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Hashing

• A searching technique called Hashing or Hash

addressing which is essentially independent of 

the number n.

• Hashing is used to index and retrieve items in a

database because it is faster to find the item

using the shorter hashed key than to find it using

the original value.• A bucket in a hash file is unit of storage (typically

a disk block) that can hold one or more records.

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Hash function

• Hash functions are mostly used in hash tables,

to quickly locate a data record given its search

key.

 – If element e has key k and h is hash function, then

e is stored in position h(k) of table

 – To search for e, compute h(k) to locate position. If 

no element, dictionary does not contain e.

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• Specifically, the hash function is used to map thesearch key to the index of a slot in the tablewhere the corresponding record is supposedly

stored.• What are the characteristics of a good hash

function?

 – A good hash function avoids collisions.

 – A good hash function tends to spread keys evenly inthe array.

 – A good hash function is easy to compute.

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Popular hash functions

• Division Method:

Choose the number n larger then the number

n of the keys in K. The number n is usually

chosen to be a prime number or a number

with a small number of divisors. This

frequently minimize the number of collisions.

The hash function H is defined byH(k)=k(mod m) or H(k) = (mod m)+1

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• Midsquare method:

The key k is squared then the hash function H

is defined by

H(k)=I

Where I is obtained by deleting digits from

both ends of K2 

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• Folding Method: The key K is partitioned into a number of parts k1,k2,….kr where each part except possibly the lasthas the same number of digits as the required

address. Then the parts are edit together ignoringthe last carry that isH(k) = k1+k2+…kr

Where the leading digit carries are ignored some

time for extra milling the even numbered partsk2,k4,… are each reversed before the addition. H(4502) = 54+20 = 74

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There are 2 broad kinds of hashing,

open hashing, and closed hashing.

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1. Open Hashing

• Each bucket in the hash table is the head of a

linked list

• All elements that hash to a particular bucket

are placed on that bucket’s linked list 

• Records within a bucket can be ordered in

several ways

 – by order of insertion, by key value order, or by

frequency of access order

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Example

0

1

2

3

4

D-1

...

...

...

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Example

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2. Closed Hashing

• A closed hash table keeps the members of the

set in the bucket table rather than using that

table to store list headers.

• only one element is in any bucket.

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Collision

• Multiple keys can hash to the same slot

0

m –1 

h(k 1) 

h(k 4) 

h(k 2)=h(k 5)

h(k 3) 

U 

(universe of keys) 

K 

(actual

keys)

k 1

k 2

k 3

k 5

k 4collision

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14

Collision Resolution Techniques

• There are two broad ways of collision resolution:

1. Separate Chaining: An array of linked list implementation.

2. Open Addressing: Array-based implementation.

(i) Linear probing (linear search)

(ii) Quadratic probing (nonlinear search)

(iii) Double hashing (uses two hash functions)

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Collision Resolution by Chaining

k 2

0

m –1 

U 

(universe of keys) 

K 

(actual

keys)

k 1

k 2

k 3

k 5

k 4

k 6

k 7k 8

k 1 k 4

k 5 k 6

k 7 k 3

k 8

The hash table is implemented as an array of linked lists.

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Open addressing

• A method in which a hash collision is resolved by

probing, or searching through alternate locations

in the array (the probe sequence) until either the

target record is found.

• Linear probing is a scheme in computer

programming for resolving hash collisions of 

values of hash functions by sequentially searchingthe hash table for a free location

 – newLocation = (startingValue + stepSize) % arraySize

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• Quadratic probing operates by taking the

original hash value and adding successive

values of an arbitrary quadratic polynomial to

the starting value.

• Double hashing here second hash function is

used.