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Ranchi University
**Course:
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MCA
**Specialization:
**Master of Computer Applications**Downloads:
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Introduction to Data Structures and
Algorithms
Data Structure is a way of collecting and organising data in such a way that we can perform
operations on these data in an effective way. Data Structures is about rendering data elements
in terms of some relationship, for better organization and storage. For example, we have
some data which has, player's name "Virat" and age 26. Here "Virat" is of String data type
and 26 is of integer data type.
We can organize this data as a record like Player record, which will have both player's name
and age in it. Now we can collect and store player's records in a file or database as a data
structure. For example: "Dhoni" 30, "Gambhir" 31, "Sehwag" 33
If you are aware of Object Oriented programming concepts, then a class also does the same
thing, it collects different type of data under one single entity. The only difference being, data
structures provides for techniques to access and manipulate data efficiently.
In simple language, Data Structures are structures programmed to store ordered data, so that
various operations can be performed on it easily. It represents the knowledge of data to be
organized in memory. It should be designed and implemented in such a way that it reduces
the complexity and increases the efficiency.
Basic types of Data Structures
As we have discussed above, anything that can store data can be called as a data structure,
hence Integer, Float, Boolean, Char etc, all are data structures. They are known as Primitive
Data Structures.
Then we also have some complex Data Structures, which are used to store large and
connected data. Some example of Abstract Data Structure are :
Linked List
Tree
Graph
Stack, Queue etc.
All these data structures allow us to perform different operations on data. We select these
data structures based on which type of operation is required. We will look into these data
structures in more details in our later lessons.

The data structures can also be classified on the basis of the following characteristics:
Characterstic
Description
In Linear data structures,the data items are arranged in a linear sequence.
Linear
Example: Array
In Non-Linear data structures,the data items are not in sequence. Example:
Non-Linear
Tree, Graph
In homogeneous data structures,all the elements are of same type. Example:
Homogeneous
Array
NonIn Non-Homogeneous data structure, the elements may or may not be of the
Homogeneous same type. Example: Structures
Static data structures are those whose sizes and structures associated
Static
memory locations are fixed, at compile time. Example: Array
Dynamic structures are those which expands or shrinks depending upon the
Dynamic
program need and its execution. Also, their associated memory locations
changes. Example: Linked List created using pointers
What is an Algorithm ?
An algorithm is a finite set of instructions or logic, written in order, to accomplish a certain
predefined task. Algorithm is not the complete code or program, it is just the core
logic(solution) of a problem, which can be expressed either as an informal high level
description as pseudocode or using a flowchart.
Every Algorithm must satisfy the following properties:
1. Input- There should be 0 or more inputs supplied externally to the algorithm.

2.
3.
4.
5.
Output- There should be atleast 1 output obtained.
Definiteness- Every step of the algorithm should be clear and well defined.
Finiteness- The algorithm should have finite number of steps.
Correctness- Every step of the algorithm must generate a correct output.
An algorithm is said to be efficient and fast, if it takes less time to execute and consumes less
memory space. The performance of an algorithm is measured on the basis of following
properties :
1. Time Complexity
2. Space Complexity
Space Complexity
Its the amount of memory space required by the algorithm, during the course of its execution.
Space complexity must be taken seriously for multi-user systems and in situations where
limited memory is available.
An algorithm generally requires space for following components :
Instruction Space: Its the space required to store the executable version of the
program. This space is fixed, but varies depending upon the number of lines of code
in the program.
Data Space: Its the space required to store all the constants and variables(including
temporary variables) value.
Environment Space: Its the space required to store the environment information
needed to resume the suspended function.
To learn about Space Complexity in detail, jump to the Space Complexity tutorial.
Time Complexity
Time Complexity is a way to represent the amount of time required by the program to run till
its completion. It's generally a good practice to try to keep the time required minimum, so
that our algorithm completes it's execution in the minimum time possible. We will study
about Time Complexity in details in later sections.
NOTE: Before going deep into data structure, you should have a good knowledge of
programming either in C or in C++ or Java or Python etc.

Asymptotic Notations
When it comes to analysing the complexity of any algorithm in terms of time and space, we
can never provide an exact number to define the time required and the space required by the
algorithm, instead we express it using some standard notations, also known as Asymptotic
Notations.
When we analyse any algorithm, we generally get a formula to represent the amount of time
required for execution or the time required by the computer to run the lines of code of the
algorithm, number of memory accesses, number of comparisons, temporary variables
occupying memory space etc. This formula often contains unimportant details that don't
really tell us anything about the running time.
Let us take an example, if some algorithm has a time complexity of T(n) = (n2 + 3n + 4),
which is a quadratic equation. For large values of n, the 3n + 4 part will become
insignificant compared to the n2 part.
For n = 1000, n2 will be 1000000 while 3n + 4 will be 3004.
Also, When we compare the execution times of two algorithms the constant coefficients of
higher order terms are also neglected.
An algorithm that takes a time of 200n2 will be faster than some other algorithm that takes n3
time, for any value of n larger than 200. Since we're only interested in the asymptotic
behavior of the growth of the function, the constant factor can be ignored too.
What is Asymptotic Behaviour
The word Asymptotic means approaching a value or curve arbitrarily closely (i.e., as some
sort of limit is taken).
Remember studying about Limits in High School, this is the same.
The only difference being, here we do not have to find the value of any expression where n is
approaching any finite number or infinity, but in case of Asymptotic notations, we use the
same model to ignore the constant factors and insignificant parts of an expression, to device a

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