CS3000:Algorithms&Data PaulHand

Day1:• CourseOverview• WarmupExercise(Induction,Asymptotics,Fun)

Jan7,2019

• Name:PaulHand• CallmePaul• NEUsinceFall2018• Office:523Lake• OfficeHours:Mon1:15-2:45

• Research:• MachineLearning,ArtificialIntelligence,ComputerVision• Algorithmsareatthecoreofallofthese!

Instructor

Discussion: Whatimpressivethingscancomputersnowdo(butcouldn’twhenyouwereborn)?

Whatdoyouthinkcomputerswillbeabletodoin10yearsthattheycan’ttoday?

Discussion:

Whatwouldyousayisdrivingcomputationaladvances?

• Whatisanalgorithm?

• Essentiallyallcomputerprograms(andmore)arealgorithmsforsomecomputationalproblem.

Algorithms

Anexplicit,precise,unambiguous,mechanically-executablesequenceofelementaryinstructionsforsolvingacomputationalproblem.

-JeffErickson

• WhatisAlgorithms?

• Abstractandformalizecomputationalproblems

• Identifybroadlyusefulalgorithmdesignprinciplesforsolvingcomputationalproblems

• Rigorouslyanalyzepropertiesofalgorithms• correctness,runningtime,spaceusage

Algorithms

Thestudyofhowtosolvecomputationalproblems.

Moore’sLaw

• Eachofyou:Determinehowmanyotherpeopleinthisroomhavethesamefirstnameasyou.

Acomputationalproblem

• Sometimesyourfirstinstinctapproachisreasonable.• Sometimesyourfirstinstinctisnot.

Therearemultiplewaystosolveproblems

Exampleproblemswewilllookat

ClosestPairofPoints SequenceAlignment

IntervalScheduling Findingtheshortestpath

Othergoodproblems(wewontsee)

PlantedClique TravelingSalesmanProblem

• WhatisCS3000:Algorithms&Data?

• Proofsareaboutunderstandingandcommunication,notaboutformalityorcertainty• Differentemphasisfromcoursesonlogic

• We’lltalkalotaboutprooftechniquesandwhatmakesacorrectandconvincingproof

Algorithms

Thestudyofhowtosolvecomputationalproblems.Howtorigorouslyprovepropertiesofalgorithms.

• Thatsoundshard.WhywouldIwanttodothat?

• BuildIntuition:• How/whydoalgorithmsreallywork?• Howtoattacknewproblems?• Whichdesigntechniquesworkwell?• Howtocomparedifferentsolutions?• Howtoknowifasolutionisthebestpossible?

Algorithms

• Thatsoundshard.WhywouldIwanttodothat?

• ImproveCommunication:• Howtoexplainsolutions?• Howtoconvincesomeonethatasolutioniscorrect?• Howtoconvincesomeonethatasolutionisbest?

Algorithms

• Thatsoundshard.WhywouldIwanttodothat?

• GetRich:• Manyoftheworld’smostsuccessfulcompanies(eg.Google)beganwithalgorithms.

• Manyjobinterviewshavealgorithmquestions

• Understandthenaturalworld:• Brains,cells,networks,etc.oftenviewedasalgorithms.

• Fun:• Yes,seriously,fun.

Algorithms

CourseStructureEnd4/17

FinalTBD

Start1/7

MidtermI2/20

MidtermII3/27

• HW=45%• Exams=55%• MidtermI=15%• MidtermII=15%• Final=25%

CourseStructureEnd4/17

Start1/7

DivideandConquer

DynamicProgramming

Graphs NetworkFlow

Textbook:AlgorithmDesignbyKleinbergandTardos

Moreresourcesonthecoursewebsite

FinalTBD

MidtermI2/20

MidtermII3/27

• TBD• OfficeHours:TBD• Location:TBD

• TBD• OfficeHours:TBD• Location:TBD

• TBD• OfficeHours:TBD• Location:TBD

TheTATeam

• WeeklyHWAssignments(45%ofgrade)• DueWednesdaysby2:50pm• HW1outonWednesday!DueWed1/16• Noextensions,nolatework• LowestHWscorewillbedroppedfromyourgrade

• Amixofmathematicalandalgorithmicquestions

Homework

• HomeworkmustbetypesetinLaTeX!• Manyresourcesavailable• Manygoodeditorsavailable(TexShop,TexStudio)• IwillprovideHWsource

HomeworkPolicies

• HomeworkwillbesubmittedonGradescope!• MoredetailsonWednesday

HomeworkPolicies

• Youareencouragedtoworkwithyourclassmatesonthehomeworkproblems.• Youmaynotusetheinternet• Youmaynotusestudents/peopleoutsideoftheclass

• CollaborationPolicy:• Youmustwriteallsolutionsbyyourself• Youmaynotshareanywrittensolutions• Youmuststateallofyourcollaborators• Wereservetherighttoaskyoutoexplainanysolution

HomeworkPolicies

• WewillusePiazzafordiscussions• Askquestionsandhelpyourclassmates• Pleaseuseprivatemessagessparingly

• MoredetailsonWednesday!

DiscussionForum

CourseWebsite

http://www.ccs.neu.edu/home/hand/teaching/cs3000-spring-2018/

• Prof.Schnyderteachesanothersection• Noformalrelationshipwithmysection• Willcoververysimilartopicsandsharesomematerials• Willbeoutofsync• YoushouldnotgotoOHforProf.Schnyder’sTAs

WhatAbouttheOtherSections?

Illustration:Let’scounthowmany studentsareinthisclass

• Isthiscorrect?• Howlongdoesthistakewithnstudents?

SimpleCounting

SimCount: Find first student First student says 1 Until we’re out of students: Go to next student Next student says (what last student said + 1)

RecursiveCounting-DivideandConquer

RecursiveCount: If you are the only person in group:

return 1 Else:

Split your group into two subgroups of similar size (one includes you) Appoint a leader of the other subgroup Ask that leader how many are in that subgroup Determine how many are in your subgroup. return # in your subgroup + # in other subgroup

RecursiveCounting-DivideandConquerRecursiveCount:

If you are the only person in group: return 1

Else: Split your group into two subgroups of similar size (one includes you) Appoint a leader of the other subgroup Ask that leader how many are in that subgroup Determine how many are in your subgroup. return # in your subgroup + # in other subgroup

• Howlongdoesthistakewithn=2mstudents?

ProofsbyInduction

• Claim:Foreverynumberofstudents

• Intermsofn,

RunningTime-ProofbyInduction

n = 2m

T (2m) = 3m+ 1

T (n) ⇡ 3 log2 n+ 1