The document discusses data structures and their operations. It defines data structures as the logical organization of data and divides them into linear and non-linear structures. Linear structures include arrays, linked lists, stacks, and queues which store elements sequentially. Non-linear structures include trees and graphs which have indirect relationships between elements. Common operations on data structures include traversing, searching, insertion, deletion, sorting, and merging. The complexity of algorithms is also discussed in terms of time and space requirements. Elementary data organization involves grouping data into items, records, and files to structure information.

1. Chapter 1
Data Structure
Data Structure :
The logical or mathematical model of a particular organization of data is called a data
structure.
Data Structure
Primitive Non-Primitive
Linear(Sequential) NonLinear(Random)
Array Tree
Stack Binary
Queue Binary
Linked List Search
Searching Graph
Insertion
Deletion
Update
Sorting

2. Data Structure are divided into two types :
1. Linear Data Structure
2. Non Linear Data Structure
1. Linear Data Structure :
The data structure in which elements are store or processed in sequential manner
is called linear data structure.
Data structure are divided in follows.
a. Linear Array:
It stores information in sequential order and allows to access it in random
order.
b. Linked List :
In which node is divided in two part. First is INFO part and second is
LINK part. INFO contains information about the given node and LINK
part contains address of the next element in the list.
Example:
START INFO LINK
1 2 3 4
FIG : Linked List.
START
INFO LINK
1 A
2
3
4
FIG: Memory representation of linked list.
c. Stack:
1 A 2 B 3 C 4 D X
1
A
D
B
C
3
0
4
2

3. A stack is also called as Last In First Out [LIFO] system.
Stack is a data structure in which element are inserted and deleted at only
one end is called Top at the stack.
Example:
3
2
TOP= 3 1 1
FIG : Stack
1 2 3 4 5 6 7 8 9
TOP=3 MAXSTK =9
FIG : Memory representation of Stack.
d. Queue:
A queue also called a First In First Out [FIFO] system.
Queue is a linear list element in which insertion can take place only at one
end is “REAR” and dilatation can take place only at one end is “FRONT”.
Example :
Queue
1 2 3 4 5 6
FRONT =1 N=6
REAR =5
FIG : Queue
C
B
A
A B C
A B C D E

4. 2. Non Linear Data Structure:
If there is a indirect relation between the different data item of an data structure
then it is called as Non Linear data structure.
There are two types
a. Tree:
The hierarchical representation of data is handle by using a data structure
is called as Tree. On which data is represent indifferent levels.
The first level of a tree is called as the root of the tree and if having the
left and right sub trees.
FIG : Tree
b. Graph:
The pictorial representation of information is called as graph. By using
graph we are able to representation the large amount of information in
small space the advantage of graph is that easy to understand.
Aurangabad
Nanded Pune
Mumbai
FIG : Graph
Root +
Left Right A B
a b c d a b dc

5.  Data Structure Operation:
Data Structure :
The logical or mathematical model of a particular organization of data is called a data
structure.
Data Structure Operation:
The data appearing in our data structures are processed by means of certain operations.
The particular data structure that one choose for a given situation depends largely on the
frequency with which specific operations are performed.
The following operations.
1. Traversing
2. Searching
3. Insertion
4. Deletion
5. Sorting
6. Merging
1. Traversing :
Visiting each and every element of data structure that operation is called
traversing.
2. Searching :
Finding the location of data item by using the given key value is called as
searching operation.
3. Insertion :
Insert the new data item in the existing data structure the operation is called as
insertion operation.
4. Deletion :
Removing and item from the data structure is called as deletion operation.
5. Sorting :
Arrange the data in same logical order it may be either ascending or descending
that operation is called as sorting operation.
Ex. NAME key, NUMBER key.

6. 6. Merging :
Combine the records of two sorted files in a single file and the resultant file is
also a sorted file then that operation is called as merging.
Ex. Copying and concatenation.
 Complexity of algorithm :
Data Structure :
The logical or mathematical model of a particular organization of data is called a data
structure.
Complexity of algorithm :
The complexity is nothing but a quality of measurement factor of an algorithm. It is a
function which text algorithm as an inputs and return the required space and execution time
of that algorithm.
The time and space these are two basic things related to represent the quality of
algorithm.
Consider R is algorithm and N is the size of the input data. The time and space use to
by the algorithm are the two main measure for the efficiency of the algorithm.
The time is measured by counting the number of operation is sorting and searching
algorithm.
Ex. The number of comprisen the space is measured by counting the maximum of
memory needed by the algorithm.
 Time Space Trade off Complexity :
The space time trade off refers to a choice between algorithmic solution of data
processing problem that allow one to decrease the running time of an algorithmic solution
by increasing the space to store the data and vice-versa.
There are divided into three case
1. Average Case
2. Best Case
3. Worst Case
1. Average Case :

7. Average case is number of comprisen are required to execute the given
algorithm.
Therefore Cn=n/2.
2. Best Case :
Small number of comprisen are required to execute the given algorithm.
3. Worst Case :
Maximum number of comprisen are required.
Therefore Cn=n.
 Elementary Data Organization :
Data Structure :
The logical or mathematical model of a particular organization of data is called a data
structure.
Elementary Data Organization :
Data are simply values or set of values. A data item refers to a single unit of values.
Data items that are divided into sub items are called group items those that are not are called
elementary items.
Example :
Student NAME may be divided into three sub items – first NAME, middle
NAME and last NAME but the social security number would normally treated as a single
item.
Collection of data are frequently organized into a hierarchy of fields records and files.
In order to make these term move precise we introduction some additional terminology.
An entity is some thing that has certain attributes or properties which may be
assigned values. The values them selves may be either number or non- numeric.
Ex. Possible attributes and their corresponding values for on entity an student of a
given organization.
Attributes : NAME AGE ROLL_NO CLASS
Values : Raj 21 4 BSC I

8. OR
 Elementary Data Organization :
Data Structure :
The logical or mathematical model of a particular organization of data is called a data
structure.
Elementary Data Organization :
Data Structure are simply values or set of values data item refers to single elementary
unit which represent our data. Data items are of two types as
1. Elementary Data Item
2. Group Data Item
The data item which consist of single values is refers as elementary data item and
the data item which consist of subparts it refers as group data item the following
example.
Ex. Possible attributes and their corresponding values for on entity an student of a given
organization.
Attributes : NAME AGE ROLL_NO CLASS
Values : Raj 21 4 BSC I
Here , in the example NAME ,AGE and ROLL_NO are the elementary data item
where as CLASS is a group data item.

9. Questions :
1. What is Data structure? Explain in detail.
2. What is elementary DS?
3. What is complexity of algorithm?
4. What is linear data structure? Explain in detail.
5. What is DS? Explain Operation of DS.
6. Short note
a. Group items.
b. Entity of elementary data structure .
c. Time space trade off complexity.