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Tafelia Technical
university
TTU

*Hash table or hash map is a data
structure that uses a hash function to
map identifying values, known as
keys(e.g., a person's name), to their
associated values (e.g., their telephone
number).
*The hash function is used to transform
hash)
the key into the index (the hash) of an
array element (the slot or bucket) where
bucket)
the corresponding value is to be sought.

Ideally, the hash function should map each
possible key to a unique slot index, but this ideal
is rarely achievable in practice (unless the hash
keys are fixed .

HASH TABLE TYPES
There are two types of Hash Tables: Open-addressed Hash Tables and Separate-
Open- Separate-
Tables.
Chained Hash Tables
An Open-addressed Hash Table is a one-dimensional array indexed by
Open-
integer values that are computed by an index function called a hash function
function.
A Separate-Chained Hash Table is a one-dimensional array of linked lists indexed by
Separate-
integer values that are computed by an index function called a hash function
function.
Hash tables are sometimes referred to as scatter tables
tables.”chain”.
Typical hash table operations are:

Initialization.
— Initialization.
— Insertion.
Insertion.
— Searching
Deletion.
— Deletion.

Separate chained hash table
• Linked list at each table location
• The table entries are pointers to list
heads

There are two types of hashing :
1. Static hashing: In static hashing, the hash function
maps search-key values to a fixed set of locations.
2. Dynamic hashing: In dynamic hashing a hash table
can grow to handle more items. The associated hash
function must change as the table grows.

The load factor of a hash table is the ratio of the number of
keys in the table to the size of the hash table.

The higher the load factor, the slower the retrieval.

With open addressing, the load factor cannot exceed 1. With chaining, the load
factor often exceeds 1.

hash function
f:
index = f(key, arrayLength) The hash function calculates
an index within the array from the data key.
arrayLength is the size of the array. For assembly
language or other low-level programs, a trivial hash
function can often create an index with just one or two
inline machine instructions

A hash function h, is a function which transforms a
function,
key from a set, K, into an index in a table of size n:
h: K -> {0, 1, ..., n-2, n-1}
{0 n- n-
A key can be a number, a string, a record etc.
The size of the set of keys, |K| to be relatively very
|K|,
large.
It is possible for different keys to hash to the same
array location.
This situation is called collision and the colliding keys
are called synonyms.

A good hash function should:

— Minimize collisions.

— Be easy and quick to compute.

— Distribute key values evenly in the hash table.

— Use all the information provided in the key.

1. Division Remainder (using the table size as the divisor)

Computes hash value from key using the % operator.

Table size that is a power of 2 like 32 and 1024 should be avoided,
for it leads to more collisions.
Prime numbers not close to powers of 2 are better table size values.

h(key) = key mod size
(remainder of key divided by size)
where size is the table size m

2. Folding

It involves splitting keys into two or more parts and then
combining the parts to form the hash addresses.
To map the key 25936715 to a range between 0 and 9999, we
can:
— split the number into two as 2593 and 6715 and
— add these two to obtain 9308 as the hash value.
Very useful if we have keys that are very large.
A great advantage is ability to transform non-integer keys into
integer values.

2. Truncation or Digit/Character Extraction

Works based on the distribution of digits or
characters in the key.
If search key is string we first convert it to
integer”ASCLL” then use hash table
H(“note”)=78+79+84+69

Advantages
The main advantage of hash tables
over other table data structures is
speed. This advantage is more
apparent when the number of entries
is large (thousands or more.

HASH TABLE APPLICATIONS
Database systems
Symbol tables The tables used by compilers to maintain information
tables:
about symbols from a program.

Data dictionaries Data structures that support adding, deleting, and
dictionaries:
searching for data. Although the operations of a hash table and a data
dictionary are similar, other data structures may be used to implement
data dictionaries. Using a hash table is particularly efficient.

Network processing algorithms Hash tables are fundamental
algorithms:
components of several network processing algorithms and applications,
including route lookup, packet classification, and network monitoring.

EXAMPLE
Suppose that we want to store 10,000 students records
(each with a 5-digit ID) in a given containerThe id
field in this class can be used as a search key for
records in the container.

class StudentRecord {
String name; // Student name
double height; // Student height
long id; // Unique id
}

Example 1: Introduction to Hashing
Name ID h(r) = id % 13
Al-Otaibi, Ziyad 985926 6
Al-Turki, Musab Ahmad Bakeer 970876 10
Al-Saegh, Radha Mahdi 980962 8
Al-Shahrani, Adel Saad 986074 11
Al-Awami, Louai Adnan Muhammad 970728 5
Al-Amer, Yousuf Jauwad 994593 2
Al-Helal, Husain Ali AbdulMohsen 996321 1

0 1 2 3 4 5 6 7 8 9 10 11 12

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