This document provides an outline and overview of hashing and hash tables. It defines hashing as a technique for storing data to allow for fast insertion, retrieval, and deletion. A hash table uses an array and hash function to map keys to array indices. Collision resolution techniques like linear probing are discussed. The document also summarizes the Hashtable class in .NET, which uses buckets and load factor to avoid collisions. Examples of hash functions and using the Hashtable class are provided.

1. DATA STRUCTURE
Chapter 10: Hashing & hash
table
Prepared & Presented by
Mr. Mahmoud R. Alfarra
2011-2012
College of Science & Technology
Dep. Of Computer Science & IT
BCs of Information Technology
http://mfarra.cst.ps

2. Out Line
 Introduction
 What is hashing?
 What is a hash function?
 Example: Hash function
 The Hashtable class
2

3. Introduction
 Hashing is a very common technique for storing
data in such a way the data can be inserted,
retrieved and deleted very quickly.
 Hashing uses a data structure called a hash
table.
 Operations that involve searching, such as
finding the minimum or maximum value, are not
performed very quickly. For these types of
operations, Binary search tree is preferred.
 The .NET Framework library provides a very
useful class for working with hash tables, the
3

4. What is hashing?
4
 A hash table data structure is designed around
an array. The array consists of elements 0
through some predetermined size, though we
can increase the size later if necessary.
 Each data item is stored in the array based on
some piece of the data, called the key.
 To store an element in the hash table, the key
is mapped into a number in the range of 0 to
the hash table size using a function called a
hash function.

5. What is hashing?
5

6. What is hashing?
6
Given a student ID find the record (entry)
Keys

7. What is a hash function?
7
Presented & Prepared by: Mahmoud R. Alfarra
Choosing a hash function depends on the data
type of the key you are using.
If your key is an integer, the simplest function is to
return the key modulo the size of the array.
f(k) = k%size
f(4) = 4%10 = 4

8. What is a hash function?
8
Presented & Prepared by: Mahmoud R. Alfarra
A hash table supports
 fast retrieval O(1)
 fast deletion O(1)
 fast insertion O(1)

9. Hash method works something like this
zzzzzzzz
Domain: "!" .. "zzzzzzzz" Range: 0 ... 9996
hash(key)
AAAAAAAA 8482
hash(key)
1273
Convert a String key into an integer that will be in the
range of 0 through the maximum capacity-1
Assume the array capacity is 9997

10. Hash method
 What if the ASCII value of individual chars of the
string key added up to a number from ("A") 65 to
possibly 488 ("zzzz") 4 chars max
 If the array has size = 309, mod the sum
390 % TABLE_SIZE = 81
394 % TABLE_SIZE = 85
404 % TABLE_SIZE = 95
 These array indices store these keys
81
85
95
abba
abcd
able

11. Example: hash function using string
11
Presented & Prepared by: Mahmoud R. Alfarra
Could use String keys each ASCII character equals
some unique integer
"able" = 97 + 98 + 108 + 101 == 404

12. 81
82
83
84
85
86
308
A hash table after three insertions
Using the too simple hash code method
"abba"
Keys
80
...
0
Insert objects
with these three
keys:
"abba"
"abcd"
"abce"
...
"abcd"
"abce"

13. Collision occurs while inserting "baab"
can't insert "baab"
where it hashes to
same slot as
"abba"
Linear probe
forward by 1,
inserting it
at the next
available slot
"baab"
Try [81]
Put in [82]
81
82
83
84
85
86
308
"abba"
80
...
0
...
"abcd"
"abce"
"baab"

14. Wrap around when collision occurs at end
Insert
"KLMP"
"IKLT"
both of
which have
a hash
value of
308
81
82
83
84
85
86
308
"abba"
80
...
0
...
"abcd"
"abce"
"baab"
"KLMP"
"IKLT"

15. Find object with key (baab)
81
82
83
84
85
86
308
"abba"
80
...
0
...
"abcd"
"abce"
"baab"
"KLMP"
"IKLT"
"baab" still
hashes to 81,
but since [81]
does not hold
it, linear probe
to [82]
At this point,
you could
return a
reference to it
or remove it

16. The Hashtable class
16
‫البيانات‬ ‫تراكيب‬ ‫مساق‬
‫إعداد‬ ‫العلمية‬ ‫المادة‬
/
‫أ‬
.
‫ا‬ َّ‫الفــر‬ ‫رفيق‬ ‫محمود‬
 The Hashtable class is a special type of
Dictionary object, storing key–value pairs,
where the values are stored based on the
hash code derived from the key.
 The strategy the class uses to avoid collisions
is the concept of a bucket.

17. The Hashtable class
17
‫البيانات‬ ‫تراكيب‬ ‫مساق‬
‫إعداد‬ ‫العلمية‬ ‫المادة‬
/
‫أ‬
.
‫ا‬ َّ‫الفــر‬ ‫رفيق‬ ‫محمود‬
 A bucket is a virtual grouping of objects
together that have the same hash code.
 If two keys have the same hash code, they are
placed in the same bucket.
 Otherwise, each key with a unique hash code
is placed in its own bucket.
 The number of buckets used in a Hashtable
objects is called the load factor.

18. Instantiating a Hashtable
Object
18
‫البيانات‬ ‫تراكيب‬ ‫مساق‬
‫إعداد‬ ‫العلمية‬ ‫المادة‬
/
‫أ‬
.
‫ا‬ َّ‫الفــر‬ ‫رفيق‬ ‫محمود‬
 The Hashtable class is part of the
System.Collections namespace, so you must
import System.Collections at the beginning of
your program.
 A Hashtable object can be instantiated in one
of three ways.
 You can instantiate the hash table with an
initial capacity or by using the default capacity.

19. Instantiating a Hashtable
Object
19
 The following code demonstrates how to use
these three constructors:
Hashtable symbols = new Hashtable();
HashTable symbols = new Hashtable(50);
HashTable symbols = new Hashtable(25,
3.0);
The ratio of the number of elements in the hash table to the table size is
called the load factor.
Capacity (# of elements)

20. Adding Data to a Hashtable
Object
20
‫البيانات‬ ‫تراكيب‬ ‫مساق‬
‫إعداد‬ ‫العلمية‬ ‫المادة‬
/
‫أ‬
.
‫ا‬ َّ‫الفــر‬ ‫رفيق‬ ‫محمود‬
 Key–value pairs are entered into a hash table
using the Add method.
 This method takes two arguments:
1. The key
2. The value associated with the key.
 The key is added to the hash table after
computing its hash value.

21. Adding Data to a Hashtable
Object
21
 Here is some example code:
Hashtable symbols = new Hashtable(25);
symbols.Add("salary", 100000);
symbols.Add("name", "David Durr");
symbols.Add("age", 43);
symbols.Add("dept", "Information Technology");

22. Thank You …
22
Remember that: question is the key of knowledge

23. Ahl Eljanna 
‫السموات‬ ‫عرضها‬ ‫وجنة‬ ‫ربكم‬ ‫من‬ ‫مغفرة‬ ‫إىل‬ ‫وسارعوا‬
‫للمتقني‬ ‫أعدت‬ ‫واألرض‬
23
‫ق‬ ‫سورة‬