CSE326:DataStructures Lecture#12 BartNiswonger SummerQuarter2001 - - PDF document

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CSE326:DataStructures Lecture#12

BartNiswonger SummerQuarter2001

Today’sOutline

• UnixTutorial

– Whatdoyouwantcovered?

• Midterm

– Amortizedtime – ADTvsDataStructure

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IntermediateUnixTutorial

• 2minutes
• 3thingsyoulove aboutunix
• 3thingsyouhate
• 5thingsyouwishyouknew howtodo
• 1giftidea

AsymptoticTime

• Boundsworst-case runningtime

– Overm operations

• Worst-caseforsingle operationmaybe

reallybad,butworst-caseform

• perationsisbounded

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ADTvsDataStructure

AbstractDataType

– Abstract – Operations& semantics – Data-less – One – Nonotionofrunning timeorcomplexity

Datastructures

– Concreteimplementation – Setofalgorithms a – Holdsdata – Many – Veryparticularrunning timesandcomplexities

• Dictionaryoperations

– create – destroy – insert – find – delete

• Storesvalues associatedwithuser-specified

keys

– values maybeany(homogenous)type – keys maybeany(homogenous)comparabletype

DictionaryADT

• kimchi

– spicycabbage

• KrispyKreme

– tastydoughnut

• kiwi

– Australianfruit

• kale

– leafygreen

• Krispix

– breakfastcereal

insert find(kiwi)

• kohlrabi
• upscaletuber
• kiwi
• Australianfruit

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HashTableApproach

But…isthereaprobleminthispipe-dream? f(x) Kiwi Kimchi Kale Kohlrabi Kumquat

HashTable DictionaryDataStructure

• Hashfunction:maps

keystointegers

– result:canquicklyfind therightspotforagiven entry

• Unorderedandsparse

table

– result:cannotefficiently listallentries, – Cannotfindminandmax efficiently, – Cannotfindallitems withinaspecifiedrange efficiently.

f(x)

Kiwi Kimchi Kale Kohlrabi Kumquat

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HashTableTerminology

hashfunction collision keys loadfactor

• =#ofentriesintable

tableSize

f(x) Kimchi Kale Kohlrabi Kumquat Kiwi table

HashTableCode(FirstPass)

Value&find(Key&key){ intindex=hash(key) %tableSize; returnTable[index]; }

Whatshouldthehash functionbe? (forintegers) Whatshouldthetable sizebe? Howshouldwe resolvecollisions?

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AGoodHashFunction…

…iseasy(fast)tocompute(O(1)and practically

fast).

…distributesthedataevenly(hash(a)

hash(b))

…usesthewholehashtable(forall0

k<size, there’sanisuchthathash(i)%size=k).

AGoodHashFunctionforIntegers

• Choose

– tableSizeisprime – hash(n)=n%tableSize

• Example:

– tableSize=7 insert(4) insert(17) find(12) insert(9) delete(17)

3 2 1 6 5 4

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GoodHashFunctionforStrings?

• Iwanttobeableto:

insert(“kale”) insert(“Krispy Kreme”) insert(“kim chi”)

GoodHashFunctionforStrings?

• SumtheASCIIvaluesofthecharacters.
• Consideronlythefirst3characters.

– Usesonly2871outof17,576entriesinthetableon Englishwords.

• Lets=s1s2s3s4…s5:choose

– hash(s)=s1 +s2128+s31282 +s41283 +…+sn128n

• Problems:

– hash(“really,reallybig”)=well…somethingreally,really big – hash(“onething”)%128=hash(“otherthing”)%128 Thinkofthestringasabase128number.

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EasytoComputeStringHash

• UseHorner’sRule

int hash(Strings){ h=0; for(i=s.length()- 1;i>=0;i--){ h=(si +128*h)%tableSize; } returnh; }

UniversalHashing

• Foranyfixedhashfunction,therewillbe

somepathological setsofinputs

– everythinghashestothesamecell!

• Solution:UniversalHashing

– Startwithalarge(parameterized)classofhash functions

• Nosequenceofinputsisbadforallofthem!

– Whenyourprogramstartsup,pickoneofthehash functionstouseatrandom (fortheentiretime) – Now:nobadinputs,onlyunluckychoices!

• Ifuniversalclasslarge,oddsofmakingabadchoicevery

low

• Ifyoudofindyouareintrouble,justpickadifferenthash

functionandre-hashthepreviousinputs

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“Random”VectorUniversalHash

• Parameterizedbyprimesizeandvector:

a=<a0 a1 …ar>where0<=ai <size

• Representeachkeyasr+1integerswhereki <

size

– size=11,key=39752==><3,9,7,5,2> – size=29,key=“helloworld”==> <8,5,12,12,15,23,15,18,12,4> ha(k)= size k a

r i i i

mod

• ✁

dotproductwitha“random”vector!

UniversalHashFunction

• Strengths:

– worksonanytypeaslongasyoucanformki’s – ifwe’rebuildingastatictable,wecantrymanya’s – arandoma hasguaranteedgoodpropertiesno matterwhatwe’rehashing

• Weaknesses

– mustchooseprimetablesizelargerthananyki

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HashFunctionSummary

• Goalsofahashfunction

– reproduciblemappingfromkeytotableentry – evenlydistributekeysacrossthetable – separatecommonlyoccurringkeys(neighboring keys?) – completequickly

• ExampleHashfunctions

– h(n)=n%size – h(n)=stringasbase128number%size – OneUniversalhashfunction:dotproductwithrandom vector

HowtoDesignaHashFunction

• Knowwhatyourkeysare
• Studyhowyourkeysaredistributed
• Trytoincludeallimportantinformationina

keyintheconstructionofitshash

• Trytomake“neighboring”keyshashtovery

differentplaces

• Prunethefeaturesusedtocreatethehash

untilitruns“fastenough”(veryapplication dependent)

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Collisions

• Pigeonholeprinciple sayswecan’tavoidall

collisions

– trytohashwithoutcollisionm keysinton slotswithm >n – trytoput6pigeonsinto5holes

• Whatdowedowhentwokeyshashtothesame

entry?

– openhashing:putlittledictionariesineachentry – closedhashing:pickanextentrytotry shoveextrapigeonsinonehole!

ToDo

• ProjectII
• Homework4
• ReadChapter5(fast!)

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ComingUp

• Morehashing
• Coolstuff!
• ProjectIII