Programming Algorithm

ALGORITHM

Definition:

Algorithm is defined as “a sequence of instructions designed in such a way that if the instructions are executed in the specified sequence, the desired result will be obtained”

It is also defined as “any problem whose solution can be expressed in a list of executable instruction”.

·           Set of step-by-step instructions that perform a specific task or operation

·           Natural language NOT programming language.

·           Algorithm is the sequence of steps to be performed in order to solve a problem by the computer.

·           Three reasons for using algorithms are efficiency, abstraction and reusability.

·           Algorithms can be expressed in many different notations, including natural languages, pseudocode, flowcharts and programming languages.

·           Analysis of algorithms is the theoretical study of computer program performance and resource usage, and is often practiced abstractly without the use of specific programming language or implementation.

·           The practical goal of algorithm analysis is to predict the performance of different algorithms in order to guide program  design decisions.

·           Most algorithms do not perform the same in all cases; normally an algorithm’s performance varies with the  data passed to it.

·           Typically, three cases  are recognized: the best case, average case and worst case Worst case analysis of algorithms is considered to be crucial to applications such as games, finance and robotics.

·           O-notation, also known as Big O-notation, is the most common notation used to express an algorithm’s performance in formal manner.

Characteristics of algorithm

1.  In the algorithm each and every instruction should be precise and unambiguous.

2.        The instruction in an algorithm should not be repeated infinitely.

3.        Ensure that the algorithm will ultimately terminate.

4.        The algorithm should be written in sequence.

5.        It looks like normal English.

6.        The desired result should be obtained only after the algorithm terminates.

Qualities of a good algorithm

Time - Lesser time required.

Memory  - Less memory required.

Accuracy - Suitable or correct solution obtained.

Sequence - Must be sequence and some instruction may be repeated in number of times or until particular condition is met.

Generability - Used to solve single problem and more often algorithms are designed to handle a range of input data.

Examples of algorithm

Problem 1: Find the area of a Circle of radius r.

Inputs to the algorithm:

Radius r of the Circle.

Expected output:

Area of the Circle

Algorithm:

Step 1: Start

Step2: Read input the Radius r of the Circle

Step3: Area ←PI*r*r // calculation of area

Step4: Print Area

Step 5: Stop

Problem2: Write an algorithm to read two numb rs and find th ir sum.

Inputs to the algorithm:

First num1.

Second num2.

Expected output:

Sum of the two numbers.

Algorithm:

Step1: Start

Step2: Read\input the first num1.

Step3: Read\input the second num2.

Step4: Sum← num1+num2 // c lcul tion of sum

Step5: Print Sum

Step6: Stop

Problem 3: Convert temperature Fahrenheit to Celsius

Inputs to the algorithm:

Temperature in Fahrenheit

Expected output:

Temperature in Celsius

Algorithm:

Step1: Start

Step 2: Read Temperature in Fahrenheit F

Step 3: C ← 5/9*(F-32)

Step 4: Print Temperature in Celsius: C

Step5: End

Problem 4: Find the largest number between A and B

Inputs to the algorithm:

A, B

Expected output:

Largest A or B

Algorithm:

Step 1: Start

Step 2:Read A, B

Step 3: If A is less than B, then

Big=B

Small=A

Print A is largest

Else

Big=A

else

Step 5: Stop

Small = B  

Step 4: Write (Display) BIG, SMALL

Step 5: Stop

Problem 5: To determine student’s average grade and indicate whether successful or fail.

Step 1: Start

Step 2: Input mid-term and final

Step 3: average=(mid-term + final)/2

Step 4: if (average < 60) then

Print “FAIL”

Print “SUCCESS”

Problem 6: A algorithm to find the l rgest v lue of any three numbers.

Step1: Start

Step2: Read/input A,B and C

Step3: If (A>=B) and (A>=C) then Max=A

Step4: If (B>=A) and (B>=C) then Max=B

Step5:If (C>=A) and (C>=B) then Max=C

Step6: Print Max

Step7: End

Problem 7: An algorithm to calculate even numbers between 0 and 99.

Step 1: Start

Step 2: Read n or Initialize n=99

Step 3: Initialize i=2

Step 4: If i<=n, then goto step 5 else goto step 7

Step 5: If i%2=0, then goto step 5.1,5.2 else goto step 6

Step 5.1:Print i

Step 5.2:i=i+1 goto step 4

Step 6: i=i+1 goto step4

Step 7: Stop