Chapter 1 Raptor

8/10/2019 Chapter 1 Raptor

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MT 512: Programming Design Page no: 1

1.INTRODUCTION AND OVERVIEW

1.1COMPUTER ORGANIZATION

A computer, in short, is an information processor. Data and information can be enteredinto the computer as inputand then processed to produce output(see Figure 1.1)

Input Computer Output

Figure 1.1: Structure of a Computer

The physical components of a computer together with devices that perform the input andoutput are referred to as hardware. A set of computer instruction performed by thecomputer is called a computer program. A significant part of this course deals with

problem solving and how to design computer programs. The set of programs written for a

computer is referred to as software.

Functional Components of a computer

Generally, Computer hardware is divided into four main functional areas. These are Inputdevices, Output devices, Central Processing Unit (CPU) and Memory, see Figure 1.2

below.

INPUT

CONTROLUNIT

ALU

MEMORY

OUTPUT

Figure 1.2: Basic structure of a computer


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1. Input Devices:Allows getting data into the computer. A simple example of input device is keyboard.

2. Output devices:Shows the result after processing data or information.

3. Central Processing Unit (CPU)It is electronic circuit that manipulates data into the required information. That is,

CPU executes the computer instruction. It consists of two parts, Arithmetic LogicUnit (ALU) and Control Unit (CU).

- Arithmetic Logic UnitIt the Brain of the computer system, i.e., performs the most important operation

of the computer system arithmetic and logic operation on the data.

- Control UnitDirects and coordinates the execution of stored program instruction.

4. MemoryThere are two kinds of computer memory: primaryand secondary. Primary memory

is accessible directly by the processing unit. Random Access Memory (RAM) is an

example of primary memory. As soon as the computer is switched off the contents ofthe primary memory is lost. You can store and retrieve data much faster with primary

memory compared to secondary memory. Secondary memory is used to store datapermanently. An example of this type of memory includes floppy disks, magnetic

disk. Primary memory is more expensive than secondary memory. Because of this the

size of primary memory is less than that of secondary memory.

Computer memory is used to store two things: (i) instructions to execute a program

and (ii) data. When the computer is doing any job, the data that have to be processed

are stored in the RAM. This data may come from an input device like keyboard orfrom a secondary storage device like a floppy disk.

In computer all information are stored in the form of bits. A bit is a binary digit,which is either 0 or 1. A unit of 8 bits is known as Byte.

Computer memory is expressed in terms of the number of bytes it can hold. Thenumber of bytes is expressed as kilobytes, 2 to the 10th power (2

10), or 1024 bytes.

kilobyte is abbreviated KB, or simply K. Thus, the memory of a 640K computer can

store 640 x 1024, or 655,360 bytes of data. Memory capacity is most often expressed

in terms of a megabyte (1024 x 1024), abbreviated MB. One megabyte is roughly

one million bytes. Some large computers express memory in terms of gigabytes(abbreviated GB)-billions of bytes.


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1.2 COMPUTER PROGRAMMING

1.2.1 Program

Computer is a dumb machine and it cannot do any work without instruction from the

user. It performs the instructions at tremendous speed and with accuracy. It is you to

decide what you want to do and in what sequence. So a computer cannot take its owndecision as you can. Therefore, it requires specific logically related instructions that the

developer feeds into a computer to solve a particular problem. These instructions are

termed as program.

We can acquire a program in two ways; packaged software and custom software.

Package software is a readymade set of programs while custom software is a set of

programs that a written according to the users requirements.

1.2.2 Programming Languages

What language will a programmer use to communicate with the computer? Surely not the

English language, which-like any human language-can be loose and ambiguous and full

of slang, variations, and complexities. A programming language is needed. A

programming languageis a set of rules that provides a way of telling the computer whatoperations to perform.

A programming language, the key to communicating with the computer, has certaindefinite characteristics. It has a limited vocabulary. Each word" in it has precise

meaning. Even though a programming language has limitations, it can still be used in astep-by-step fashion to solve complex problems. There is not, however, just one

programming language; there are many.

There are various kinds of programming languages used to create programs. An example

of these languages includes COBOL, BASIC, FORTRAN, C, C++, and Pascal. All

languages have a grammar of their own -known as syntaxof the language.

Programs written in any language are represented in a binary form (series of 1s and 0s) so

that the computer can execute them. Thus, all programs written in different programming

languages are translatedinto the binary code before the computer can execute them.

1.2.3 Program Specifications

Before a program is written, a detail specification must be drawn up showing exactly

what is to be done by the program. This may have already been done for the programmer

or by another more senior programmer or a system analyst. It is very important that aprogrammer should not start trying to write a computer program before a clear

specification has been created. Usually, such as a specification is in three main parts:


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a) Input: a description of the format of the input data.

b) Output: a description of the format of output data.

c) Processing: a description of the processes of the program must follow to get theoutput from the input.

1.2.4 Programming Circle

When preparing problem solutions for the computer, it is not enough just to know the

rules of a computer language. Problem-solving skills are essential to successfulprogramming. In solving a problem, developing a program requires five steps.

i. Defining the problemii. Planning the solution

iii. Coding the Programiv. Testing the Programv. Documentation

i. Defining the Problem

Analyzing system requirements, i.e., kind of input, processing, and output required.

ii. Planning the solution

To solve programming problem, one must follow a methodical approach, i.e., design anordered set if activities that will convert a given input into the desired an algorithm (An

algorithm is a step-by-step procedure to solve a given problem) for the problem. Analgorithm consists of three main components. These are input, process and output.

Algorithms implemented by a computer are known as computer programs. A programconsists of basically the following operations: -

a) Sequence- in orderb) Selection - Choosing from set (e.g., ifelse)c) Iteration RepetitionThese three operations are sufficient to describe any algorithm.

There are many approaches to planning solution, the common one are flowcharts and

pseudocode. We will discuss these approaches in incoming chapters

iii. Coding the ProgramWe need a language to express an algorithm. A computer algorithm requires a computer

language. There are many high-level languages, each with a different compiler, such asFORTRAN, COBOL, C, C++, Pascal, ADA, ALGOL, BASIC, etc.

iv. Testing the Program


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Once the program code is written, it is very unlikely that it will be perfect on the first run.

Programming errors are common in the early versions of the program. Most programmersuse the phase: desk-checking, translating and debugging.

Desk-checking: Tracing down the program code to discover any error that might be

there. Similar to proof reading and may uncover several errors.

Translating: A translator is a program that converts the code into a language, which the

computer can understand. A compiler is a translator and has in-built capabilities ofdetecting errors and produce a listing of them. These are mostly errors due to the

wrong syntax in the use of the language.

Debugging: Detecting errors (bugs) by running the program. Most of the errors in this

phase are due to the logic of the program

v. Documenting the Program

Documenting the program is a detailed description of the programming cycle and specificfacts about the program. Documenting is an on-going process needed to supplement

human memory and help organize program planning. Documentation is also critical tocommunication with other who might have an interest in your program. Typical

documentation materials include origin and nature of the problem, brief description of the

program, logic tools such as flowcharts and pseudocode, and testing results. Commentson the program code are also an important part of documentation.


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2. ALGORITHMS, FLOWCHARTS, DATA TYPES

AND PSEUDOCODE

2.1 ALGORITHMS

The term algorithmoriginally referred to any computation performed via a set of rules

applied to numbers written in decimal form. The word is derived from the phonetic

pronunciation of the last name of Abu Ja'far Mohammed ibn Musa al-Khowarizmi, whowas an Arabic mathematician who invented a set of rules for performing the four basic

arithmetic operations (addition, subtraction, multiplication and division) on decimal

numbers.

An algorithm is a representation of a solution to a problem. If a problem can be defined

as a difference between a desired situation and the current situation in which one is, then

a problem solution is a procedure, or method, for transforming the current situation to thedesired one. We solve many such trivial problems every day without even thinking about

it, for example making breakfast, travelling to the workplace etc. But the solution to such

problems requires little intellectual effort and is relatively unimportant. However, thesolution of a more interesting problem of more importance usually involves stating the

problem in an understandable form and communicating the solution to others. In the case

where a computer is part of the means of solving the problem, a procedure, explicitlystating the steps leading to the solution, must be transmitted to the computer. This

concept of problem solution and communication makes the study of algorithms important

to computer science.

Throughout history, man has thought of ever more elegant ways of reducing the amountof labour needed to do things. A computer has immense potential for saving time/energy,

as most (computational) tasks that are repetitive or can be generalised can be done by a

computer. For a computer to perform a desired task, a method for carrying out some

sequence of events, resulting in accomplishing the task, must somehow be described tothe computer. The algorithm can be described on many levels because the algorithm is

just the procedure of steps to take and get the result. The language used to describe an

algorithm to other people will be quite different from that which is used by the computer,however the actual algorithm will in essence be the same. An example of an algorithm

people use would be a recipe to make a cake.

"4 extra large eggs, beaten1&1/2 C. stock

1/2 teaspoon salt1 scallion, minced

1 C. small shrimp or lobster flakes

1 t. soy sauce

1 Tablespoon oil1. Mix all the ingredients, except the oil, in a deep bowl.


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2. Put 1" water in wide pot, then place deep bowl of batter inside.3. Cover pot tightly and steam 15 min.4. Heat oil very hot and pour over custard.5. Steam 5 more min. Serves 4 people"

This breaks down 'Making Chinese egg custard' into smaller steps. To make the productone still needs to know how to execute each of the steps in the procedure and understandall of the terms.

Definition:

A procedure is a finite sequence of well-defined instructions, each of which can be

mechanically carried out in a finite amount of time.

The procedure must break up the problem solution into parts that the recipient party can

understand and execute. In the case of a computer, the problem solution is usually in theform of a program that encompasses the algorithm and explains to the computer a clearly

defined procedure for achieving the solution. The procedure must consist of smaller steps

each of which the computers understand. There may be no ambiguities in the translationof the procedure into the necessary action to be taken. A program is then just a specific

realisation of an algorithm, which may be executed on a physical device.

A computer is essentially a physical device designed to carry out a collection of primitiveactions. A procedure is a sequence of instructions written in terms of which evoke a

proper operation. To make effective use of an algorithm on a computer one must not onlyfind and understand a solution to the problem but also convey the algorithm to the

computer, giving the correct sequence of understood commands that represent the same

algorithm.

Definition:Analgorithm is procedure consisting of a finite set of unambiguous rules (instructions)

which specify a finite sequence of operations that provides the solution to a problem, or

to a specific class of problems for any allowable set of input quantities (if there are

inputs). In other word, an algorithm is a step-by-step procedure to solve a given

problem

Alternatively, we can define an algorithm as a set or list of instructions for carrying outsome process step by step. A recipe in a cookbook is an excellent example of an

algorithm. The recipe includes the requirements for the cooking or ingredients and the

method of cooking them until you end up with a nice cooked dish.

In the same way, algorithms executed by a computer can combine millions of elementary

steps, such as additions and subtractions, into a complicated mathematical calculation.Also by means of algorithms, a computer can control a manufacturing process or co-


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ordinate the reservations of an airline as they are received from the ticket offices all overthe country. Algorithms for such large-scale processes are, of course, very complex, but

they are built up from pieces.

One of the obstacles to overcome in using a computer to solve your problems is that of

translating the idea of the algorithm to computer code (program). People cannot normallyunderstand the actual machine code that the computer needs to run a program, soprograms are written in a programming language such as C or Pascal, which is then

converted into machine code for the computer to run.

In the problem-solving phase of computer programming, you will be designing

algorithms. This means that you will have to be conscious of the strategies you use to

solve problems in order to apply them to programming problems. These algorithms can

be designed though the use of flowchartsor pseudocode.

2.2 FLOWCHARTS

Flowcharting is a tool developed in the computer industry, for showing the stepsinvolved in a process. A flowchart is a diagram made up of boxes, diamondsand other

shapes, connected by arrows- each shape represents a step in the process, and the arrows

show the order in which they occur. Flowcharting combines symbols and flowlines, to

show figuratively the operation of an algorithm.

In computing, there are dozens of different symbols used in flowcharting (there are evennational and international flowcharting symbol standards). In business process analysis, a

couple of symbols are sufficient. A box with text inside indicates a step in the process,

while a diamond with text represents a decision point. See the figure for an example.

If the flowchart is too messy to draw, try starting again, but leaving out all of the decision

points and concentrating on the simplest possible course. Then the session can go backand add the decision points later. It may also be useful to start by drawing a high-level

flowchart for the whole organisation, with each box being a complete process that has to

be filled out later.

From this common understanding can come a number of things - process improvement

ideas will often arise spontaneously during a flowcharting session. And after the session,

the facilitator can also draw up a written procedure - a flowcharting session is a good wayof documenting a process.

Process improvement starts with an understanding of the process, and flowcharting is thefirst step towards process understanding.


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Flowcharting Symbols

There are 6 basic symbols commonly used in flowcharting of assembly languageprograms: Terminal, Process, input/output, Decision, Connector and Predefined Process.

This is not a complete list of all the possible flowcharting symbols, it is the ones usedmost often in the structure of Assembly language programming.

Symbol Name Function

Process Indicates any type of internal operation

inside the Processor or Memory

input/output Used for any Input / Output (I/O) operation.Indicates that the computer is to obtain data

or output results

Decision Used to ask a question that can

be answered in a binary format (Yes/No,

True/False)

Connector Allows the flowchart to be drawn without

intersecting lines or without a reverse flow.

Predefined Process Used to invoke a subroutine or an

interrupt program.

Terminal Indicates the starting or ending of the

program, process, or interrupt program.

Flow Lines Shows direction of flow.

Generally, there are many standard flowcharting symbols.

General Rules for flowcharting

1. All boxes of the flowchart are connected with Arrows. (Not lines)2. Flowchart symbols have an entry point on the top of the symbol with no other

entry points. The exit point for all flowchart symbols is on the bottom except forthe Decision symbol.

3. The Decision symbol has two exit points; these can be on the sides or the bottomand one side.


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4. Generally a flowchart will flow from top to bottom. However, an upward flowcan be shown as long as it does not exceed 3 symbols.

5. Connectors are used to connect breaks in the flowchart. Examples are:

From one page to another page.

From the bottom of the page to the top of the same page.

An upward flow of more then 3 symbols6. Subroutines and Interrupt programs have their own and independent flowcharts.7. All flow charts start with a Terminal or Predefined Process (for interrupt

programs or subroutines) symbol.

8. All flowcharts end with a terminal or a contentious loop.

Flowcharting uses symbols that have been in use for a number of years to represent the

type of operations and/or processes being performed. The standardised format provides a

common method for people to visualise problems together in the same manner. The useof standardised symbols makes the flow charts easier to interpret, however, standardising

symbols is not as important as the sequence of activities that make up the process.

FlowchartingTips

Chart the process the way it is really occurring. Do not document the way a writtenprocess or a manager thinks the process happens.

People typically modify existing processes to enable a more efficient process. If thedesired or theoretical process is charted, problems with the existing process will not

be recognised and no improvements can be made.

Note all circumstances actually dealt with.

Test the flow chart by trying to follow the chart to perform the process charted. Ifthere is a problem performing the operation as charted, note any differences andmodify the chart to correct. A better approach would be to have someone unfamiliar

with the process try to follow the flow chart and note questions or problems found.

Include mental steps in the process such as decisions. These steps are sometimes leftout because of familiarity with the process, however, represent sources of problems

due to a possible lack of information used to make the decision can be inadequate orincorrect if performed by a different person.

Examples of Algorithms and Flowcharts

Example 1. Design an algorithm and the corresponding flowchart for adding the testscores as given below:

26, 49, 98, 87, 62, 75


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1

a) Algorithm

1. Start

2. Sum = 03. Get the first testscore4. Add first testscore to sum5. Get the second testscore6. Add to sum7. Get the third testscore8. Add to sum9. Get the Forth testscore10. Add to sum11. Get the fifth testscore12. Add to sum

13. Get the sixth testscore14. Add to sum15. Output the sum16. Stop

b) The corresponding flowchart is as follows:

Start

Sum = 0

Get first testscore

Add First testscore

To sum

Get second testscore

Add second testscore

To sum


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1

Get third testscore

Get Forth testscore

Get Fifth testscore

Get Six testscore

Output Sum

STOP

The algorithm and the flowchart above illustrate the steps for solving the problem of

adding six testscores. Where one testscore is added to sum at a time. Both the algorithm

and flowchart should always have a Start step at the beginning of the algorithm orflowchart and at least one stopstep at the end, or anywhere in the algorithm or flowchart.

Since we want the sum of six testscore, then we should have a container for the resulting

sum. In this example, the container is called sumand we make sure that sum should startwith a zero value by step 2.

Add third testscoreto sum

Add forth testscoreto sum

Add fifth testscore to sum

Add sixth testscore tosum


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Example 2:The problem with this algorithm is that, some of the steps appear more thanonce, i.e. step 5 get second number, step 7, get third number, etc. One could shorten the

algorithm or flowchart as follows:

1. Start

2. Sum = 03. Get a value4. sum = sum + value5. Go to step 3 to get next Value6. Output the sum7. Stop

Start

Get a value

STOP

This algorithm and its corresponding flowchart are a bit shorter than the first one. In this

algorithm, step 3 to 5 will be repeated, where a number is obtained and added to sum.

Similarly the flowchart indicates a flowline being drawn back to the previous stepindicating that the portion of the flowchart is being repeated. One problem indicates that

these steps will be repeated endlessly, resulting in an endless algorithm or flowchart. The

algorithm needs to be improved to eliminate this problem. In order to solve this problem,we need to add a last value to the list of numbers given. This value should be unique so

that, each time we get a value, we test the value to see if we have reached the last value.

In this way our algorithm will be a finite algorithm which ends in a finite number of steps

as shown below. There are many ways of making the algorithm finite.

The new list of numbers will be 26, 49, 498, 9387, 48962, 1, -1. The value 1 is a unique

number since all other numbers are positive.

1. Start2. Sum = 03. Get a value

Sum =

Sum = sum + value

Output


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4. If the value is equal to 1, go to step 75. Add to sum ( sum = sum + value)6. Go to step 3 to get next Value7. Output the sum8. Stop

Corresponding flowchart

START

Get a value

Value Yes

= -1

No

Output Sum

STOP

3. DATA TYPES

Although some contemporary languages allow programmers to invent his own data

types, and define their related operations, there are a number of traditional data types

found in most languages:

Integer

Integers are numeric data items, which are either positive or negative including zero, i.e.1, 488, -22, 0, 456. Some programming languages put restrictions on the magnitude of

integers which may be used in program instructions. These restrictions are usually

dependent on the size of the memory location of the computer in which the languagemay run.

Sum = 0

Sum = Sum + Value


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Real Numbers

There are two types of real numbers, Fixed-Point and Floating Point.

Fixed Point

Fixed point data items are numbers which have embedded decimal point i.e. 1.5,458.4589, -0.569.

Floating Point

Floating point data items are numbers, which are, held as binary fractions by a computer.The numbers are expressed in a form where you have a mantissa and an exponent, for

example

Number Mantissa Exponent12.3 = 0.123 * 10

2 0.123 2

123000 = 0.123 * 106 0.123 6

0.000123 =0.123 * 10

-3

0.123 -3

Floating point representation of data is used to overcome the restrictions placed on the

magnitude of numbers by the size of computers memory locations.

Character

Character data, sometimes referred to as string data, may consist of any digits, letters ofthe alphabet or symbols which, the internal coding system of the computer is capable of

representing. Many programming languages require character data to be enclosed byquotation marks when used in program instructions, for example PRINT HAPPY NEW

YEAR.

BooleanBoolean data items are used as status indicators and may contain only one of two possible

values: True or False.

DATA ITEM

There are two basic methods of using data items in a program:

a) ConstantsData items are sometimes required to keep their values throughout the program, hence theterm constant. A constant is a specific value or character string used explicitly in an

operation. Consider the constant values 47.5, 1, and 13 in the example below.

Multiply by 47.5

Add 1 to

If = 13Print PLEASE INPUT TODAYS DATE


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b) Variables and Variable names

A variable is a symbolic name assigned to a data item by the programmer. At anyparticular time, a variable will stand for one particular data, called the value of a variable,

which may change from time to time during a computing process. The value of a variablemay change many times during the execution of a program. A variable is usually given aname by the programmer.

Assignment

The assignment operation has the form:

variable := expression. (Pascal)variable = expression. (C/C++/Java)

The assignment operation is used to assign a name to a value. Thus it is used wheneveryou need to keep track of a value that is needed later. Some typical uses include:

initialize a variable ( count = 0 )

increment/decrement a counter ( count = count + 1 ) accumulate values ( sum = sum + item )

capture the result of a computation ( y = 3*x + 4 )

swap two values ( t = x; x = y; y = t )

The assignment operator is not commute i.e. x = e is not the same as e = x. The variable

must be declared. Variables used in the expression must be defined (have values). The

type of the expression must be compatible with the type of the variable.

The order in which assignments are performed is important for example, if the first andsecond assignments in the swap sequence were interchanged, x and y would end up

assigned to the same value. The input operation and the output operation share some of

the same constraints.

2.5 PSEUDOCODE

Pseudocodeis one of the tools that can be used to write a preliminary plan that can be

developed into a computer program. Pseudocode is a generic way of describing analgorithm without use of any specific programming language syntax. It is, as the namesuggests, pseudo code it cannot be executed on a real computer, but it models and

resembles real programming code, and is written at roughly the same level of detail.

Pseudocode, by nature, exists in various forms, although most borrow syntax from

popular programming languages (like C, Lisp, or FORTRAN). Natural language is used

whenever details are unimportant or distracting.


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Computer science textbooks often use pseudocode in their examples so that all

programmers can understand them, even if they do not all know the same programming

languages. Since pseudocode style varies from author to author, there is usually anaccompanying introduction explaining the syntax used.

In the algorithm design, the steps of the algorithm are written in free English text and,although brevity is desired, they may be as long as needed to describe the particular

operation. The steps of an algorithm are said to be written in pseudocode.

Many languages, such as Pascal, have a syntax that is almost identical to pseudocode and

hence make the transition from design to coding extremely easy.

The following section deal with the control structures (control constructs) Sequence,Selection and Iteration or Repetition.

CONTROL STRUCTURES OR LOGICAL STRUCTURES

The key to better algorithm design and thus to programming lies in limiting the control

structure to only three constructs. These are illustrated below:

The sequence structure

The first type of control structures is called the sequence structure. This structure is themost elementary structure. The sequence structure is a case where the steps in an

algorithm are constructed in such a way that, no condition step is required. The sequencestructure is the logical equivalent of a straight line.

For example, suppose you are required to design an algorithm for finding the average ofsix numbers, and the sum of the numbers is given. The pseudocode will be as follows

Start

Get the sum

Average = sum / 6

Output the average

Stop

The corresponding flowchart will appear as follows:


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Start

Get the sum

Output sum

Stop

Example 3: This is the pseudo-code required to input three numbers from the keyboard

and output the result.

Use variables: sum, number1, number2, number3 of type integer

Accept number1, number2, number3

Sum = number1 + number2 + number3

Print sum

End program

Example 4: The following pseudo-code describes an algorithm which will accept two

numbers from the keyboard and calculate the sum and product displaying the answer onthe monitor screen.

Use variables sum, product, number1, number2 of type real

display Input two numbers

accept number1, number2

sum = number1 + number2

print The sum is , sum

product = number1 * number2

print The Product is , product

end program

Decision Structure or Selection Structure

The decision structure or mostly commonly known as a selection structure, is case where

in the algorithm, one has to make a choice of two alternatives by making decision

depending on a given condition.

Average = sum/6


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Selection structures are also called caseselection structures when there are two or morealternatives to choose from.

This structure can be illustrated in a flowchart as follows:

True Condition False

In pseudocode form we get

If condition is true

Then do task A

else

Do Task-B

In this example, the condition is evaluated, if the condition is true Task-A is evaluated

and if it is false, then Task-B is executed.

A variation of the construct of the above figure is shown below

False

Condition

True

From the above structure, we have the following

Task-A Task-B

Task-A


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If condition is true then

Do Task-A

In this case, if condition is false, nothing happens. Otherwise Task-A is executed.

The selection requires the following Choose alternative actions as a result of testing a logical condition

Produce code to test a sequence of logical tests

Making Choices

There are many occasions where a program is required to take alternative actions. For

example, there are occasions where we need to take action according to the user choice.

All computer languages provide a means of selection. Usually it is in the form of Ifstatement and our pseudo-code is no exception to this.

We will use the if statement together with logical operators to test for true or false asshown below.

Ifa = b

print a = b

The action is only taken when the test is true.

The logical operators used in our pseudo-code are

= is equal to

> is greater than< is less than

>= is greater than or equal


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if choice = m then ans = number1 * number2

if choice = a then ans = number1 + number2

if choice = s then ans = number1 - number2

display ans

Compound Logical Operators

There are many occasions when we need to extend the conditions that are to be tested.

Often there are conditions to be linked.

In everyday language we say things likeIf I had the time and the money I would go on

holiday. Theandmeans thatboth conditions must be truebefore we take an action. We

might also sayI am happy to go to the theatre or the cinema. The logical link this time

isor. Conditions in if statements are linked in the same way. Conditions linked with andonly result in an action when all conditions are true. For example, if a >b and a > c then

display a is the largest. Conditions linked with an orlead to an action when either or

both are true.

Example 6:The program is to input a examination mark and test it for the award of a

grade. The mark is a whole number between 1 and 100. Grades are awarded according tothe following criteria:

>= 80 Distinction

>= 60 Merit>= 40 Pass

< 40 fail

The pseudo-code is

Use variables: mark of type integer

If mark >= 80 display distinction

If mark >= 60 and mark < 80 display merit

If mark >= 40 and mark < 60 display pass

If mark < 40 display fail

An if statement on its own is often not the best way of solving problems. A more elegant

set of conditions can be created by adding an elsestatement to the if statement. The else

statement is used to deal with situations as shown in the following examples.

Example 7: A person is paid at top for category 1 work otherwise pay is at normal rate.

If the work is category 1

pay-rate is top

Else

pay-rate is normal


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The else statement provides a neat way of dealing with alternative condition. In pseudo-code we write

If work = cat1 then p-rate: = top

Else p-rate = normal

OrIf work = cat1 then

p-rate: = top

Else

p-rate = normal

The following example illustrate the use of if else statements in implementing double

alternative conditions.

If salary < 50000 then

Tax = 0

ElseIf salary > 50000 AND salary < 100000 then

Tax = 50000 * 0.05

Else

Tax = 100000 * 0.30

The case statementRepeating the if else statements a number of times can be somewhat confusing. An

alternative method provided in a number of languages is to use a selector determined bythe alternative conditions that are needed. In our pseudo-code, this will called a case

statement.

Example 8: The following program segment outputs a message to the monitor screen

describing the insurance available according to a category input by the user.

Use variables: category of type character

Display input category

Accept category

If category = U

Display insurance is not available

Else

If category = A then

Display insurance is double

Else

If category = B then

Display insurance is normal

Else

If category = M then

Display insurance is medically dependent

Else

Display entry invalid


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This can be expressed in a case statement as follows:

Use variables: category of type character

Display input category

Accept category

DO case of categoryCASE category = U

Display insurance not available

CASE category = A

Display insurance is double

CASE category = B

Display insurance is normal

CASE category = M

Display insurance is medically dependent

OTHERWISE

Display entry is invalid

ENDCASEInstead of using the word otherwise, one can use else.

Repetition or Iteration Structure

A third structure causes the certain steps to be repeated.

Condition False

True

The Repetition structure can be implemented using

Repeat Until Loop The While Loop

The For Loop

Any program instruction that repeats some statement or sequence of statements a numberof times is called an iterationor a loop. The commands used to create iterations or loops

Task


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are all based on logical tests. There three constructs for iterations or loops in our pseudo-code.

The Repeat Until loop.The syntax is

REPEATA statement or block of statements

UNTIL a true condition

Example 9:A program segment repeatedly asks for entry of a number in the range 1 to100 until a valid number is entered.

REPEAT

DISPLAY Enter a number between 1 and 100

ACCEPT number

UNTIL number < 1 OR number > 100

Example 10. A survey has been carried out to discover the most popular sport. The

results will be typed into the computer for analysis. Write a program to accomplish this.

REPEAT

DISPLAY Type in the letter chosen or Q to finish

DISPLAY A: Athletics

DISPLAY S: Swimming

DISPLAY F: Football

DISPLAY B: Badminton

DISPLAY Enter data

ACCEPT letter

If letter = A then

Athletics = athletics + 1

If letter = S then

Swimming = Swimming + 1

If letter = F then

Football = Football + 1

If letter = B then

Badminton = Badminton + 1

UNTIL letter = Q

DISLAY Athletics scored, athletics, votes

DISLAY Swimming scored, swimming, votes

DISLAY Football scored, football, votes

DISLAY Badminton scored, Badminton, votes

The WHILE loopThe second type of iteration we will look at is the while iteration. This type of conditional

loop tests for terminating condition at the beginning of the loop. In this case no action isperformed at all if the first test causes the terminating condition to evaluate as false.


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The syntax isWHILE(a condition is true)

A statement or block of statements

ENDWHILE

Example 11: A program segment to print out each character typed at a keyboard until thecharacter q is entered.

WHILE letter q

ACCEPT letter

DISPLAY The character you typed is, letter

ENDWHILE

Example 12: Write a program that will output the square root of any number input until

the number input is zero.

In some cases, a variable has to be initialised before execution of the loop as shown in

the following example.

Use variable: number of type realDISPLAY Type in a number or zero to stop

ACCEPT number

WHILE number 0

Square = number * number

DISPLAY The square of the number is, square

DISPLAY Type in a number or zero to stop

ACCEPT number

ENDWHILE

The FOR LoopThe third type of iteration, which we shall use when the number of iterations is known in

advance, is a for loop. This, in its simplest form, uses an initialisation of the variable as astarting point, a stop condition depending on the value of the variable. The variable is

incremented on each iteration until it reaches the required value.

The pseudo-code syntax will be:

FOR(starting state, stopping condition, increment)

Statements

ENDFOR

Example 13.

FOR (n = 1, n


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In the example, n is usually referred as the loop variable, or counting variable, or index of

the loop. The loop variable can be used in any statement of the loop. The variable should

not be assigned a new value within the loop, which may change the behaviour of theloop.

Example 14: Write a program to calculate the sum and average of a series of numbers.The pseudo-code solution is:

Use variables: n, count of the type integer

Sum, number, average of the type real

DISPLAY How many numbers do you want to input

ACCEPT count

SUM = 0

FOR (n = 1, n


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The corresponding flowchart will be as follows:

Start

Input a number

True

I > n

False Output Sum

Stop

Exercise

1. Design an algorithm and the corresponding flowchart for finding the sum ofthe numbers 2, 4, 6, 8, , n

2. Using flowcharts, write an algorithm to read 100 numbers and then display thesum.

3. Write an algorithm to read two numbers then display the largest.4. Write an algorithm to read two numbers then display the smallest5. Write an algorithm to read three numbers then display the largest.6. Write an algorithm to read 100 numbers then display the largest.

Sum = 0

I = 1

Sum = sum + number

I = I + 1


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CHAPTER

3

ALGORITHMIC PROBLEM SOLVING

In this chapter you will learn about

What an algorithm is.

The relationship between data and algorithm.

The characteristics of an algorithm.

Using pseudo-codes and flowcharts to represent algorithms.


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32 Chapter 3 Algorithmic Problem Solving

3.1 Algorithms

In Chapter 2, we expounded the working of problem solving from a general

perspective. In computing, we focus on the type of problems categorically

known as algorithmic problems, where their solutions are expressible in the

form of algorithms.

An algorithm1is a well-defined computational procedure consisting of a

set of instructions, that takes some value or set of values, as input, and

produces some value or set of values, as output. In other word, an algorithm

is a procedure that accepts data, manipulate them following the prescribed

steps, so as to eventually fill the required unknown with the desired value(s).

AlgorithmInput Output

Tersely put, an algorithm, a jargon of computer specialists, is simply a

procedure. People of different professions have their own form of procedure

in their line of work, and they call it different names. A cook, for instance,

follows a procedure commonly known as a recipe that converts the

ingredients (input) into some culinary dish (output), after a certain number of

steps.

An algorithm, whose characteristics will be discussed later, is a form that

embeds the complete logic of the solution. Its formal written version is

called a program, or code. Thus, algorithmic problem solving actually

comes in two phases: derivation of an algorithm that solves the problem, and

conversion of the algorithm into code. The latter, usually known as coding,

is comparatively easier, since the logic is already present it is just a matter

of ensuring that the syntax rules of the programming language are adhered to.The first phase is what that stumbles most people, for two main reasons.

Firstly, it challenges the mental faculties to search for the right solution, and

secondly, it requires the ability to articulate the solution concisely into step-

by-step instructions, a skill that is acquired only through lots of practice.

Many people are able to make claims like oh yes, I know how to solve it,

but fall short when it comes to transferring the solution in their head onto

paper.

Algorithms and their alter ego, programs, are the software. The machine

that runs the programs is the hardware. Referring to the cook in our analogy

again, his view can be depicted as follows:

1The term algorithm was derived from the name of Mohammed al-Khowarizmi, a Persian mathematician in the ninth

century. Al-KhowarizmiAlgorismus (in Latin)Algorithm.


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3.1 Algorithms 33

recipe

(software)

Cooking utensils

(hardware)+

ingredients

Ah-gong

bah-kut-teh

The first documented algorithm is the famousEuclidean algorithmwritten

by the Greek mathematician Euclid in 300 B.C. in his Book VII of the

Elements. It is rumoured that King Ptolemy, having looked through the

Elements, hopefully asked Euclid if there were not a shorter way to geometry,

to which Euclid severely answered: In geometry there is no royal road!

The modern Euclidean algorithm to compute gcd (greatest common

divisor) of two integers, is often presented as followed.

1. LetAandBbe integers withA>B0.

2. IfB= 0, then the gcd isAand the algorithm ends.3. Otherwise, find qand rsuch that

A= qB+ rwhere 0 r


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3.2 Data Types And Data Structures

In algorithmic problem solving, we deal with objects. Objects are data

manipulated by the algorithm. To a cook, the objects are the various types of

vegetables, meat and sauce. In algorithms, the data are numbers, words, lists,

files, and so on. In solving a geometry problem, the data can be the length ofa rectangle, the area of a circle, etc. Algorithm provides the logic; data

provide the values. They go hand in hand. Hence, we have this great truth:

Program = Algorithm + Data Structures

Data structures refer to the types of data used and how the data are

organised in the program. Data come in different forms and types. Most

programming languages provides simple data types such as integers, real

numbers and characters, and more complex data structures such as arrays,

records and files which are collections of data.

Because algorithm manipulates data, we need to store the data objects

into variables, and give these variables names for reference. For example, inmathematics, we call the area of a circle A, and express A in terms of the

radius r. (In programming, we would use more telling variable names such as

area and radius instead of A and r in general, for the sake of readability.)

When the program is run, each variable occupies some memory location(s),

whose size depends on the data type of the variable, to hold its value.

3.3 Characteristics Of An Algorithm

What makes an algorithm an algorithm? There are four essential properties

of an algorithm.

1.

Each step of an algorithm must be exact.

This goes without saying. An algorithm must be precisely and

unambiguously described, so that there remains no uncertainty. An

instruction that says shuffle the deck of card may make sense to

some of us, but the machine will not have a clue on how to execute it,

unless the detail steps are described. An instruction that says lift the

restriction will cause much puzzlement even to the human readers.

2.

An algorithm must terminate.

The ultimate purpose of an algorithm is to solve a problem. If the

program does not stop when executed, we will not be able to get any

result from it. Therefore, an algorithm must contain a finite numberof steps in its execution. Note that an algorithm that merely contains

a finite number of steps may not terminate during execution, due to

the presence of infinite loop.


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3.3 Characteristics Of An Algorithm 35

3.

An algorithm must be effective.

Again, this goes without saying. An algorithm must provide the

correct answer to the problem.

4. An algorithm must be general.

This means that it must solve every instance of the problem. Forexample, a program that computes the area of a rectangle should work

on all possible dimensions of the rectangle, within the limits of the

programming language and the machine.

An algorithm should also emphasise on the whats, and not the hows,

leaving the details for the program version. However, this point is more

apparent in more complicated algorithms at advanced level, which we are

unlikely to encounter yet.

3.4 Pseudo-Codes And Flowcharts

We usually present algorithms in the form of some pseudo-code, which is

normally a mixture of English statements, some mathematical notations, and

selected keywords from a programming language. There is no standard

convention for writing pseudo-code; each author may have his own style, as

long as clarity is ensured.

Below are two versions of the same algorithm, one is written mainly in

English, and the other in pseudo-code. The problem concerned is to find the

minimum, maximum, and average of a list of numbers. Make a comparison.

Algorithm version 1:

First, you initialise sumto zero, minto a very big number, and maxto avery small number.

Then, you enter the numbers, one by one.

For each number that you have entered, assign it to numand add it to the

sum.

At the same time, you compare numwith min, if numis smaller than min,

let minbe numinstead.

Similarly, you compare numwith max, if numis larger than max, let max

be numinstead.

After all the numbers have been entered, you divide sumby the numbers of

items entered, and let avebe this result.

End of algorithm.


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Algorithm version 2:

sumcount0 { sum= sum of numbers;

count= how many numbers are entered? }

min? { minto hold the smallest value eventually }

max? { maxto hold the largest value eventually }

for each numentered,increment count

sumsum+ num

if num< minthen minnum

if num> maxthen maxnum

avesum/count

Note the use of indentation and symbols in the second version. What

should minand maxbe initialised with?

Algorithms may also be represented by diagrams. One popular

diagrammatic method is the flowchart, which consists of terminator boxes,process boxes, and decision boxes, with flows of logic indicated by arrows.

The flowchart below depicts the same logic as the algorithms above.

start

sumcount0

min?

max?

end of

input?

increment count

sumsum+ num

nummax?

min

num

maxnum

Yes

Yes

Yes

No

No

No

avesum/count

end

Terminator box

Process box

Decision box

Whether you use the pseudo-code or the flowchart to represent your

algorithm, remember to walk through it with some sets of data to check thatthe algorithm works.


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3.5 Control Structures 37

3.5 Control Structures

The pseudo-code and flowchart in the previous section illustrate the three types

of control structures. They are:

1. Sequence

2.

Branching (Selection)

3. Loop (Repetition)

These three control structures are sufficient for all purposes. The sequence

is exemplified by sequence of statements place one after the other the one

above or before another gets executed first. In flowcharts, sequence of

statements is usually contained in the rectangular process box.

The branch refers to a binary decision based on some condition. If the

condition is true, one of the two branches is explored; if the condition is false,

the other alternative is taken. This is usually represented by the if-then

construct in pseudo-codes and programs. In flowcharts, this is represented by

the diamond-shaped decision box. This structure is also known as the selection

structure.

The loopallows a statement or a sequence of statements to be repeatedly

executed based on some loop condition. It is represented by the while and

for constructs in most programming languages, for unbounded loops and

bounded loops respectively. (Unbounded loops refer to those whose number of

iterations depends on the eventuality that the termination condition is satisfied;

bounded loops refer to those whose number of iterations is known before-

hand.) In the flowcharts, a back arrow hints the presence of a loop. A trip

around the loop is known as iteration. You must ensure that the condition for

the termination of the looping must be satisfied after some finite number of

iterations, otherwise it ends up as an infinite loop, a common mistake made byinexperienced programmers. The loop is also known as the repetitionstructure.

Combining the use of these control structures, for example, a loop within a

loop (nested loops), a branch within another branch (nested if), a branch within

a loop, a loop within a branch, and so forth, is not uncommon. Complex

algorithms may have more complicated logic structure and deep level of

nesting, in which case it is best to demarcate parts of the algorithm as separate

smaller modules. Beginners must train themselves to be proficient in using and

combining control structures appropriately, and go through the trouble of

tracing through the algorithm before they convert it into code.

3.6 Summary

An algorithm is a set of instructions, and an algorithmic problem lends itself to

a solution expressible in algorithmic form. Algorithms manipulate data, which

are represented as variables of the appropriate data types in programs. Data

structures are collections of data.

The characteristics of algorithms are presented in this chapter, so are the

two forms of representation for algorithms, namely, pseudo-codes and

flowcharts. The three control structures: sequence, branch, and loop, which

provide the flow of control in an algorithm, are introduced.


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Exercises

In the exercises below, you are asked to find the answers by hand, and jot

down the steps involved for the generalized versions. You need not write

programs for them yet you will be doing that later you need only to

discover the steps and put them down into an algorithm.

1. Our coins come in denominations of 1 cent, 5 cents, 10 cents, 20 cents,

50 cents and 1 dollar. Assuming that there are unlimited number of

coins, how would you devise a coin-change algorithm to compute the

minimum number of coins required to make up a particular amount?

For example, for 46 cents you need 4 coins: two 20-cent coins, one 5-

cent coin, and one 1-cent coin.

2. How would you sort 10 numbers in increasing order? Do you know any

of the basic sorting techniques?

3.

A word is a palindrome if it reads the same when the order of itscharacters is reversed. For instance, 123321, RADAR and step on

no pets are palindromes. Derive an algorithm to determine if a word is

a palindrome.

4. Two words are anagramsof each other if they differ only by the order

of their characters. For example, HATE and HEAT, NOW and

WON, reset and steer are anagrams, but sell and less are not.

Write an algorithm to determine if two given words are anagrams.

5.

How do you test for primality? That is, given a positive integer, how

do you determine that it is a prime number?

6. In a mastermindgame, the code maker hides a secret code consisting of

4 digits, and the code breaker is to provide 4-digit guess codes until he

gets the code right. The code maker gives feedback in this manner, a

sinkis awarded to a perfect match of a digit plus its position, and a hit

refers to a right match of digit but in the wrong position. How do you

devise an algorithm to provide the correct feedback? First, work on the

special case that no digit in the code should be repeated. Then work on

the general case where digits can be duplicated.


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4. PROGRAMMING APPROACHES

Organizations and individuals are continually searching for more efficient ways to

perform the software development process.

One-way of reducing the time and cost of development is to standardize softwareprograms and the programming process. The benefits of standardized programs are that

they are easier to code, maintain, debug, and modify.

In recent years, a variety of techniques have appeared attempting to minimize differences

in the way programmers' design and develop software. A few of the most commonly used

techniques for standardization are described in this lesson.

Programming Approaches: Nonstructured Vs. Structured Approaches

Structured programming is a standardization technique used for software development.This approach works by having all programmers use the same structured designtechniques. Structured programmingwas invented to address the shortcomings of non-

structured programming, which frequently employed GO TO branch points to transfer

from one part of the program to another part. Using GO TOcodes, one could transfer

backward, forward, or anywhere else within the program. The problem is that theconnections between parts of the program by using GO TO commands can become quite

haphazard.

The haphazard and sometimes convoluted pattern of linkages between parts of the

program has been called spaghetti code. This type of programming is difficult to

understand and debug. Non-structured programming of this nature is now viewed as anineffective programming strategy.

To develop good software, developers have to carefully think out and design the

programs. In the earliest days of computing, programmers wrote software according to

their own whims, with the result that programs were often confusing and difficult to workwith. Software today is expected to follow recognised design principles. The prevailing

design standards are structured programmingand structured design.

4.1 STRUCTURED PROGRAMMING

Structured programming makes use of the control structures (sequence, selection andrepetition). Structured programming does not use GO TO commands. The sequence

principle implies that program instructions should be executed in the order in which they

appear. The selection principle implies that instructions may be executed selectivelyusing IF-THEN and/or IF-THEN-ELSE statements. These statements work in the

following way. IF a condition is met or is true, THEN a specific set of instructions will be

executed. If the condition is false, then another set of instructions will be executed.


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For example, IF an employee works 40+ hours a week, THEN calculate gross pay basedon an overtime rate of time and a half. If the employee does not work 40+ hours a week,

THEN calculate gross pay based on the normal hourly pay rate. IF-THEN-ELSE works in

a similar way, but in this case the word ELSE is substituted for a false case, a condition

that is not met. IF the employee works 40+ hours a week, then calculate gross pay baseon a time and a half pay rate, ELSE calculate gross pay based on the normal rate.

Alternatively when there are many options, one can employ the CASE statement.

The iterationprinciple indicates that one part of the program can be repeated or iterated a

limited number of times. In most computer languages, the iteration may be activated by

using REPEAT ---UNTIL or using the WHILE loop and the FOR loop.

4.2 STRUCTURED DESIGN

According to structured design principles, a program should be designed from the top-

down or bottom-up as a hierarchical series of modules. A module is a logical way ofpartitioning or subdividing a program so that each module performs one or a small

number of related tasks.

4.2.1 Modular Programming

The Modular Approach to programming involves breaking a program down into

subcomponents called modules. Each module is composed of an independent or self-contained set of instructions. Modules are also referred to as routines, subroutines, or

subprograms or procedures. Each module is designed to perform a specific task in theoverall program, such as to calculate the gross pay of an employee in a payroll program.

The advantage of modular programming is the ability to write and test each moduleindependently and in some cases reuse modules in other programs. A program consists of

multiple modules. In addition, there is a main module in the program that executes the

other modules.

You can use the following approaches in order to design a program consisting of

modules.

4.2.2 Top-Down Design or Top-Down Decomposition

One programming approach that has proven to be most productive is called top-downdecomposition. Top-down decomposition is the process of breaking the overall procedure

or task into component parts (modules) and then subdivide each component module until

the lowest level of detail has been reached. It is called top-down design or top-down

decomposition since we start "at the top" with a general problem and design specificsolutions to its sub problems. In order to obtain an effective solution for the main


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problem, it is desirable that the subproblems (subprograms) should be independent of

each other. Then each sub-problem can be solved and tested by itself.

The top level of the decomposition is the level of the overall plan. Unfortunately there is

no single formula that will decompose a complex problem into individual tasks. The

strategy involves top-down reduction of the processing until a level is reached whereeach of the individual processes consists of one self-contained task, which is relatively

easy to understand and can be programmed in a few instructions.

This stepwise process may create multiple layers or levels of modules beginning with a

main module at the top. The second level might contain intermediate modules, and the

third level minor modules. The program is developed from the top in stepwise fashion.

Using this method, a complex problem is separated into simpler parts, which can be

programmed easily. At each stage, the instructions or steps can be checked for errors inlogic, corrected or modified without any effect on the other subprograms. The result will

be a truly modular program that satisfies the requirement, which says a good programcan be modified easily.

This programming strategy focuses on developing a software program conceptually

before coding begins. A programming team will likely create a diagram that looks much

like an organisational chart with the main module at the top and subordinate modulesdown below connected by lines with each box representing a program module. The chart

shows how modules relate to each other but does not depict the details of the program

instructions in each module. The structure chart is usually referred to as a HierarchicalProgram Organisation (HIPO)

Example top-down decomposition

The payroll system of a company can contain the following modules or tasks

Master file

Earnings

Deductions

Taxing

Net earning

Print reports

The tasks given above can be depicted in a hierarchical chart (Hierarchical ProgramOrganisation) as shown below.


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Identifying and diagramming the relationship between modules in this fashion allows

programmers to focus on the overall organisation and logic of the program without

getting bogged down in the details. Once the overall structure of the program is finalised,detail coding of individual modules can proceed.

It is the set of principles that enable a problem to be solved by breaking it down intomanageable parts, step-by-step from the overall problem specification, in stages through

to the actual code.

4.2.3 Bottom-up Design

Already existing facilities/designs are used/taken into consideration as a model for a new(better) design. Using Bottom-up design strategy, we take an already existing computer

program as a model for our new program. We try to utilise the existing facilities or design

in a way, which gives out program a better performance.

4.2.3 Stepwise Refinement

Stepwise refinement is a top-down design strategy. The program is developed by

successively refining levels of procedural detail. In each step of the refinement, one orseveral instructions of the given program are decomposed into more detailed instructions.

This successive decomposition or refinement of specifications terminates when all

instructions are expressed in terms of any underlying computer or programminglanguage.

Every refinement step implies some design decisions. It is important that the programmer

is aware of the underlying criteria.

PAYROLL PROBLEM

Master File Earnings Deductions Taxing

CreateMaster

File

UpdateMaster

File

CreateEarning

File

UpdateEarning

File

CreateDeduction

File

UpdateDeduction

File

Create orupdate Tax

File


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4.3 SUB-PROGRAMS

In top down design, the problem is broken down into sub-problems. The main problem issolved by the corresponding main program. Solutions to the sub-problems are provided

by subprograms, known as procedures, functions, or subroutine depending on the

programming language. A subprogram performs or executes the computer instructions

required to solve a given subproblem.

4.3.1 User defined Sub Programs and FunctionsA Sub Program is a part of a program that performs one or more related tasks, has its own

name, is written as a separate part of the program, and is accessed via a call statement.

A Function returns a value to the program and shares many of the same characteristics as

a Sub Program (e.g., has its own name, is written as a separate part of the program).

Pros and Cons of Using Procedures

Disadvantage -- Procedure calls consume execution time and memory.

Advantage -- Procedures make the program easier to write, test, debug andmaintain.

Within a program we can normally identify sub-tasks that are performing a specific

function. Where program features clearly identify sub-tasks it is good practice toimplement each sub-task in its own, stand-alone, sub-program.

The advantages of a separate sub-program are considerable:

A stand-alone sub-program can be written and tested independently.

Once written, the sub-program can be called a number of times within aprogram.

The sub-program is referred to by a meaningful name chosen by the

programmer, which helps greatly in understanding the code. The sub-program can also be used in subsequent programs.

The ability to reuse a sub-program is obviously useful. We can include an existing

subprogram in another program whenever you need it.

Main Problem

SubproblemA

SubproblemB

SubproblemC

Main Program

Sub-program A

Sub-program B

Sub-Program C


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4.3.2 Procedures and Functions

A function or procedure is a sub-program that exists to perform a specific, single task. Ithas its own inputs and its own outputs (often called parameters), it can also define its own

variables. It may return the values to the referencing or invoking program or procedure A

function is a special sort of procedure that has a single output.

Procedures

A procedure has a header, followed by declarations of variables used within the

procedure known as local variables (identifiers) and finally statements that are to beperformed when the procedure is invoked.

The procedure header is the mechanism used to give a name to the procedure. Theprocedure header also may contain the values that can be communicated between the

procedure and its invocation known as parameters.

The general structure for defining a procedure (in C++) is:

void Procedure_Name(parameter){

.

//List of Statements.}

Example

void WelcomeNote (){

Cout


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A function is a special sort of sub-program - it is used when a sub-program is neededwhich takes a number of inputs and returns a single output value (as with cube above).

This is typical of many algebraic functions (sine, cosine, exp, log, cube) but is otherwise

fairly unusual since the sub-programs that we want to define quite often have either no

output at all (as with manythanks) or very many outputs - in these cases we use aprocedure.

Parameters

As weve seen, procedures and functions can take a list of quantities called parameters.

Initially you might like to regard the parameters as the inputs to the module (but this is

not always true, as we shall see). For example:

void sum_and_difference( float a, float b){

float total, difference;

total =a+bdifference =a-b

cout


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void main()

{

float val1, val2;float total, difference;

val1=2;val2=4;

sum_and_difference(val1,val, total, difference);

cout


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5. CODING THE PROGRAM

Coding the Program refers to the process of transferring a pseudocode program or

flowchart into a computer program using a programming language. The program

statements are written in such a way that they are in accordance with the language syntax.

There is a compulsory set of programming rules to foster the habit of following some

convention consistently. These conventions are designed to improve code readability; onthe premises that far more human time is spent reading code than writing it, that far more

human time is spent modifying existing code than writing entire programs from scratch,

that far more code is written by groups of people than by single individuals. In particular,

following these rules will make it easier for the grader to grade your work and theinstructors to assist you if you are having difficulty.

5.1 NAMES

Choose your names carefully. As part of program documentation, names must clearlyindicate both the kind of thing being named and its role in the program.

5.1.1 Variable names:

One has two choices, and you should choose one and follow it consistently. Variable

names only one word long can begin either with a lower case or an upper case and

thereafter are lower case including other acceptable characters.

Guidelines for choosing meaningful names:

In general, choose English words, which describe the thing being named.

Use simple names for variables used briefly and locally. For example, a loopcounter might be a single letter.

Otherwise, avoid using lots of one- and two- character names like x or b2.

Use common prefixes/suffixes to associate names of the same general type orcategory.

Avoid deliberate misspellings and meaningless suffixes to create variables withsimilar names, e.g. if the name indexis used, do not define another variable with aname like indx, ndex, or index2.

Avoid names that are similar to each other and thus possibly confusable.

Never use acronyms as abbreviations, instead, if your names are getting long youmay eliminate vowels (e.g., frstElmnt), or use an unambiguous prefix (e.g.,

firstElem), but NOT fe.


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5.1.2 Indentation

Maintain consistent indentation throughout your code. Examples:

if (condition) thenstatements

elsestatementsend if ...

for (...)

statements

end for ...

Rightward Drift. As you get more and more deeply nested block of code, indentation

pushes you farther and farther to the right, until eventually you have hardly any room towrite a line of code. To avoid this, you can do two things:

Use a modest size indentation. Four spaces is probably optimal. If you anticipateproblems with rightward drift, you could even try two or three, although this is

not as easy to read.

5.1.3 Comments

Comments should help the reader of your code to understand it. Like any other form ofexpression, it should not be flowery or repetitive. In particular observe the following

guidelines

All internal documentation must be written in English. Avoid comments thatsimply rephrase your code in English, without summarizing it or adding any

information.

For each variable, give a one-line comment stating the use of the variable. Thesemay follow the variable declaration, as

in:

int i; /* loop variable */

for (i = 0; i < sizeOfArray; 1)someArray[i] = 0;

}


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Or you may use a comment block to identify the use of several variables together. Before

each major section of the program, give the purpose of that section.

At the end of statement blocks unless the block is only a couple lines long, there should

be a comment indicating which block is being ended. See the examples above.

Comment Blocks like the one used above should have a running line of /s or asterisks

which clearly identifies the block as a comment, even if the beginning or end of the

comment is not visible on the page or screen.

5.1.4 Keep Line Lengths Under 80 characters

On many machines and in many software packages, this is a standard line length. It

makes it easier for others to read and/or print your programs.

5.1.5 Make judicious use of White Space

Sometimes the simple insertion of a blank line here and there to help group a few lines of

code which work together to achieve a sub-goal can make the program much easier to

read. But don't put in too much white space or the reader will not be able to see enough ofthe code at a time.


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6. PROGRAM TESTING

What is Program Testing?

Program testing is a formal evaluation technique in which software requirements, design,

or code are examined in detail by a person or group other than the author to detect faults,violations of development standards, and other problems.

Assuming your program has compiled successfully with no warning messages, what

comes next? The answer is testing, but this is not as simple as it seems. Any programneeds testing in order to show that it works in the desired fashion. Most programs need

some form of input, and most of these can accept a potentially infinite number of inputs.

It is a good guess that we cannot test our programs on all inputs, and in fact it can be

proved that no amount of testing can prove, in general, that a program works, i.e. that itmeets the requirements laid down in the specification, or problem description. We can,

however, prove that certain kinds of programs work correctly, but this is a hard job,involving complex mathematics and special-purpose computer tools.

The rest of us need to test our programs by choosing appropriate inputs, observing thebehaviour of the program with these inputs, and comparing the outputs with the ones

expected by examining the description.

Program correctness

A program is correct, if it exactly meets its given specification.

Consequently, the correctness of a program is always expressed relative to its

specification. A major problem in determining the correctness of a program is thedifficulty of finding a complete and adequate specification, which is often described in

abstract mathematical or physical statements

The best software is that which has been tested by thousands of users under thousands of

different conditions over years. Then it is known as "stable". Yet, this does not mean, that

the software is now flawless, free of bugs. It generally means that there are plenty of bugs

in it, but the bugs are well identified and fairly well understood. There is simply no wayto assure that software is free of flaws. Though software is mathematical in nature, it

cannot be "proven" like a mathematical theorem; software is more like language, withinherent ambiguities, with different definitions, different assumptions, and differentlevels of meaning that can conflict.

Debugging


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Debugging is the process of locating, analyzing, and correcting suspected

errors.

In computers, debugging is the process of locating and fixing or bypassing bug(errors)

in computer program code. To debug a program is to start with a problem, isolate the

source of the problem, and then fix it. A user of a program that does not know how to fixthe problem may learn enough about the problem to be able to avoid it until it is

permanently fixed. When someone says they've debugged a program or "worked the bugs

out" of a program, they imply that they fixed it so that the bugs no longer exist.

Debugging is a necessary process in almost any new software development process,

whether a commercial product or an enterprise or personal application program. Forcomplex products, debugging is done as the result of the unit test for the smallest unit of a

system, again at component test when parts are brought together, again at system test

when the product is used with other existing products, and again when users try theproduct out in a real world situation.

Because most computer programs contain thousands of lines of code, almost any new

product is likely to contain a few bugs. Invariably, the bugs in the functions that get mostuse are found and fixed first. An early version of a program that has lots of bugs is

referred to as "buggy."

Debugging tools help identify coding errors at various development stages. Some

programming language packages include a facility for checking the code for errors as it is

being written.

Strategies for Testing

The idea of testing a program is twofold: the first is to see whether the program works ina manner that fits the problem description; the second is to break it, i.e. to find a set of

circumstances in which it fails. Only when we know how a program fails can we improveit.

A testing strategy is necessary because without a clear goal, testing can be a very hit-or-miss affair. Many programmers take this approach by default, and tie it in specifically to

a debugging strategy, which actually is a different topic.

Black Box Testing

Black box testing refers to the development of test cases that are focused on what the

software is supposed to do. That is, we are checking to see if the functionality is correct,

without regard to how the software accomplishes a specified task. Black box testing iscalled that because the tester cannot "see" inside the module or component being tested.


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This is the type of tests that are performed from a user perspective when we are doing

supported by tools that execute the software for us.

White Box Testing

White box testing might be more appropriately named clear box testing. In this type of

test, the tester knows how the software module or component is implemented. In this

scenario, the tester is trying to ensure that the software does not fail. Automation of whitebox testing is more difficult than black box testing. This type of test is usually done from

the developer perspective during unit testing where one of the test resources is the source

code. We need to know how the software has been written so that we can test its possiblefailure points.

Software testing is becoming increasingly important. It is important to do it well,especially when we are involved in component-based development where we don't know

exactly what other components our software may interact with. Adherance to thedevelopment specification and a properly working interface are essential. Some

companies, like Microsoft, have a tester for every developer because the test process is so

important.

Typical Input

Most testing should be done using typical input values that the program design is

supposed to cater for. The problem description will often contain ranges or even absolute

values that the program should expect to handle. Of course, even these can be too manyor too complex for exhaustive testing, so the tester can choose appropriate values.

Some programs do not place restrictions on their input values, but even if they do not,

programs need to be tested on typical values. In some cases, these will be sets of typical

inputs, not just one. The problem with testing on a single value is that the program maywork perfectly on your chosen typical representative value, but fail on another because it

handles the typical value specially without your knowledge. Choosing more than onetypical value can minimize this problem. These typical inputs also become part of the test

suite.

Special Input

Often programs will fail when presented with data that is zero or absent, or too small. It

can also be that the data is too big, or too long. A good strategy in these cases is topresent the program with the simplest possible case (typically zero or absent data) and

then to present it with a complex case involving large values, long strings, or largenumbers of items. If the program passes these tests, it may still fail on typical input

data, and several tests should be run on data that represents the typical case.


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It is useless to rely on one representative input, and even when several tests havesucceeded, suspicion is still appropriate, and more probing is often necessary before

feeling happy about the program. For instance a program that expects to read a namemight get an empty string; a program that expects a number of inputs of the same kind

may get none; a program that stores a maximum of 100 names might get exactly 100. Alist of values might be terminated by a special sentinel value, or perhaps a negative valuewhere the norm is positive. The program should be able to cater for these, without failing,

so they become part of the test suite

Invalid Input

Many inputs have range restrictions, so the extreme end of the range, and beyond, shouldbe tested. Names of one character; ages less than zero, or greater than 150; car speeds

over 500 m.p.h., and so on.

These ranges should be tested at their extremes, and beyond to be safe. Even morecommon is the program that tests for valid input but does not test for invalid input. If anumber between 1 and 5 is supposed to be input, and the user puts in 6 (or 10000!) what

happens? If a response should be y or n, what happens with a z? Programs that

behave gracefully under this kind of fire are called robust. Programs that crash when

presented with invalid input are just useless!.

Having assembled the test suite (and this could be as small as a handful of values for

small programs) the program should be executed using the inputs and its behaviour

observed and recorded. This is rather like experimentation. If the program succeeds on all

inputs, i.e. its observed behaviour matches the expected behaviour, as extracted from thespecification, then you are done! Mostly, however, and especially for programs of any

size, disasters of various sorts will occur. How to fix these disasters is a job fordebugging. However, they would not have occurred if comprehensive testing had not

been carried out.

Program Verification

Verification means that the characteristics of modules or programs are thoroughly

checked according to their specifications. A prog

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