ProgrammingSection 3

WHAT IS AN ALGORITHM?

An algorithm is a sequence of precise instructions for solving a problem in a finite number of steps.

Properties/Characteristics:

Algorithms must: be precise, be unambiguous, be logically sequenced, give the correct solution an all cases, and eventually end.

Algorithmic structure

Header : Algorithm’s name or title

Declaration : Brief description of algorithm and variables used. i.e. A statement of purpose as well as the initialization of variables

Body : Sequence of steps

Terminator : An end statement

ALGORITHMIC STRUCTUREProblem:

Write an algorithm that prompts a student to enter his/her name and age, accepts the name and age and then display a welcoming message on the screen such as “hello Michael! You are 16 years old!”

Write the algorithm identifying the header, declaration, body and terminator.

ALGORITHMIC STRUCTURE

Algorithm Student data {Header}This algorithm displays a student’s name and age on the screen. {declaration}StartDisplay “Enter your name:”Accept NameDisplay “Enter your age:”Accept AgeDisplay “Hello”, NameDisplay “You are”, Age, “years old”Stop {Terminator}

{Body}

EXAMPLE• Write an algorithm that will read the radius of a circle and

calculate and display its perimeter.

Input Processing Output

radiusAccept radiusCalculate circumferenceStore results in circumferenceDisplay circumference

circumference

Step 1: startStep 2: read radiusStep 3: circumference 2 * 3.14* radius Step 4: write circumferenceStep 5: stop

EXAMPLE• Write an algorithm that displays the area of a rectangle by

accepting length and width from the user.

Input Processing Output

length, widthAccept length, widthCalculate areaStore results in areaDisplay area

Area

Step 1: start Step 2: read length, widthStep 3: area length * width Step 4: write areaStep 5: stop

EXAMPLE• Write an algorithm to read three numbers and find their

product.Input Processing OutputThree numbers (num1, num2,num3)

Accept numbersCalculate productStore results in productDisplay product

Product

Step 1: startStep 2: read num1, num2, num3Step 3: product num1*num2*num3 Step 4: write product Step 5: stop 

FLOWCHARTS VERSUS PSEUDOCODE• Pseudocode is more concise, closely resembles programming

language

• Flowchart gives good view of the structure and flow of the logic

• Beginners tend to follow the logic easier when using flowcharts rather than pseudocode

• Longer, more complex solutions are better represented using pseudocode.

FLOWCHARTS VERSUS PSEUDOCODE• Usage is a matter of preference for experienced programmers

• Students should be asked to use both flowcharts as well as pseudocode to represent algorithms

• Flowcharts must use special geometrical objects that designate the basic steps of a program:

Input/Output

Processing/ Assignment

Decision Start/ Stop

Flow of Control

PSEUDOCODE AND FLOWCHART

• Start• Get num1, num2, num3• Average (num1 + num2 + num3)/3• Print Average• Stop

Start

Read num1, num2, num3

Average (num1+num2+num3)/3

Print Average

Stop

Draw flowcharts for the following programs:• Program to accept the price of an item and calculate its VAT at

15%. start

read price

vat price *.15

write vat

stop

Example • Program to accept money in US dollars and convert it to its equivalent

local currency.

read us

ec us *2.71

write ec

stop

start

Distinguish between variables and constants;

• Variable = the name identifies what the value represents.

• Constant = A value (Alphabetical/numerical) that never changes during processing.

(Eg. the value of PI)•

Use appropriate data typesData Types Examples

String “Hello”, “Carl” “New York” “Mary”

Character a,e,i,o,f,h,j,k,h

Real or Floating point 2.3, 45.6, 36.3, 88.1, 3.5,

Boolean Yes, No, True, False,

Integer/Whole numbers 1,4,988,99,88,66,

Control Structures• That are commonly used in programming languages.

• Sequencing- Execute one single instruction, in a section of program, after another.

• Selection- Choose, depending on a tested condition, between two, or more pathways through a section of a program.

• Repetition/Looping- Executing a single instruction, or group of instructions, one or more times.

EXAMPLE OF CONTROL STRUCTURES

Sequence

SELECTION STRUCTURES

• IF … THEN … ELSE construct syntax: • IF (expression) THEN

{Statements} executed only if condition is TRUEELSE

{Statements} executed only if condition is FALSE ENDIF • Only one group of statements could be executed each time

the program is executed.

SELECTION STRUCTURES

Get MarkIF Mark >= 50 THEN PRINT “ Well done”ELSE PRINT “Must do better”ENDIFStop

• “Well done” will be printed should the student’s mark be 50 or greater.

• If the mark is less than 50

then the statement “Must do better” would be printed.

REPETITION STRUCTURES

• Repetition or Loop or Iteration structures allow statements to be repeated a fixed number of times or until some condition evaluates to false.

• There are three repetition constructs:

1. FOR Loop - counted loop

2. REPEAT Loop - conditional loop

3. WHILE Loop - conditional loop

The basic structure of the loop is:

• Initialise a variable to a star value (usually determines

whether or not the loop is executed)

• Test variable against condition

• Execute the body of the loop

• Update the value of the start variable

Loop StatementThere are two types of loop statements:Indefinite: This refers to when you do not know beforehand how

many times to repeat the loop. (WHILE and REPEAT loops)

General Form of the WHILE-DO loopWHILE (condition) StatementExample.

Age = 16WHILE (age <21) DOBEGINOutput "You cannot drink"

Age = age + 1 ENDOutput "The loop has ended"

REPEAT LOOP

Definite

• This refers to when you know beforehand how many times to repeat the loop. (FOR loop)

Note:i. The symbols := must go togetherii. Variable must be in order so it can be counted.iii. Variable begins with start value.iv. Loop variable is increased every time the loop goes around.v. The loop will terminate/end when the counter reaches the value of the final expression

INITIALIZATION OF VARIABLES• Variables that are used as counters or used to store totals should always

be assigned an initial value of 0 before they are incremented.This is called initialization

Counters• This is the process of counting the number of times a value is entered or a

statement is carried out. You can also allow your counter to begin at 0 and then increment (increase accordingly).

• E.g.• Counter <--- 0

Counter <---- Counter + 1• In the example above, counter is initially set at 0, which means that every

time the assignment statement is executed, the value of the counter variable is increased by 1.

•

Draw flowcharts for the following• . Algorithm:

Set the number = 1Set the total = 0While (number <= 100)

total = total + numbernumber = number + 1

End WhileDisplay total

While Loop Start

Set number = 1

number <= 100

Set total = 0

total = total + number

number = number + 1

Display total

End

No

Yes

Use of relational operators:The following relational operators are used:

Table 1 Relational Operators

OperatorName

Symbol Description

Equal = Returns true if both sides are equal.

Greater than >Returns true if the variable on the left is greater than the

variable on the right.

Less than <Returns true if the variable on the left is less than the variable

on the right.

Greater than or equal to >=Returns true if the variable on the left is greater than or equal

to the value of the variable on the right.

Less than or equal to <=Returns true if the variable on the left is less than or equal to

the value of the variable on the right.

Not equal to <> Returns true if both sides are not equal.

exampleTable 2 truth table for relational operators

Operator Symbol Example (Assume A = 20, B = 15) True when False when Result

= A = B A and B are same or equal

A and B are different

False

> A > B A is greater than B

A is not greater than B

True

< A < B A is less than B A is not less than B

False

>= A >= B A is greater than or equal to B

B is greater than A

True

<= A <= B A is less than or equal to B

B is less than A False

<> A <> B A is not equal to B

A and B are same or equal

True

Logical Operators

• The logical operators are used for Boolean expressions. A Boolean expression can be in one of two states: True or False. Depending on the state of the expression.

• The three basic types of logical operators are: NOT, AND, OR

NOT OPERATOR

• NOT is a unary operator — it is applied to only one value and inverts it:

• · not true = false

• · not false = true

AND OPERATOR

• AND yields TRUE ONLY if both values are TRUE:

• · TRUE and FALSE = FALSE• · TRUE and TRUE = TRUE• · FALSE and TRUE = FALSE• · FALSE and FALSE - FALSE

OR OPERATOR

• OR yields TRUE if at least one value is TRUE:

• · TRUE or TRUE = TRUE• · TRUE or FALSE = TRUE• · FALSE or TRUE = TRUE• · FALSE or FALSE = FALSE

EXAMPLE• A = 10, B = 12, C = 14, D = 11• 1. A = B (FALSE)• 2. A > B (FALSE)• 3. (A < C) AND (B < D) (FALSE)• 4. (A>B) OR (A < 5 (FALSE)• )5. (D>A) AND (C > D) ( TRUE)• 6. (A>B) OR ((A+B)<(A *B)) (TRUE) 10>12 (f) 0R 10+12<10*12• 7. NOT (B>D) (TRUE)

22 120

Arithmetic OperationsSome arithmetic operations offered by Darwin.

Operation Symbol Example Result

addition + 101+27 128

subtraction - 15-3 12

multiplication * 5*3 15

division / 6/2 3

test algorithms for correctnessWe use a trace table which is one that is completed by

tracing the instruction in the algorithm with appropriate data to arrive at solutions.

• The column headings of a trace table record the names of all the variables used in the algorithm.

• The rows record the state of the variables after every instruction execution.

Copy the following trace table. Complete the trace table, given that the number 4 is the input value for X.

Read X For M = 1 to X doY = X – MZ = 5 * Y – MENDPrint ZWhat does the algorithm prints?

234

3210

14

2-4

Z= 14,8,2,-4

The algorithm prints -4

test algorithms for correctness;

3*2 6 2+13 1-106*318 3+03 0-1-1

use the top-down design approach to problem solving.

• Top-Down Design Approach or Modular Programming as it is sometimes called involves breaking a problem into a set of smaller problems, called sub-problems or modules, followed by breaking each sub-program into a set of tasks, then breaking each task into a set of actions. This is called stepwise refinement

• General Rule in modular programming is that a module should be comprised of statements that contribute to a single, specific task..

Steps in Modularization:1. Define the problem

2. From the processing section, identify the tasks that will determine the

modules that will make up the program. Each non-trivial task should

constitute a module.

3. Construct a hierarchy chart showing the modules and the relationship

between them.

4. Formulate the algorithm for the main module in either pseudocode or

flowchart.

5. Develop sub-algorithms for each module.

6. Test the algorithm for correctness.

Advantages of the Top-Down Design Method: • 1. It makes the problem solution more manageable.

It is easier to comprehend the solution of a smaller and less complicated problem that to grasp the solution of a large and complex problem.

•2. It is easier to test segments of solutions, rather than the entire solution at once.

•3. A simplified solution takes less time to develop and will be more readable.

•4. The program will be easier to maintain.

A Hierarchy chart

• or structure chart is a tree-like structure that shows visually the relationships between the modules of a program

EXAMPLE 1.1:

Given a list of students test scores, find the highest and

lowest score as well as the average score.

Four sub-problems can be identified here:

1. Sub-problem 1: read list of test scores

2. Sub-problem 2: find_the_highest_score

3. Sub-problem 3: find_the_lowest_score

4. Sub-problem 4: find_the_average

A Hierarchy chart

Flowchart for the above algorithm is:

distinguish between low-level and high-level programming languages;

• Low level languages- These are languages which are machine dependent; that is, when a code is written on a particular machine, it can only be understood by that machine.

• High level languages- These are languages that are machine independent; that is, when a code is written on a particular machine, it is not limited to execution on that machine only but can also run on other similar machines.

distinguish among the differegenerations of programming languages

First Generation Language- These are also called machine languages and are characterized by ones and zeros, which make up a binary code. A sample instruction might be 100111000 01100110

Second-generation language- These are also called assembly languages and are characterized by abbreviated words, called mnemonics. A sample code might be ‘Add 12,8’

Cont’dThird- generation Languages- These are designed so that it is easier for the programmer to understand. A compile converts the statements of a specific language into machine language.

• Fourth generation language (4Gls)- These are designed to be closer to natural language than a 3GL. Languages for accessing databases are often described as 4GLs.

*A sample instruction might be EXTRACT ALL CUSTOMERS WHERE 'PREVIOUS PURCHASES' TOTAL MORE THAN $1000.

• Fifth Generation- Programming that uses a visual or graphical development interface to create the source code. They are often described as very high level language.

To get the object code from the source code,• We use a translator programme. Three types of such

programmes are interpreters, compilers and assemblers.

• Interpreter- Translates the source code, line by line. If an error is detected, translation is stopped.

• Compiler-Translates all instructions at once and produces a stand-alone object code that can be executed.

• Assembler-Translates mnemonic-type instructions [Assembly Language] to machine code.

List the sequence of steps associated withimplementing a program;

• Creating source code• Compiling• Linking• Executing • Maintaining.

Difference between

• Sources codes are programmes written in high-level or assembly-level language

• Object codes are machine codes which have been converted to machine language by the compile

• Compilers-A compiler is a computer programme which translates source codes to machine language. It does so, first, by converting the codes of the high-level language and storing it as object codes.

• Source Code------Compiler------Object Code

explain commonly used terms andconcepts in programming;

• Logic errors occur when the programmer makes mistakes in the sequence of the program statements such using the wrong formula or function.

• Syntax errors occur when a mistake is made in the programming language rules . For example if a keyword such as input or print is spelt incorrectly or an endif was left out.

• Run-time errors occur as the program compiles or runs. These errors are usually due to unexpected events such as division by zero or lack of memory for the computer to manipulate the data or a loop with no end.

• Example: for x = 1 to 3

• Debugging is the process of finding errors in the source code (detection), understanding why they occurred (diagnosis) and correcting them.

• Testing-As you complete your program, you must ensure that it works for any correct input data that the user gives it. The testing phase is to detect errors or problems in the program.

• Test data: the values that are used to test or check the correctness of the program. The test data should include a wide range of sample data including extreme values and inputs that are not valid.

Executing the program• If you have translated the program to its object code without

errors, you can now execute the program and see the results. The final two terms commonly used with program execution are:

• Program loading: Copying of a programme from the hard disk of the computer to memory so it can be used.

• Linking: Combining various parts of a programme to produce a single executable file.

•

Declare variables

• It is important to declare our variables when writing out programmes because they occupy space in memory that we can use to assign values and the compiler needs to know, in advance, the type of data that will be stored in it. These types include:

• Integer - stores whole numbers• Real - stores fractional numbers in the decimal format• Character - stores a single character such as a letter• String - stores a collection of characters

Declare constants;

The assignment statement • The assignment statement is used to store a value in a variable

after the operation (i.e. +,-,*, or /) has been performed.

• VARIABLE = Expression (i.e. what is to be calculated)

• Examples of assignment statements are: • 1. NUM1 = 5 (i.e. Store the value 5 in the variable NUM1) • 2. SUM = NUM1 + 50 (i.e. Add 50 to the value stored in NUM1,

then store the total in the variable name sum) • 3. Product = NUM1*SUM(i.e. Multiply the content of NUM1 by

the content of SUM)

The input statement

• The input statement is used to fetch data from some external source and store the data in a variable. The data stored in the variable can then be manipulated by the pseudocode.

• Examples of input statement used by pseudocode developers are:

• Read• Input• Fetch• Get

Pseudocode example one • Write a pseudocode to read two numbers into variable A and B.

• SolutionRead ARead B

Pseudocode example two

• Write a pseudocode to read the name and score for three persons.

• For this question, we need to store six pieces of data, three names and three test grades, respectively. Hence, six variables are needed. Our variable will be called:

• NAME1, NAME2, NAME3, GRADE1, GRADE2 and GRADE3.

Pascal • Writeln (pronounced as "write-line") statement displays the

data on screen and then moves the cursor to the next new line. while Write statement does not.

• examples of Writeln Write• Writeln('a');• Writeln('Hello');• Writeln('How are you ?');• Writeln; • Writeln('a', 'b', 'c');

Write('Macintosh ');Write('Computer.');Write('Hello');

Read/Readln

• Readln statement will cause the computer to advance (move) the cursor to the beginning of the next line after execution while read statement will not.

• Example of Readln Read• Readln(a,b);• Readln(c,d);• Readln(e,f);

Read;Read;

ARRAY

• An Array is a powerful data structure that stores variable data having the same data type.

DECLARE an Array

• Var• myArray : Array[1..20] of Integer;• <arrayName> : Array[n..m] of <Data Type>;

Assigning values to array?

• To assign values to a particular integer of an array, we do it like this:

• myArray[5] := 10; myArray[1] := 25;

•<arrayName>[index] := <relevant data>

Reading array

• Reading a value from an array is done as follows:

• Var myVar : Integer; myArray : Array[1..5] of Integer;

Begin myArray[2] := 25; myVar := myArray[2]; End.

• Just like ordinary variables, arrays should be initialised, otherwise scrap data will remain stored in them. If we want to intialise 2 whole 20-sized integer and boolean arrays to 0 and false respectively, we do it like this:

Var i : Integer; myIntArray : Array[1..20] of Integer; myBoolArray : Array[1..20] of Boolean;

Begin For i := 1 to 20 do Begin myIntArray[i] := 0; myBoolArray[i] := false; End;

End.

Introducing User-Defined Data Types

• Built-in data types are the ones we used lately, such as Integer, Boolean and String. Now we will learn how to specify our own customised data types and this is just how it is done:

Type<myDataType> = <particularDataType>;