters1and2

Homework1

• Due09/07/2016beforeclass

• 4problemstobrushupyourDiscreteMath

• Needtopasswithatleast80%tostayinclass

• Startearly,soyoucanconsultwiththeTAsandProf.Bogdanov.

Backtoourdefinition

• Algorithm:awelldefined(computational)proceduretosolveaproblem

• Tospecifytheproblemweneed:– Input:Whatisgiven?–Output:Whatisneeded?

Exampleproblemspecifications

• Findingthemaximum– Input: Asequenceofnumbers<x1,x2…xn>– Output: Thelargestnumberamongx1,x2…xn

• Sortinginnon-decreasingorder– Input: Asequenceofnumbers<x1,x2…xn>– Output: Apermutation(reordering)of<x’1,x’2…x’n>suchthatx’1≤x’2≤…≤x’n

Instanceandcorrectness

• Asequencesuchas<-7,4,9,2,17,8>isaninstance oftheproblem(i.e.valuesforallrequiredinputs,satisfyingstatedconstraints)

• Asortingalgorithmtransformsthesequence<-7,4,9,2,17,8>into<-7,2,4,8,9,17>

• Analgorithmiscorrect ifforeveryinstanceithalts withthecorrectoutput.

Whatkindofproblemsaresolvedbyalgorithms?

TheInternet

• Internetroutingalgorithms– DecidehowtohandlepacketsthroughInternetpaths

– YouwillstudyDijkstra’salgorithmforfindingtheshortestpath

• Internetapplications.E.g.GoogleSearchusesPageRank– Aroughestimateofpageimportance

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Otherexamplesinclude

• Electroniccommerce– Privacyofuserinformation– Persistencyacrossmultipleserverinstances

• Manufacturing/commercial/politicalenterprises– Politicalcandidates– howtospendcampaignmoneytomaximizethechanceofwinning

– Airlinecompanies– assigncrewstoflightstominimizeexpenses

– Internetserviceprovider– wheretobuildinfrastructuretominimizedelaysandmaximizeInternetbandwidth

Twocommoncharacteristics

• Manycandidatesolutions– Findingonethatis”thebest”canpresentquiteachallenge

• Practicalapplications– Presentsopportunitiestonarrowthescopeàeasiertofind“thebest”solution

Morebasics

• PseudocodeandAlgorithmAnalysisbyexample

• Insertionsort

Exampleofinsertionsortonaninstance

• Whichisthealgorithm?• Whichistheinput?• Whichistheoutput?• Whatistheinstance?

Thealgorithm

Theinput

Theoutput

<5,2,4,6,1,3>

Insertionsort(pseudocode)

Thisstepcanbereachedwheni=0orifA[i]≤key.Inbothcaseskeyisplaceds.t. A[1…i]issorted

Whatisalgorithmanalysis?

• Estimating(predicting)theresourcesneededbyanalgorithm– Time: howlongwouldittake– Memory: howmuchmemoryitwouldrequirefortheuseddatastructures

• Ourgoalistofindthebestalgorithmamongalternativesintermsofminimumresourcerequirements.

• Howtoquantifyimportantalgorithmcharacteristicsandomittediousdetails?

Analysis• Resourcesareexpressedasafunctionofthesizeoftheinput

• Thesizeoftheinputdependsontheproblem:– Sorting: numberofelementsbeingsortedn– Integermultiplication:sizeoftheintegers(i.e.numberofbitstobemultiplied)

• Execution(running)timeofanalgorithm:thenumberofprimitiveoperationsexecuted– e.g.assignment,comparisons,arithmeticops.…– typicallyassumedthatoperationstakeconsttime– allowsmachineindependencefortheanalysis

Worstcase

• Whenusingrunningtimewewillmeanworst-casetime– thelargestrunningtimeforanyinputofafixedsize n– Noteitisalsopossibletodefineaverage(orexpected)timeassumingwehavepickedaninstanceatrandomfromallpossibleinstances,butwewillmostlikelynotdiscussthishere

• Inasensewewillbepessimistsaboutouralgorithms,alwaysexpectingtheworstpossibleinput.

Advantagesofbeingpessimist

• Worst-casetimeanalysis– Providesanupperboundonanyinput,i.e.thealgorithmwillnevertakemorethanthis.

– Forsomealgorithms,worst-caseoccursoften– Helpsusprovisionwithredundancy(oftenagoodideainbuildingsoftwaresystems)

Sanitycheck

• Supposecomputerswereinfinitely-fastandcomputermemorywasfree.– Wouldyouhaveanyreasontostudyalgorithms?– Yes!Youstillneedtodemonstratethatyoursolutionterminates(halts) andgainsthecorrect answer.

• But...memoryisnotfreeandCPUstaketimetocompleteaprimitiveoperation.– Efficient useofresourcestogaincorrectanswers.

Announcements

• Nexttime:InsertionSort– ReadthroughChapters1and2fromthebook

• Homework1posted,DueonSep.7• Gooverthesyllabusonyourownandaskquestionsasnecessary