01 Introduction to analysis of Algorithms.pptx

22CS404 ANALYSIS OF ALGORITHMS
UNIT I : INTRODUCTION TO ALGORITHM ANALYSIS
Introduction to Algorithm Analysis – Notion of Time and
Space Complexity – Algorithm efficiency – Asymptotic
Notations – Recurrence Relations – Solving Recurrence
equations - Iteration Method, Recurrence Tree Method
and Master’s Theorem - Mathematical analysis for
Recursive and Non-recursive algorithms - Empirical
analysis of algorithm. Brute Force Approach: General
Approach – Algorithm Analysis –Applications.

INTRODUCTION
• An algorithm is an effective method for finding out the
solution for a given problem. It is a sequence of
instruction. That conveys the method to address a
problem
• Algorithm : Step by step procedure to solve a
computational problem is called Algorithm.
or
• An Algorithm is a step-by-step plan for a
computational procedure that possibly begins with an
input and yields an output value in a finite number of
steps in order to solve a particular problem.

INTRODUCTION
• An algorithm is a set of steps of operations to solve a
problem performing calculation, data processing, and
automated reasoning tasks.
• An algorithm is an efficient method that can be
expressed within finite amount of Time and space.
• The important aspects of algorithm design include
creating an efficient algorithm to solve a problem in
an efficient way using minimum time and space.
• To solve a problem, different approaches can be
followed. Some of them can be efficient with respect
to time consumption, whereas other approaches may
be memory efficient.

Properties of Algorithm
To Evaluate An Algorithm we have to Satisfy the following
Criteria:
1. INPUT: The Algorithm should be given zero or more input.
2. OUTPUT: At least one quantity is produced. For each input the
algorithm produced value from specific task.
3. DEFINITENESS: Each instruction is clear and unambiguous.
4. FINITENESS: If we trace out the instructions of an algorithm,
then for all cases, the algorithm terminates after a finite
number of steps.
5. EFFECTIVENESS: Every instruction must very basic so that it
can be carried out, in principle, by a person using only pencil
& paper.

Difference between Algorithm, Pseudocode
and Program
Algorithm : Systematic logical approach which is a
well-defined, step-by-step procedure that allows a
computer to solve a problem.
Pseudocode : It is a simpler version of a programming
code in plain English which uses short phrases to write
code for a program before it is implemented in a specific
programming language.
Program : It is exact code written for problem following
all the rules of the programming language.

Differences
Algorithm Program
1.At design phase 1.At Implementation phase
2.Natural language 2.written in any
programming language
3.Person should have 3.Programmer
Domain knowledge
4.Analyze 4.Testing

Algorithm can be described (Represent) in four
ways.
1.Natural language like English:
When this way is chooses, care should be taken, we
should ensure that each & every statement is definite.
(no ambiguity)
2. Graphic representation called flowchart:
This method will work well when the algorithm is small&
simple.
3. Pseudo-code Method:
In this method, we should typically describe algorithms as
program, which resembles language like Pascal & Algol
(Algorithmic Language).
4.Programming Language:
we have to use programming language to write algorithms like
Algorithm Specification

How To Write an Algorithm
Step-1:start Step-1: start
Step-2:Read a,b,c Step-2: Read a,b,c
Step-3:if a>b Step-3:if a>b then go to step 4
if a>c otherwise go to step 5
print a is largest Step-4:if a>c then
else print a is largest otherwise
if b>c print c is largest
print b is largest Step-5: if b>c then
else print b is largest otherwise
print c is largest print c is largest
Step-4 : stop step-6: stop

PSEUDO-CODE CONVENTIONS
1. Comments begin with // and continue until the end of line.
2. Blocks are indicated with matching braces { and }.
3. An identifier begins with a letter. The data types of variables
are not explicitly declared.
node= record
{
data type 1 data 1;
data type n data n;
node *link;
}
4. There are two Boolean values TRUE and FALSE.
Logical Operators
AND, OR, NOT
Relational Operators
<, <=,>,>=, =, !=

5. Assignment of values to variables is done using the
assignment statement. <Variable>:= <expression>;
6. Compound data types can be formed with records. Here is an
example,
Node. Record
{
data type – 1 data-1;
.
.
.
data type – n data – n;
node * link;
}
Here link is a pointer to the record type node. Individual data
items of a record can be accessed with  and period.
PSEUDO-CODE CONVENTIONS (Cont…)

…
7. The following looping statements are employed.
For, while and repeat-until While Loop:
While < condition > do
{
<statement-1>
..
..
<statement-n>
}
For Loop:
For variable: = value-1 to value-2 step step do
{
<statement-1>
.
.
.
<statement-n>
}

repeat-until:
repeat
<statement-1>
.
.
.
<statement-n>
until<condition>
8. A conditional statement has the following forms.
 If <condition> then <statement>
 If <condition> then <statement-1>
Else <statement-1>

Case statement:
Case
{
: <condition-1> : <statement-1>
.
.
.
: <condition-n> : <statement-n>
: else : <statement-n+1>
}
9. Input and output are done using the instructions read &
write. No format is used to specify the size of input or output
quantities

10. There is only one type of procedure: Algorithm, the heading
takes the form, Algorithm Name (Parameter lists)
consider an example, the following algorithm fields &
returns the maximum of n given numbers:
1. algorithm Max(A,n)
2. // A is an array of size n
3. {
4. Result := A[1];
5. for i:= 2 to n do
6. if A[i] > Result then
7. Result :=A[i];
8. return Result;
9. }

Issue in the study of algorithm
1. How to create an algorithm.
2. How to validate an algorithm.
3. How to analyses an algorithm
4. How to test a program.

1.How to create an algorithm: To create an
algorithm we have following design technique
a) Divide & Conquer
b) Greedy method
c) Dynamic Programming
d) Branch & Bound
e) Backtracking
Issue in the study of algorithm (Cont…)

2.How to validate an algorithm:
Once an algorithm is created it is necessary to show that it
computes the correct output for all possible legal input , this
process is called algorithm validation.
3.How to analyses an algorithm:
Analysis of an algorithm or performance analysis refers to task
of determining how much computing Time & storage
algorithms required.
a) Computing time-Time complexity: Frequency or Step count
method
b) Storage space- To calculate space complexity we have to use
number of input used in algorithms.

4.How to test the program:
Program is nothing but an expression for the algorithm using
any programming language. To test a program we need
following
a) Debugging: It is processes of executing programs on sample
data sets to determine whether faulty results occur & if so
correct them.
b) Profiling or performance measurement is the process of
executing a correct program on data set and measuring the
time & space it takes to compute the result.

Need of Algorithm
1.To understand the basic idea of the problem.
2.To find an approach to solve the problem.
3.To improve the efficiency of existing techniques.
4.To understand the basic principles of designing the algorithms.
5.To compare the performance of the algorithm with respect to
other techniques.
6.It is the best method of description without describing the
implementation detail.
7.The Algorithm gives a clear description of requirements and
goal of the problem to the designer.
8.A good design can produce a good solution.
9.To understand the flow of the problem.

01 Introduction to analysis of Algorithms.pptx

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