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DATASTRUCTURES

MAHESH GOYANI

MAHATMA GANDHI INSTITUE OF TECHNICAL EDUCATION & RESEARCH CENTER

mgoyani@rediffmail.com

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HASHING

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Hashing provides O(1) constant time complexity for searching.

Generally, array index works as an searching index if there is one toone correspondence between key and element.

In practice, it is very tough to maintain 1-1 relationship between keyand element if data is too large, like ID = 12345.

TERMINOLOGY

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31300

49001

52202

Empty

12704

Empty

65606

00

01

02

03

04

05

06

98

99

Index Record

31300

49001

52202

12704

65606

00

01

02

03

04

05

06

98

99

Index Record

Hashed Insertion Linear Insertion

COMPARISION

Key = 12704

Hash Fun.Key % 100

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COLLISION

If two number appears with the same hash value, like 12345 and 23645, thanboth has to the same location ARRAY [45]. This is known as collision.

Collision is one of the problem while designing the good hash function.

Minimization ofcollision is also too difficult.

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LINEAR PROBING

A simple approach to resolving collisions is to store the colliding record in tonext available record.

Actual SceneOrder ofInsertion Index

00

01

02

03

04

05

06

07

08

..

..

99

14001

14001

00104

001045000350003

77003 77003

42504 42504

33099

33099

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DELETION

Actual SceneIndex

00

01

02

03

04

05

06

07

08

..

..

99

14001

00104

50003

77003

42504

33099

Linear probing solves one problem butgenerates another

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CLUSTERING

Actual SceneIndex

00

01

02

03

04

05

06

07

08

..

..

99

14001

00104

50003

77003

42504

33099

Record with key 03,04,05,06 and 07 wouldbe inserted at array room 7, that is array room7 is five times as likely as array room 8 to befilled.

Clustering results in to inconsistentefficiency of insertion and retrieval.

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REHASHING

If the hash function produces a collision, the hash value is usedas the input to rehash function.

In Linear probing : (hash value + 1) % array size

For rehashing with linear probing:

(Hash value + constant) % array size

constant and Array Size should be relatively prime, so that itcan cover all the odd and even digit

Quadratic Probing :

(Hash Value + i2) % Array Size Pseudo random Generator probing :

(Hash Value + random()) % Array Size

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BUCKET & CHAINING

99

..

07

06

05

04

03

02

01

00

INDEX

RECORD

10100 10100

33303 11103 22203

33306 11106 22206