Hashing (DASTAL)

8/14/2019 Hashing (DASTAL)

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Hashing


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Hashing

Hashing is the transformation of a

string of characters into a usually

shorter fixed-length value or key that

represents the original string. Hashing

is used to index and retrieve items in adatabase because it is faster to find the

item using the shorter hashed key than

to find it using the original value. It isalso used in many encryption

algorithms.


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Hash Table

Is a data structure that

associates keys with values

A small phone book as a hash table.
http://en.wikipedia.org/wiki/File:HASHTB08.svg


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Hash Table (1)

The primary operation it supports

efficiently is a lookup: given a key (a

person's name), find the corresponding

value (that person's telephone number). It

works by transforming the key using ahash function into a hash, a number that

is used as an index in an array to locate

the desired location where the values

should be.


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Hash Function

The hashing algorithm

is any well-defined procedure or

mathematical function which converts a

large, possibly variable-sized amount of

data into a small datum, usually a singleinteger that may serve as an index into an

array. The values returned by a hash

function are called hash values, hashcodes, hash sums, or simply hashes.


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Hash Function


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1.Direct Hashing The key is the address without anyalgorith-mic manipulation. The data structure must

therefore contain an element for everypossible key.

While the situations where you can use

direct hashing are limited, when it can beused it is very powerful because itguarantees that there are no synonyms.


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001 Elmer

002 Markh

005 Reymund

007 Hubert

100 Rollyn

HashFunction

005100002

5100

2

Address

Key


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2.Subtration MethodSometimes we have keys that areconsecutive but do not start from one.

Example:A company may have only 100

employees, but the employee numbersstart from 1000 and go to 1100. In this

case, we use a very simple hashing functionthat subtracts 1000 from the key todetermine the address.


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3.Digit ExtractionSelected digits are extracted from the keyand used as the address.

Example:Using six-digit employee number to

hash to a three-digit address (000-999), wecould select the first, third, and fourth

digits.

379452 = 394121267 = 112

378845 = 388=


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379452 Elmer

121267 Markh

378845 Hubert

160252 Arno045128 Rollyn

HashFunction

121267045128379452

33071

Divides the key by thearray size and usesthe remainder + 1

[001]

[006][005]

[004]

[003]

[002]

[007]

[306]

[307]

.

.

.

.

.

4.Mod division


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5.Midsquare Hashing The key is squared and the addressselected from the middle of the squarednumber.

Example:

9452 * 9452 = 89340304 : address is3403

As a variation, we can select a portion ofthe key, and then use them rather than thewhole key.

379452 : 379 * 379 = 143641 : address


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6.Folding Methods There are two folding methods that areused:

Fold Shift, the key value is divided intoparts whose size matches the size of therequired address. Then, the left and rightparts are shifted and added with the middle

part. Fold Boundary, the left and right numbers

are folded on a fixed boundary betweenthem and the center number. This resultsin a two outside values being reverse


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12

345678936

8

32

145698776

4

1

123456789

1

123

789

Discarded

123

Key

Digitsreversed

789

Digitsreversed


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Collision


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Collision

Is the event that occurs when a hashingalgorithm produce an address for aninsertion key and that address is alreadyoccupied.Home Address

The address produced by hashingalgorithm.Prime Area

The memory that contains all of the homeaddresses.

Probe Calculation of address and test for success.


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[1] [5] [9] [17]

1. hash(A)

2. hash(B) 3. hash(C)

B & ACollides C & B

Collides

A BC


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Collision Resolution

The process of finding alternate location

Collision strategy techniques:

Separate chaining

Open addressing

Coalesced hashing

Perfect hashing Dynamic perfect hashing

Probabilistic hashing

Robin hood hashing

Cache-conscious collision resolution


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Separate Chaining

Sometimes called simply

chaining or direct chaining, inits simplest form each slot in the

array is a linked list, or the

head cell of a linked list, where

the list contains the elements

that hashed to the samelocation. Insertion requires

finding the correct slot, then

appending to either end of the

list in that slot
http://en.wikipedia.org/wiki/File:HASHTB32.svg


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Open Addressing

Open addressing hash tables store the records directly

within the array. This approach is also called closedhashing. A hash collision is resolved byprobing, or

searching through alternate locations in the array

(following aprobe sequence) until either the target record

is found, or an unused array slot is found, which indicatesthat there is no such key in the table.


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379452 Elmer

121267 Markh

378845 Hubert

160252 Arno

045128 Rollyn

HashFunction

070918

166702

Collision is resolvedby adding one(1) tothe current address

[001]

[006]

[005]

[004]

[003]

[002]

[007]

[306]

[307]

.

.

.

.

.Linear Probing

070918 Redjie

166702 Reymund


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Quadratic ProbingThe increment is the collision probe number

squared.

Probe Collision Probe2 and New

Num Location Increment Address

1 1 12 = 1 12 2 22 = 4 3

3 6 32

= 9 54 15 42 = 16 75 31 52 = 25 96 56 62 = 36 11


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Key OffsetIs a double hashing method that produces

different collision path for different keys.

Formula:

offset = (key / listsize)adress = ((offset + old address) modulo

listsize) + 1

For example if the key is 166702 and thelistsize is 307, using the modulo division

offset = (166702 / 307) = 543

address = ((543 + 002) modulo 307) + 1= 239


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379452 Elmer

070918 Redjie

121267 Markh

378845 Hubert

160252 Arno

045128 Rollyn

[001]

[006]

[005]

[004]

[003]

[002]

[007]

[306]

[307]

.

.

.

.

.

166702 Reymund

572556 Angelus


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H h lli i l d b li bi (i t l 1)
http://en.wikipedia.org/wiki/File:HASHTB12.svghttp://en.wikipedia.org/wiki/File:HASHTB12.svghttp://en.wikipedia.org/wiki/File:HASHTB12.svg

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Hashing (DASTAL)