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Hashing
1. ANJUMAN COLLEGE
OF ENGINEERING AND
TECHNOLOGY,
SADAR, NAGPUR.
DATA STRUCTURE AND PROGRAM
DESIGN
2017-18
Computer science and
Engineering
Seminar on:
Hashing
Guided by: Prof. Farhina Sheikh
6. HASHING
Hashing is the process of indexing and
retrieving element (data) in a data structure to
provide faster way of finding the element
using the hash key.
In hashing time required to search an element
doesn’t depend on the number of element.
Using hashing data structure, an element is
searched with constant time complexity.
Hashing provides very fast access to records
on certain search conditions.
7. HASH FUNCTION
A hash function is a function which
takes a piece of data (i.e. key) as input
and outputs an integer (i.e. hash value)
which maps the data to a particular
index in the hash table.
8. CHARACTERISTICS OF
HASH FUNCTION
It should be easy and quick to
compute.
It should ideally be mathematically
one-to-one the set of relevant key
values.
The number of collision should be less
while placing the records in the hash
table.
It should achieve even distribution of
the key values that actually occur across
9. HASH TABLE
Hash Table also known as Hash Map is a
data structure which uses hash function
to generate key corresponding to the
associated value.
It is a tables from which an item can be
searched in o(1) time using a hash
function to form address from the key
10. STATIC HASHING
Primary Area: # primary pages fixed, allocated
sequentially, never deallocated; (say M buckets).
•A simple hash function: h(K) = f(K) mod M
Overflow area: disjoint from the primary area. It
keeps buckets which hold records whose key
maps to full bucket.
•Adding the address of an overflow bucket to a
primary area bucket is called chaining.
Collision does not cause a problem as long as
there is still room in the mapped bucket.
Overflow occurs during insertion when a record is
hashed to the bucket that is already full.
11. EXAMPLE
Assume f(k) = k. Let M = 5. So, h(k) = k mod
5
Bucket factor = 3 records
0 35 60
1 6 46
2 12 57 62
3 33
4 44
17
12. PROBLEMS OF STATIC
HASHING
The main problem with static hashing: the number
of buckets is fixed:
• Long overflow chains can develop and degrade
performance.
• On the other hand, if a file shrinks greatly, a lot of
bucket space will be wasted.
There are some other hashing techniques that
allow dynamically growing and shrinking hash
index. These include:
• Linear hashing
• Extendible hashing
14. DIVISION METHOD
In this method, we choose a number m (i.e.,
memory locations) larger than the number of n
(i.e. number of records) of keys which uniquely
determine records). The number of usually
chosen to be a prime number or a number
without small divisors since this frequently
minimizes the number of The hash function H is
defined by:
H(K)=K(mod m)
Here K (mod m) denotes the remainder when K
is divided by m. The second formula is used
15. For example, a company has 68 employees and
they have been assigned 4-digit employee
number. Assume L (memory addresses in the
table) of 100 two digit addresses: 00, 01, 02...99.
Applying the above hash function, say, for
employee numbers:
3205, 7148, 2345
Here, we choose a prime number m close to 99,
such as 97 then
H (3205) = 4
H (7148) = 67
H(2345) = 17
16. That is, dividing 3205 by 97 gives a
remainder of 4, dividing 7148 by 97 gives a
remainder of 67 and dividing 2345 by 97
gives a remainder of 17. In the other case
where the memory addresses begin with 01
rather than 00, we choose the hash function:
H(3205) = 4+1=5
H(7148) = 67+1=68
H(2345) = 17+1=18
17. Ques:- Given following list of element
{63, 92, 84, 33, 90, 69, 97, 91}
Use Division method of hashing to sort the
hashing.
Solution:-
Formula :-
• h(k) = k mode m
Given,
k= keys element.
• The keys element is:
63 92 84 33 90 69 97 91
m= Total no of Buckets.
• Total no of Buckets is 8 because we have 8
