introdution to algorithms

7/29/2019 Introdution to Algorithms

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What is Algorithm?

It is a sequence of instructions to be carried

out in order to solve a specific problem. In

designing a solution, we write step by step

procedures for solving the problem. Such

process is called algorithm. Algorithm can be

written in any language according to the

convenience of the program developer.


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To add two numbers.

Read the Value of A and B.

SUM = A+B.

Display SUM. Stop.


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To Multiply two numbers.

Read the Value of A and B.

PRODUCT = A*B.

Display PRODUCT. Stop.


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1. Start

2. sum = 0

3. Get the first number

4. Add first number to sum (sum= sum+ first number)

5. Get the second number

6. Add to sum 7. Get the third number

8. Add to sum

9. Get the Forth number

10. Add to sum

11. Get the fifth number

12. Add to sum 13. Get the sixth number

14. Add to sum

15. Output the sum


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Example : Write an algorithm to determine astudents final grade and indicate whether it ispassing or failing. The final grade is calculated asthe average of four marks.

Start Step 1: Input M1,M2,M3,M4

Step 2: GRADE (M1+M2+M3+M4)/4Step 3: if (GRADE < 50) then Print FAIL

Step 4: if (GRADE < 50) then Print PASS

Stop


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Write an algorithm and draw a flowchart to

find Greatest of three numbers.

AlgorithmStartStep1: Read A, B, C

Step2: If A > B is True, then check whether A > C,if yes then Print A is greatest otherwise C isgreatest.Step3: If A > B is False, then check whether B > C,

if yes then Print B is greatest otherwise C isgreatest.

Stop.


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characteristics of algorithm

1. Finiteness : An algorithm must terminate after a finite number of steps andfurther each steps must be executable in finite amount of time.

2. Each step of an algorithm must be precisely defined; the action to becarried out must be rigorously and unambiguously specified for each

case.

3. Input: An algorithm has zero or more, but only finite number of inputs.zero input example: ASCII chart of 0-255

4. Output: An algorithm has one or more output.

5. Effectiveness: Should be effective that means each of the operation to beperformed in an algorithm must be sufficiently basic that it can, inprinciple, be done exactly and in a finite length of time, by a person usingpencil and paper and should be computer programming languageindependent


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The Flowchart

A Flowchart

shows logic of an algorithm

emphasizes individual steps and their

interconnections

e.g. control flow from one action to the next


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INTRODUCTION FLOWCHART

The flowchart is a means of visually presenting

the flow of data, the operations performed and the

sequence in which they are performed to solve a

problem.

A flowchart is a diagrammatic representation that

represents the sequence of operations to be

performed to get the solution of a problem.Flowcharts are generally drawn in the early stages

of formulating computer solutions.


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INTRODUCTION FLOWCHART

These flowcharts play a vital role in the

programming of a problem and are quite

helpful in understanding the logic of

complicated and lengthy problems. Once the

flowchart is drawn, it becomes easy to write

the program in any high level language.

flowcharts are helpful in explaining theprogram to others.


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Flowcharts are usually drawn using

some standard symbols;

1. Start or end of the program

2. Computational steps or

processing function of a

program

3. Input or output operation

4. Decision making and

branching5. Connector or joining of two

parts of program


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Flowcharts symbols

6.Magnetic Tape

7.Magnetic Disk8.Offpageconnector

9.Flow line


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Flowchart Symbols

Basic

Oval

Parallelogram

Rectangle

Diamond

Hybrid

Name Symbol Use in Flowchart

Denotes the beginning or end of the program

Denotes an input operation

Denotes an output operation

Denotes a decision (or branch) to be made.The program should continue along one of

two routes. (e.g. IF/THEN/ELSE)

Denotes a process to be carried out

e.g. addition, subtraction, division etc.

Flow line Denotes the direction of logic flow in the program


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Example

Draw a flowchart to find the sum of first 50natural numbers.

Algorithm

Start. Initialize n and sum to zero(n=0;sum=0).

Add 1 to n(n=n+1).

Add n to sum(sum=sum+n).

Is n=50? If no go to step 3.

Print sum.

Stop.


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Advantages of Using Flowchart

Communication: Flowcharts are better way ofcommunicating the logic of a system to all concerned.

Effective analysis: With the help of flowchart, problemcan be analyzed in more effective way.

Proper documentation: Program flowcharts serve as agood program documentation, which is needed forvarious purposes.

Efficient Coding: The flowcharts act as a guide orblueprint during the systems analysis and programdevelopment phase.

Proper Debugging: The flowchart helps in debuggingprocess.


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LIMITATIONS OF USING FLOWCHARTS

Complex logic: Sometimes, the program logic

is quite complicated. In that case, flowchart

becomes complex and clumsy.

Alterations and Modifications: If alterations

are required the flowchart may require re-

drawing completely.

The essentials of what is done can easily be

lost in the technical details of how it is done.


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Example :Draw a flowchart to determine a students final

grade and indicate whether it is passing or failing. The final

grade is calculated as the average of four marks.

PRINT

PASS

Step 1: Input M1,M2,M3,M4

Step 2: GRADE (M1+M2+M3+M4)/4

Step 3: if (GRADE


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Example 3

Write an algorithm and draw a flowchart that will

read the two sides of a rectangle and calculate its

area.


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Example 3

Algorithm

Step 1: Input W,L

Step 2: A L x W

Step 3: Print A

START

Input

W, L

A L x W

PrintA

STOP


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Example 4

Write an algorithm and draw a flowchart to findGreatest of three numbers.

Algorithm

Start

Step1: Read A, B, CStep2: If A > B is True, then check whether A > C,if yes then Print A is greatest otherwise C isgreatest.

Step3: If A > B is False, then check whether B > C,if yes then Print B is greatest otherwise C isgreatest.

Stop.


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To find volume and surface area of a

cylinder

introdution to algorithms

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