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Hash Tables (Java)Hash Tables (Java)

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Algonquin CollegeAlgonquin College

Created by Rex WoollardCreated by Rex Woollard

Linear SearchLinear Search

�� O(O(nn))

�� Suitable for very short listsSuitable for very short lists

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Binary SearchBinary Search

�� O(logO(log22 nn))

�� Suitable for very large data setsSuitable for very large data sets

�� Array organizationArray organization

�� Best if few insertions / deletionsBest if few insertions / deletions

Overview: Hash Function and Searching 1Overview: Hash Function and Searching 1

�� Array organizationArray organization

�� Access array elements with indexAccess array elements with index

�� Convert key into indexConvert key into index

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Overview: Collisions with Hashing: InsertionOverview: Collisions with Hashing: Insertion

�� Multiple objects have same indexMultiple objects have same index

�� Need mechanism to find opening Need mechanism to find opening

Overview: Hashing MethodsOverview: Hashing Methods

�� Many methods to generate indexMany methods to generate index

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Direct HashingDirect Hashing

�� Array organizationArray organization

�� Access array elements with indexAccess array elements with index

�� Convert record key into corresponding indexConvert record key into corresponding index

Hash FunctionHash Function

�� Key value too large for direct hashingKey value too large for direct hashing

�� Limited slots in hash tableLimited slots in hash table

�� Hash function generate even distributionHash function generate even distribution

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Hash Function: FoldingHash Function: Folding

�� Use leading and trailing digitsUse leading and trailing digits

�� Add them to middle digitsAdd them to middle digits

�� Leading and trailing digits could be reversedLeading and trailing digits could be reversed

�� Discard resulting overflowDiscard resulting overflow

Hash Function: RotationHash Function: Rotation

�� Keys are clusteredKeys are clustered

�� Move least significant Move least significant

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Hash Function: Dealing with Strings 1Hash Function: Dealing with Strings 1

A 65 a 97

B 66 b 98

C 67 c 99

: : : :

Z 90 z 122

�� Many keys are strings of charactersMany keys are strings of characters

�� Must convert to indexMust convert to index

�� Perform arithmetic on character values (integer)Perform arithmetic on character values (integer)

Hash Function: Using ModulusHash Function: Using Modulus

A 65 a 97

B 66 b 98

C 67 c 99

: : : :

Z 90 z 122

public static int createPoorHashCode(String sKey) {

int nSum = 0;

int nIndex = 0;

while (nIndex < sKey.length())

nSum = nSum + sKey.charAt(nIndex++);

return nSum % nTableSize;

}

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Hash Function: Need Better DistributionHash Function: Need Better Distribution

A 65 a 97

B 66 b 98

C 67 c 99

: : : :

Z 90 z 122

HendersonHenderson

Henry

HillHill

HobartHobart

Hopkins

public static int createPoorHashCode(String sKey) {

int nSum = 0;

int nIndex = 0;

while (nIndex < sKey.length())

nSum = nSum + sKey.charAt(nIndex++);

return nSum % nTableSize;

}

Collision Resolution: OverviewCollision Resolution: Overview

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Open Addressing: Linear ProbeOpen Addressing: Linear Probe

�� Collision: search for next available slotCollision: search for next available slot

�� Might be adjacentMight be adjacent

�� Might be some distance if there is clusteringMight be some distance if there is clustering

Open Addressing: PseudorandomOpen Addressing: Pseudorandom

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BucketsBuckets

�� Each index location can hold several recordsEach index location can hold several records

Chaining with Linked ListsChaining with Linked Lists

List ObjectList Object

ListNode ObjectListNode Object

HashTable object holds a Reference to HashTable object holds a Reference to Array of References to List ObjectsArray of References to List Objects

Array of References to List ObjectsArray of References to List Objects

New ListNode ObjectNew ListNode ObjectKey in Data: Key in Data: RequiemRequiem

New ListNode ObjectNew ListNode ObjectKey in Data: Key in Data: WaterMusicWaterMusic

Data ObjectData Object

Reference to HashTable objectReference to HashTable object

�� Hash table of references to Linked ListsHash table of references to Linked Lists

�� All collisions reside at the same indexAll collisions reside at the same index

�� Lists can grow to accommodate collisionsLists can grow to accommodate collisions

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Open Addressing: Unsuccessful Search

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BigBig--O: Open AddressingO: Open Addressing

80% Load Factor80% Load FactorOpen Addressing: Successful Search

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Open Addressing: Successful Search

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Open Addressing: Unsuccessful Search

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BigBig--O: Open AddressingO: Open Addressing

Variable Load FactorVariable Load Factor

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BigBig--O: ChainingO: Chaining

Chaining: Search

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Chaining: Search

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Variable Load FactorVariable Load Factor

100% Load Factor100% Load Factor

BigBig--O: ChainingO: ChainingChaining: Search

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Chaining: Search

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Chaining: Search

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100% Load Factor100% Load Factor

Chaining: Search

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Variable Load FactorVariable Load Factor

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Chaining: Unsuccessful Search

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At a 200% At a 200% load factor, load factor,

performance performance remains remains excellentexcellent

Open Addressing: Unsuccessful Search

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Chaining versus Open AddressingChaining versus Open Addressing

At a 100% At a 100% load factor, load factor,

performance performance is disastrousis disastrous