What is Algorithm-

Algorithm is a finite sequence of instructions, each of which has a clear meaning and can be performed with a finite amount of effort in a finite length of time. No matter what the input values may be, an algorithm terminates after executing a finite number of instructions.

Algorithms was developed by an Arab mathematician. It is chalked out step-by-step approach to solve a given problem. It is represented in an English like language and has some mathematical symbols like ->, >, <, = etc. To solve a given problem or to write a program you approach towards solution of the problem in a systematic, disciplined, non-adhoc, step-by-step way is called Algorithmic approach. Algorithm is a penned strategy(to write) to find a solution.

We represent an algorithm using a pseudo language that is a combination of the constructs of a programming language together with informal English statements. The ordered set of instructions required to solve a problem is known as an algorithm.

The characteristics of a good algorithm are:

·         Precision – the steps are precisely stated (defined).

·         Uniqueness – results of each step are uniquely defined and only depend on the input and the result of the preceding steps.

·         Finiteness – the algorithm stops after a finite number of instructions are executed.

·        Input – the algorithm receives input.

·         Output – the algorithm produces output.

·         Generality – the algorithm applies to a set of inputs.

Example

Algorithm/pseudo code to add two numbers

Step 1: Start

Step 2:Read the two numbers in to a,b Step 3: c=a+b

Step 4: write/print c Step 5: Stop.

Step5:Stop

 Algorithm to find out number is odd or even? 

step 1 : start

step 2 : input number

step 3 : rem=number mod 2 step 4 : if rem=0then

print "number even" else

print "number odd" endif

step 5 :stop

FLOW CHART :

A Flow chart is a Graphical representation of an Algorithm or a portion of an Algorithm. Flow charts are drawn using certain special purpose symbols such as Rectangles, Diamonds, Ovals and small circles. These symbols are connected by arrows called flow lines.

(or)

The diagrammatic representation of way to solve the given problem is called flow chart.

Flowchart is a diagrammatic representation of an algorithm. Flowchart is very helpful in writing program and explaining program to others. Symbols Used In Flowchart Different symbols are used for different states in flowchart, For example: Input/output and decision making has different symbols. The table below describes all the symbols that are used in making flowchart

The Computers are  all  around  us.  We  use  them for doing various tasks in a faster and more accurate manner. For example, using a computer or smartphone, we can book train tickets online.

India is a big country and we have an enormous railway network. Thus, railway reservation is a complex task. Making reservation involves information about many aspects, such as details of trains (train type, types of berth and compartments in each train, their schedule, etc.), simultaneous booking of tickets by multiple users and many other related factors.

It is only due to the use of computers that today, the booking of the train tickets has become easy. Online booking of train tickets has added to our comfort by enabling us to book tickets from anywhere, anytime.

We usually use the term computerisation to indicate the use of computer to develop software in order to automate any routine human task efficiently. Computers are used  for  solving  various  day-to-day  problems and thus problem solving is an essential skill that a computer science student should know. It is pertinent to mention that computers themselves cannot solve a problem. Precise step-by-step instructions should be given by us to solve the problem. Thus, the success of a computer in solving a problem depends on how correctly and precisely we define the problem, design a solution (algorithm) and implement the solution (program) using a programming language. Thus, problem solving is the process of identifying a problem, developing an algorithm for the identified problem and finally implementing the algorithm to develop a computer program 

When problems are straightforward and easy, we can easily find the solution. But a complex problem requires a  methodical  approach  to find the right solution. In other words, we have to apply problem solving techniques. Problem solving begins with the precise identification of the problem and ends with a complete working solution in terms of  a  program  or  software. Key steps required for solving a problem using a computer.

1.   Analysing the problem

It is important to clearly understand a problem before we begin to find the solution for it. If we are not clear as to what is to be solved, we may end up developing a program which may not  solve  our  purpose.  Thus, we need to read and analyse the problem statement carefully in order to list the principal components of the problem and decide the core functionalities that our solution should have. By analysing a problem, we would be able to figure out what are the inputs that our program should accept and the outputs that it should produce.

2.   Developing an Algorithm

It is essential to device a solution before writing a program code for a given problem. The solution is represented in natural language and is called an algorithm. We can imagine an algorithm like a very well-written recipe for a dish, with clearly defined steps that, if followed, one will end up preparing the dish. We  start  with  a  tentative  solution  plan  and  keep on refining the algorithm  until  the  algorithm  is  able to capture  all  the  aspects  of  the  desired  solution.  For a given problem, more than one algorithm  is  possible and we have to select the most suitable solution. 

1   Coding

After finalising the algorithm, we need to convert the algorithm into the format which can be understood by the computer to generate the desired solution. Different high level programming languages can be used  for writing a program.

It is equally important to record the details of the coding procedures followed and document the solution. This is helpful when revisiting the programs at a later stage. 

2. Testing and Debugging

The program created should be tested on various parameters. The program should meet the requirements of the user. It must respond within the expected time. It should generate correct output  for  all  possible  inputs. In the presence of syntactical errors, no output will be obtained. In case the output generated is incorrect, then the program should be checked for logical errors, if any. Software                 industry follows standardised testing methods like unit or component testing, integration testing, system testing, and acceptance testing while developing complex  applications.  This  is  to  ensure that the software meets all the business and technical requirements and works as expected. The errors or defects found in the testing phases are debugged or rectified and the program is again tested. This continue still all the errors are removed from the program. Once the software application has been developed, tested and delivered to the user, still problems in terms of functioning can come up and need to be resolved from time to time. The maintenance of the solution, thus, involves fixing the problems faced by the user, nswering the queries of the user and even serving the request for addition or modification of features.

 ALGORITHM

In our day-to-day life we perform activities by following certain sequence of steps. Examples of activities include getting ready for school, making breakfast, riding a bicycle, wearing a tie, solving a puzzle and so on. To complete each activity, we follow a sequence of steps. Suppose following are the steps required for an activity ‘riding a bicycle’:

1)        remove the bicycle from the stand,

2)        sit on the seat of the bicycle,

3)        start peddling,

4)        use breaks whenever needed and

5)        stop on reaching the destination.

Let us now find Greatest Common Divisor (GCD) of two numbers 45 and 54.

Note: GCD is the largest number that divides both the given numbers.

Step 1: Find the numbers (divisors) which can divide the given numbers

Divisors of 45 are: 1, 3, 5, 9, 15, and 45

Divisors of 54 are: 1, 2, 3, 6, 9, 18, 27,

and 54

Step 2: Then find the largest common number from these two lists.

Therefore, GCD of 45 and 54 is 9

Hence, it is clear that we need to follow a sequence of steps to accomplish the task. Such a finite sequence

of  steps  required  to  get  the  desired  output  is  called an algorithm. It will lead to the desired result in a finite amount of time, if followed correctly. Algorithm has a definite beginning and a definite end, and consists of a finite number of steps.

1   Why do we need an Algorithm?

A programmer writes a program to instruct the computer to do certain tasks as desired. The computer then follows the steps written in the program code. Therefore, the programmer first prepares a  roadmap  of  the  program to be written, before actually writing the code. Without a roadmap, the programmer may not be able to clearly visualize the instructions to be written and may end up developing a program which may not work as expected. Such a roadmap is nothing but the algorithm which is the building block of a computer program. For example, searching using a search engine, sending a message, finding a word in a document, booking a taxi through an app, performing online banking, playing computer

games, all are based on algorithms.

Writing an algorithm is mostly considered as a first step to programming. Once we have an algorithm to solve a problem, we can write the computer program for giving instructions to the computer in high level language. If the algorithm is correct, computer will run the program correctly, every time. So, the purpose of using an algorithm is to increase the reliability, accuracy and efficiency of obtaining solutions.

(A) Characteristics of a good algorithm

•   Precision — the steps are precisely stated or defined.

•   Uniqueness — results of each step are uniquely defined and only depend on the input and the result of the preceding steps.

•   Finiteness —  the  algorithm  always  stops  after  a

finite number of steps.

•   Input — the algorithm receives some input.

•   Output — the algorithm produces some output.

(B)     While writing an algorithm, it is required to clearly identify the following:

•   The input to be taken from the user

•   Processing or  computation to be  performed to get the desired result

•   The output desired by the user

4.1   REPRESENTATION OF ALGORITHMS

Using their algorithmic thinking skills, the software designers or programmers analyse the problem and identify the logical steps that need to be followed to reach a solution. Once the steps are identified, the need is to write down these steps along with the  required  input and desired output. There are two common methods of representing an algorithm —flowchart and pseudocode. Either of the methods can be used to represent an algorithm while keeping in mind the following:

   •   it showcases the logic of the problem solution, excluding any implementational details

•   it clearly reveals the flow of control during execution of the program

1 Flowchart — Visual Representation of Algorithms

A flowchart is  a  visual  representation  of  an  algorithm. A flowchart is a diagram made up of boxes, diamonds and other shapes, connected by arrows. Each shape represents a step of the solution process and the arrow represents the order or link among the steps. There are standardized symbols to draw flowcharts.