Data structure

1. ABSTRACT DATA TYPES

2. INTRODUCTION
• Data items are represented within a computer
as a sequence of binary digits.
• To distinguish between the different types of
data, the term type is often used to refer to a
collection of values and the term data type to
refer to a given type along with a collection of
operations for manipulating values of the
given type.

3. • The data types known as primitives come in
two categories : simple and complex.
• Simple data types :- values that are in the
most basic forms and cannot be decomposed
into smaller parts. Ex- Integer and real types.
• Complex data types:- constructed of multiple
components consisting of simple types or
other complex types. In python objects,
strings, list and dictionaries which can contain
multiple values are all examples of complex
types.

4. ABSTRACTIONS
• An Abstractions is a mechanism for separating
the properties of an object and restricting the
focus to those relevant in the current context.
• The user of the abstractions does not have to
understand all of the details in order to utilize
the object, but only those relevant to the
current task or problem.

5. TYPES OF ABSTRACTION
• 2 TYPES:-
1.Procedural abstraction – use of
function or method knowing what it does but
ignoring how it’s accomplished.
2. Data abstraction – separation of
the properties of a data type from the
implementation of that data type.

6. ABSTRACT DATA TYPES
• An abstract data type (or ADT) is a programmer
defined data type that specifies a set of data
values and a collection of well defined operations
that can be performed on those values.
• Abstract data types are defined independent of
their implementation, allowing us to focus on the
use of the new data type instead of how it’s
implemented.
• It is a type or class object which has its own
behavior and properties.

7. • Abstract data types can be viewed like black
boxes as illustrated below

8. • It is just a class defined in a standalone
manner. The class has definitions of all the
properties and functionalities defined in it.
• Whenever the a data structure is required, the
ADT file can be imported and objects of that
class can be created and used directly.
• Abstraction means just to show the users
what they want and hide the unwanted
technical details.

9. • There are several advantages of working with
abstract data types and focusing on the
“what” instead of the “how.”
– We can focus on solving the problem at hand instead of getting
bogged down in the implementation details.
– We can reduce logical errors that can occur from accidental misuse of
storage structures and data types by preventing direct access to the
implementation.
– The implementation of the abstract data type can be changed without
having to modify the program code that uses the ADT.
– It’s easier to manage and divide larger programs into smaller modules,
allowing different members of a team to work on the separate
modules.

10. Algorithmic Complexity
• Algorithmic complexity is a very important topic in
computer science.
• Knowing the complexity of algorithms allows you to answer
questions such as
 How long will a program run on an input?
 How much space will it take?
 Is the problem solvable?
• These are important bases of comparison between different
algorithms.
• An understanding of algorithmic complexity provides
programmers with insight into the efficiency of their code.
• Complexity is also important to several theoretical areas in
computer science, including algorithms, data structures, and
complexity theory

11. COMPLEXITY
• Any algorithm should have a way to measure
it.
• The standardized way of comparing
algorithms is complexity.
• All algorithms will have two complexities:-
a. Time complexity- is the measure of running
time of an algorithm.
b. Space complexity – is the measure of total
memory used by an algorithm.

12. Average and Worst case Analysis
• Worst-case complexity: The worst
case complexity is the complexity
of an algorithm when the input is
the worst possible with respect to
complexity.
• Average complexity: The average
complexity is the complexity of an
algorithm that is averaged over all
possible inputs ( assuming a
uniform distribution over the
inputs).

13. Why Worst Case Analysis?
Worst case running time : It is the longest running time for any input of
size n. We usually concentrate on finding only the worst-case running
time, that is, the longest running time for any input of size n, because
of the following reasons:
• The worst-case running time of an algorithm gives an upper bound
on the running time for any input. Knowing it provides a guarantee
that the algorithm will never take any longer.
• For some algorithms, the worst case occurs fairly often. For
example, in searching a database for a particular piece of
information, the searching algorithm’s worst case will often occur
when the information is not present in the database.
The “average case” is often roughly as bad as the worst case.

14. Asymptotic Analysis
• Goal : to simplify the analysis of running time by
getting rid of “details” which may be affected by
specific implementation and hardware
 like “rounding” : 1,000,001 = 1,000,000
• Capturing the essence : how the running time of an
algorithm increases with the size of the input in the
limit.
 Asymptotically more efficient algorithms are best for all
but small inputs.

15. Time complexity
• Running time may vary from one processor to another,
based on their processing speed and memory.
• Based on the internal resources availability , the
running time of an algorithm may differ.
• To overcome these difficulties, asymptotic notations
were introduced.
• Time complexity gives the total runtime of an
algorithm.
• Thus when a solution is designed, every module must
be highly optimized for time complexity, in order to
prevent wastage of computer resources.

16. • The time complexity is the amount of time required by
an algorithm to execute.
• It is measured in terms of number of operations rather
than computer time; because computer time is
dependent on the hardware, processor, etc..
• Every single step of execution in a program will consume
one unit time.
• For universal standards, this unit is not assigned any
metric and computation of all the steps is done at this
basic time unit level.
Some general order that we may consider
O(c) < O(log n ) < O(n) < O(n log n) < O(nc) <O(cn) < O(n!) <O(nn),
Where c is some constant.

17. Space complexity
• The space complexity of an algorithm is the
amount of memory it needs to run to completion.
• Space complexity can be defined as : Amount of
computer memory required during the program
execution, as the function of input size.
• The difference between space complexity and
time complexity is that the spacecan be reused.