session-1_Design_Analysis_Algorithm.pptx

Design and Analysis of Algorithm
1

Muhammad ibn Musaal -
Khwarizmi
Father of Algorithm
2

Definition:
An algorithm is a finite set of instructions that accomplishes a
particular
task.
All algorithms must satisfy the following criteria.
Characteristics:
1. Input : Zero or more quantities are externally supplied.
2. Output : At least one quantity is produced.
3. Definiteness : Each instruction is clear and unambiguous.
Statements such as “add 6 or 7 to x” is not permitted”
4. Finiteness : The algorithm should terminate after a finite number of steps.
5. Effectiveness : Instruction is basic enough to be carried out.

Algorithms that are effective and definite are called computational procedures.
Example : The operating system of a digital computer.
To achieve the criterion of definiteness algorithm are written in a programming
language.
A program is the expression of an algorithm in a programming language.

Areas for the study of algorithms:
1. How to devise an algorithm
2. How to validate an algorithm
3. How to analyze an algorithm
4. How to test a program
▪ Debugging
▪ Profiling

1. How to devise an algorithm
To design new algorithm, we apply a existing design strategy.
Some of the existing strategies are
Divide and Conquer
Greedy Method
Dynamic Programming
Back Tracking
Branch and Bound etc.
2. How to validate an algorithm
To check whether the algorithm giving correct output or not for all
possible inputs.

3. How to analyze an algorithm
Based on performance measures such as space and time
i) How much time required
ii) How much space required
4. How to test a program
▪ Debugging
▪ Profiling
Debugging is a process of executing program on sample data sets, to
determine whether any fault results occur. If so correct them.
Profiling is a process of executing a correct program on sample data sets and
determine how much time/space required by program

Representation and Structure of an Algorithm:
We can describe an algorithm in many ways.
We can use a natural language like English, but if we select this option,
we must make sure that the resulting instructions are definite.
Graphic representations called flow charts are another possibility, but
they work well only if the algorithm is small and simple.
We can also represent algorithms using pseudo code that resemble C
and Pascal.

We present most of our algorithms using pseudo code that resembles C
and Pascal.
1. Comments begin with // and continue until end of the line.
2. Blocks are indicated with matching braces: { and }.
i. A compound statement
ii. Body of a procedure.
3.
i. An identifier begins with a letter.
ii. The data types of variables are not explicitly declared.
iii. The types will be clear from the context.
iv. Whether a variable is global or local to a procedure will also be
evident
from the context.
v. We assume simple data types such as integer, float, char, boolean,
and so on.
9

4. Assignment of values to variables is done using the assignment
statement.
< variable > := < expression >
5. There are two boolean values true and false. To produce these values,
logical operators and, or and not and the relational operators <, ≤,=, ≠,
≥
and > are provided.
6. Elements of multidimensional arrays are accessed using [ and ]. For
example the (i,j)th element of the array A is denoted as A[i,j].

7. The following looping statements are used: while, for and repeat
until.
i) The general form of a while loop:
while( condition ) do
{
statement_1;
:
statement_n;
}
ii) The general form of a for loop:
for variable := value1 to value2 step step do

iii) The general form of a repeat-until loop:
repeat
<statement 1>
:
<statement n>
until ( condition )
The statements are executed as long as condition is false
8. A conditional statement has the following
forms:
• if < condition > then < statement >
• if < condition > then
< statement 1>
else
< statement 2>
9. Input and output are done using the instructions read and write.
Ex: read n;
write n;
12

10. Procedure or function starts with the word
Algorithm.
General form :
Algorithm Name( <parameter list> )
{
body
}
where Name is the name of the procedure.
Simple variables to procedures are passed by value.
Arrays and records are passed by reference

WRITE AN ALGORITHM TO FIND SUM OF N NUMBERS IN THE
GIVEN LIST
Algorithm sum(a,n)
{
s:=0;
for i:=1 to n do
s:=s+a[i];
return s;
}
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WRITE AN ALGORITHM TO FIND FACTORIAL OF A GIVEN
NUMBER.
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SAMPLE QUESTIONS
• Explain the Importance of Algorithm to Solve Real World Problems
• Summarize the Characteristics of Algorithm
• What is the difference between an algorithm and a program
• Describe the concept of recursion in algorithms. Provide an example algorithm that uses recursion
• What is an algorithm? Provide a brief definition and explain its importance in computer science.
• What is effectiveness in algorithms
• What is finiteness in algorithms
• In how many ways can we describe an algorithm
• What are the steps included in writing an algorithm
• How do we validate an algorithm
• How to Analyse an algorithm
16

session-1_Design_Analysis_Algorithm.pptx

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