A complete course in Program Design using Pseudocode

A Complete Program Design Course
(using Pseudocode)
Damian Gordon

Module Description
• This module is an introduction to programming, program design
and algorithms. Students are introduced to a structured procedural
programming language and to commonly used algorithms and their
implementation.
– This module assumes no prior knowledge of programming or algorithms.
– The aims of this module are to:
– Teach the fundamentals of procedural programming
– Teach the principles of good program design, implementation,
documentation and testing.
– Teach the theory and application of elementary algorithms and data
structures.

Learning Outcomes
On Completion of this module, the learner will be able to
• Design and write computer elementary programs in a structured procedural
language.
• Use a text editor with command line tools and simple Integrated
Development Environment (IDE) to compile, link and execute program code.
• Divide a computer program into modules.
• Test computer programs to ensure compliance with requirements.
• Implement elementary algorithms and data structures in a procedural
language.

Indicative Syllabus
• Introduction: What is a program? Source code. Machine code.
Editing, Compiling, Linking Debugging. Use of an Integrated
Development Environment (IDE).
• Basic Data Types: integer, floating-point and character data and
variables.
• Basic Input-Output: Display data on a screen. Input data from the
keyboard.
• Programming Structures: Conditional statements: Boolean values
and expressions, logical and relational operators, if-statement,
case-statement, compound conditional statements.

Indicative Syllabus
• Iterative constructs: while-statements, for-statements and
nested control statements.
• Structured Programming: functions, parameter passing,
returning values.
• Introduction to Data Structures: single-dimensional arrays,
two-dimensional arrays, dynamically allocated arrays

Indicative Syllabus
• Basic Algorithms: summation, counting, numeric operations,
swapping, maximum and minimum, simple array manipulation.
• Elementary Sorting Algorithms: Internal Sorting. Exchange sort.
Interchange sort. Bubble sort. Shaker sort. Insertion sort.
• Testing and debugging: Objectives and principles of testing.
Choosing appropriate test data. Simple debugging using a
program trace.
• Documentation: Style guidelines.

Indicative Syllabus
Assessment Type Weighting
(%)
Written Assessment 70
Continuous Assessment 30

Introduction to Programming
Damian Gordon

Algorithms
• An Algorithm is a series of instructions
• Examples of algorithms include
– Musical scores
– Knitting patterns Row 1: SL 1, K8, K2 tog, K1, turn
– Recipies

Algorithms
• Problem Solving
– Analyse Problem (Analysis)
– Develop Algorithm (Design)
– Convert into programming language (Development)

Conversation
Interaction
Collaboration
Motivation
Mobility
Tracking
Globalisation
Flexibility
Traditional On-Line
Blended Learning

Diana Laurillard’s
Conversational Framework

Teacher’s
Conceptual
Model
Student’s
Conceptual
Model
Teacher’s
Constructed
World
Student’s
Experiential
Knowledge
Discussion
Interaction
Reflection on
Interaction
Adaption of actionsAdaption of world
Reflection on student
performance

Gilly Salmon’s
5-Stage Model of e-Learning

Pam Moule’s
eLearning Ladder

GroupWork
Facilitation
LengthofEngagement
ICTAccess
ICTSkills
TechnicalSupport
Information Gathering
Interactive Media
Video Conferencing
E-mail Discussions
Chat rooms
On-line Communities of
Practice
I
N
C
R
E
A
S
I
N
G

1. Feedback
2. Students’ Prior Cognitive Ability
3. Instructional Quality
4. Direct Instruction
5. Premeditation

Robert Gagné's
Nine Events of instructional Design

Gain
Attention
Inform Learner of
Objectives
Stimulate recall of prior
learning
Present
Information
Provide
Guidance
Elicit
Performance
Provide
Feedback
Assess
Performance
Enhance Retention and
Transfer

Some Challenges of Blended Learning
• Technical Issues
• Motivation of the Students
• Student Participation
• Ensuring Interactive of lessons
• Organisational Alignment

Pseudocode
• The first thing we do when designing a program is to decide on
a name for the program.

Pseudocode
• Let’s say we want to write a program to calculate interest, a
good name for the program would be
CalculateInterest.

Pseudocode
• Let’s say we want to write a program to calculate interest, a
good name for the program would be
CalculateInterest.
• Note the use of CamelCase.

Pseudocode
• So we start the program as:
PROGRAM CalculateInterest:

Pseudocode
• So we start the program as:
PROGRAM CalculateInterest:
• And in general it’s:
PROGRAM <ProgramName>:

Pseudocode
• Our program will finish with the following:
END.

Pseudocode
• Our program will finish with the following:
END.
• And in general it’s the same:
END.

Pseudocode
• So the general structure of all programs is:
PROGRAM <ProgramName>:
<Do stuff>
END.

Components
• Sequence
• Selection
• Iteration

Top-Down Design
• Top-Down Design (also known as stepwise design) is breaking
down a problem into steps.
• In Top-down Design an overview of the problem is described
first, specifying but not detailing any first-level sub-steps.
• Each sub-step is then refined in yet greater detail, sometimes
in many additional sub-steps, until the entire specification is
reduced to basic elements.

Example
• Making a Cup of Tea

Example
1. Organise everything together
2. Plug in kettle
3. Put teabag in cup
4. Put water into kettle
5. Turn on kettle
6. Wait for kettle to boil
7. Add boiling water to cup
8. Remove teabag with spoon/fork
9. Add milk and/or sugar
10. Serve

Example : Step-wise Refinement
Step-wise refinement of step 1 (Organise everything together)
1.1 Get a cup
1.2 Get tea bags
1.3 Get sugar
1.4 Get milk
1.5 Get spoon/fork.

Step-wise refinement of step 2 (Plug in kettle)
2.1 Locate plug of kettle
2.2 Insert plug into electrical outlet

Step-wise refinement of step 3 (Put teabag in cup)
3.1 Take teabag from box
3.2 Put it into cup

Step-wise refinement of step 4 (Put water into kettle)
4.1 Bring kettle to tap
4.2 Put kettle under water
4.3 Turn on tap
4.4 Wait for kettle to be full
4.5 Turn off tap

Step-wise refinement of step 5 (Turn on kettle)
5.1 Depress switch on kettle

Pseudocode
• When we write programs, we assume that the computer
executes the program starting at the beginning and working its
way to the end.
• This is a basic assumption of all algorithm design.

Pseudocode
• When we write programs, we assume that the computer
executes the program starting at the beginning and working its
way to the end.
• This is a basic assumption of all algorithm design.
• We call this SEQUENCE.

Pseudocode
• In Pseudo code it looks like this:
Statement1;
Statement2;
Statement3;
Statement4;
Statement5;
Statement6;
Statement7;
Statement8;

Pseudocode
• For example, for making a cup of tea:
Organise everything together;
Plug in kettle;
Put teabag in cup;
Put water into kettle;
Wait for kettle to boil;
Add water to cup;
Remove teabag with spoon/fork;
Add milk and/or sugar;
Serve;

Pseudocode
• Or as a program:
PROGRAM MakeACupOfTea:
Plug in kettle;
Put teabag in cup;
Add water to cup;
Add milk and/or sugar;
Serve;
END.

Organise everything together
Plug in kettle
Put teabag in cup
Put water into kettle
Turn on kettle
Wait for kettle to boil
Add boiling water to cup
Remove teabag with spoon/fork
Add milk and/or sugar
Serve

Organise everything together
Plug in kettle
Put teabag in cup
Put water into kettle
Turn on kettle
Wait for kettle to boil
Add boiling water to cup
Remove teabag with spoon/fork
Add milk and/or sugar
Serve
START
END

Pseudocode
• So let’s say we want to express the following algorithm:
– Read in a number and print it out.

Pseudocode
PROGRAM PrintNumber:
Read number;
Print out number;
END.

Pseudocode
– Read in a number and print it out double the number.

Pseudocode
PROGRAM PrintDoubleNumber:
Read number;
Print 2 * number;
END.

Variables
• We know what a variable is from maths.
• We’ve all seen this sort of thing in algebra:
2x – 10 = 0
2x = 10
X = 5

Variables
• …and in another problem we might have:
3x + 12 = 0
3x = -12
X = -4

Variables
• So a variable contains a value, and that value changes over
time.

Variables
• …like your bank balance!

Variables
• In programming, we tell the computer the value of a variable
• So, for example,
x <- 5
means “X gets the value 5”
or “X is assigned 5”

Variables
x <- 5;

Variables
x <- 5;
X

Variables
x <- 5;
X
5

Variables
• And later we can say something like:
x <- 8;

Variables
• If we want to add one to a variable:
x <- x + 1;
means “increment X”
or “X is incremented by 1”
X(new)
5
X(old)
4
+1

Variables
• We can create a new variable Y
y <- x;
means “Y gets the value of X”
or “Y is assigned the value of X”
Y
X
6
6

Variables
• We can also say:
y <- x + 1;
means “Y gets the value of x plus 1”
or “Y is assigned the value of x plus 1”
Y
X
6
7
+1

Variables
• All of these variables are integers
• They are all whole numbers

Variables
• Let’s look at numbers with decimal points:
P <- 3.14159;
means “p gets the value of 3.14159”
or “p is assigned the value of 3.14159”

Variables
• We should really give this a better name:
Pi <- 3.14159;
means “Pi gets the value of 3.14159”
or “Pi is assigned the value of 3.14159”

Variables
• We can also have single character variables:
Vitamin <- ‘B’;
means “Vitamin gets the value of B”
or “Vitamin is assigned the value of B”

Variables
• We can also have single character variables:
RoomNumber <- ‘2’;
means “RoomNumber gets the value of 2”
or “RoomNumber is assigned the value of 2”

Variables
• We can also have a string of characters:
Pet <- “Dog”;
means “Pet gets the value of Dog”
or “Pet is assigned the value of Dog”

Variables
• We also have a special type, called BOOLEAN
• It has only two values, TRUE or FALSE
IsWeekend <- FALSE;
means “IsWeekend gets the value of FALSE”
or “IsWeekend is assigned the value of FALSE”

Pseudocode
PROGRAM PrintNumber:
Read Value;
Print Value;
END.

Pseudocode
PROGRAM PrintDoubleNumber:
Read Value;
DoubleValue <- 2*Value;
Print DoubleValue;
END.

Converting Temperatures
• How do we convert from Celsius to Fahrenheit?
• F = (C * 2) + 30
• So if C=25
• F = (25*2)+30 = 50+30 = 80

PROGRAM ConvertFromCelsiusToFahrenheit:
Print “Please Input Your Temperature in Celsius:”;
Read Temp;
Print “That Temperature in Fahrenheit:”;
Print (Temp*2) + 30;
END.

• How do we convert from Fahrenheit to Celsius?
• C = (F -30) / 2
• So if F=80
• F = (80-30)/2 = 50/2 = 25

PROGRAM ConvertFromFahrenheitToCelsius:
Print “Please Input Your Temperature in Fahrenheit:”;
Read Temp;
Print “That Temperature in Celsius:”;
Print (Temp-30)/2;
END.

Selection:
IF Statement
Damian Gordon

Do you wish to print a receipt?
< YES NO >

Do you wish to print a receipt?
< YES NO >
In the interests of preserving the
environment, we prefer not to print a
receipt, but if you want to be a jerk, go
ahead.
< PRINT RECEIPT CONTINUE >

Selection
• What if we want to make a choice, for example, do we want to
add sugar or not to the tea?

Selection
• What if we want to make a choice, for example, do we want to
add sugar or not to the tea?
• We call this SELECTION.

IF Statement
• So, we could state this as:
IF (sugar is required)
THEN add sugar;
ELSE don’t add sugar;
ENDIF;

IF Statement
• Adding a selection statement in the program:
PROGRAM MakeACupOfTea:
Plug in kettle;
Put teabag in cup;
Add water to cup;
Add milk;
THEN add sugar;
ELSE do nothing;
ENDIF;
Serve;
END.

IF Statement
• Or, in general:
IF (<CONDITION>)
THEN <Statements>;
ELSE <Statements>;
ENDIF;

IF Statement
• Or to check which number is biggest:
IF (A > B)
THEN Print A;
ELSE Print B;
ENDIF;

Pseudocode
– Read in a number, check if it is odd or even.

Pseudocode
PROGRAM IsOddOrEven:
Read A;
IF (A/2 gives a remainder)
THEN Print “It’s Odd”;
ELSE Print “It’s Even”;
ENDIF;
END.

Pseudocode
• We can skip the ELSE part if there is nothing to do in the
ELSE part.
• So:
THEN add sugar;
ELSE don’t add sugar;
ENDIF;

Pseudocode
• Becomes:
THEN add sugar;
ENDIF;

START
Does A/2 give a
remainder?
Read in A

START
Does A/2 give a
remainder?
Read in A
YesPrint “It’s Odd”

START
Does A/2 give a
remainder?
No
Read in A
YesPrint “It’s Odd” Print “It’s Even”

START
END
Does A/2 give a
remainder?
No
Read in A
YesPrint “It’s Odd” Print “It’s Even”

Pseudocode
• So let’s say we want to express the following algorithm to
print out the bigger of two numbers:
– Read in two numbers, call them A and B. Is A is bigger than B, print out A,
otherwise print out B.

Pseudocode
PROGRAM PrintBiggerOfTwo:
Read A;
Read B;
IF (A>B)
THEN Print A;
ELSE Print B;
ENDIF;
END.

START
A>B?
Read in A and B
YesPrint A

START
A>B?
No
Read in A and B
YesPrint A Print B

START
END
A>B?
No
Read in A and B
YesPrint A Print B

Pseudocode
• So let’s say we want to express the following algorithm to
print out the bigger of three numbers:
– Read in three numbers, call them A, B and C.
• If A is bigger than B, then if A is bigger than C, print out A, otherwise print out C.
• If B is bigger than A, then if B is bigger than C, print out B, otherwise print out C.

Pseudocode
PROGRAM BiggerOfThree:
Read A;
Read B;
Read C;
IF (A>B)
THEN IF (A>C)
THEN Print A;
ELSE Print C;
ENDIF;
ELSE IF (B>C)
THEN Print B;
ELSE Print C;
ENDIF;
ENDIF;
END.

START
A>B?
Read in A, B and C
Yes
A>C?

START
A>B?
No
Read in A, B and C
Yes
A>C? B>C?

START
A>B?
No
Read in A, B and C
Yes
A>C? B>C?
Print C
NoNo

START
A>B?
No
Read in A, B and C
Yes
A>C? B>C?
Print A Print C
Yes
NoNo

START
A>B?
No
Read in A, B and C
Yes
A>C? B>C?
Print A Print C Print B
Yes Yes
NoNo

START
END
A>B?
No
Read in A, B and C
Yes
A>C? B>C?
Print A Print C Print B
Yes Yes
No
No

Boolean Logic
• You may have seen Boolean logic in another module already,
for this module, we’ll look at three Boolean operations:
– AND
– OR
– NOT

Boolean Logic
• Boolean operators are used in the conditions of:
– IF Statements
– CASE Statements
– WHILE Loops
– FOR Loops
– DO Loops
– LOOP Loops

Boolean Logic
• AND Operation
– The AND operation means that both parts of the condition must be
true for the condition to be satisfied.
– A=TRUE, B=TRUE => A AND B = TRUE
– A=FALSE, B=TRUE => A AND B = FALSE
– A=TRUE, B=FALSE => A AND B = FALSE
– A=FALSE, B=FALSE => A AND B = FALSE

Boolean Logic
PROGRAM GetGrade:
Read Result;
IF (A = 5 AND Age[Index] < Age[Index+1])
THEN PRINT “A is 5”;
ENDIF;
END.

Boolean Logic
PROGRAM GetGrade:
Read Result;
IF (A = 5 AND Age[Index] < Age[Index+1])
ENDIF;
END.
• Both A=5 and Age[Index] < Age[Index+1] must be
TRUE to do the THEN part of the statement.

Boolean Logic
• OR Operation
– The OR operation means that either (or both) parts of the condition
must be true for the condition to be satisfied.
– A=TRUE, B=TRUE => A OR B = TRUE
– A=FALSE, B=TRUE => A OR B = TRUE
– A=TRUE, B=FALSE => A OR B = TRUE
– A=FALSE, B=FALSE => A OR B = FALSE

Boolean Logic
PROGRAM GetGrade:
Read Result;
IF (A = 5 OR Age[Index] < Age[Index+1])
ENDIF;
END.

Boolean Logic
PROGRAM GetGrade:
Read Result;
IF (A = 5 OR Age[Index] < Age[Index+1])
ENDIF;
END.
• Either or both of A=5 and Age[Index] <
Age[Index+1] must be TRUE to do the THEN part of the
statement.

Boolean Logic
• NOT Operation
– The NOT operation means that the outcome of the condition is
inverted.
– A=TRUE => NOT(A) = FALSE
– A=FALSE => NOT(A) = TRUE

Boolean Logic
PROGRAM GetGrade:
Read Result;
IF (NOT (A = 5))
ENDIF;
END.

Boolean Logic
PROGRAM GetGrade:
Read Result;
IF (NOT (A = 5))
ENDIF;
END.
• Only when A is not 5 the program will go into the THEN part of
the IF statement, when A is 5 the THEN part is skipped.

Selection:
CASE Statement
Damian Gordon

Selection
• As well as the IF Statement, another form of SELECTION is the
CASE statement.

CASE Statement
• If we had a multi-choice question:

CASE Statement
Read Answer;
IF (Answer = ‘A’)
THEN Print “That is incorrect”;
ELSE IF (Answer = ‘B’)
ELSE IF (Answer = ‘C’)
THEN Print “That is Correct”;
ELSE IF (Answer = ‘D’)
ELSE Print “Bad Option”;
END IF;
END IF;
END IF;
END IF;

CASE Statement
PROGRAM MultiChoiceQuestion:
Read Answer;
IF (Answer = ‘A’)
ELSE IF (Answer = ‘B’)
ELSE IF (Answer = ‘C’)
THEN Print “That is Correct”;
ELSE IF (Answer = ‘D’)
ELSE Print “Bad Option”;
ENDIF;
ENDIF;
ENDIF;
ENDIF;
END.

CASE Statement
Read Answer;
CASE OF Answer
‘A’ :Print “That is incorrect”;
‘B’ :Print “That is incorrect”;
‘C’ :Print “That is Correct”;
‘D’ :Print “That is incorrect”;
OTHER:Print “Bad Option”;
ENDCASE;

CASE Statement
PROGRAM MultiChoiceQuestion:
Read Answer;
CASE OF Answer
‘A’ :Print “That is incorrect”;
‘B’ :Print “That is incorrect”;
‘C’ :Print “That is Correct”;
‘D’ :Print “That is incorrect”;
OTHER:Print “Bad Option”;
ENDCASE;
END.

CASE Statement
• Or, in general:
CASE OF Value
Option1: <Statements>;
OTHER : <Statements>;
ENDCASE;

START
END
Option1
No
Read in A
Yes
Print “Option 1”
Option2
No
Yes
Print “Option 2”
OTHER
No
Yes
Print “OTHER”

CASE Statement
Read Result;
CASE OF Result
Result => 70 :Print “You got a first”;
Result => 60 :Print “You got a 2.1”;
Result => 40 :Print “You got a 3”;
OTHER :Print “Dude, you failed”;
ENDCASE;

CASE Statement
PROGRAM GetGrade:
Read Result;
CASE OF Result
Result => 70 :Print “You got a first”;
Result => 40 :Print “You got a 3”;
OTHER :Print “Dude, you failed”;
ENDCASE;
END.

Iteration:
WHILE Loop
Damian Gordon

WHILE Loop
• Consider the problem of searching for an entry in a phone
book with only SELECTION:

WHILE Loop
Get first entry;
IF (this is the correct entry)
THEN write down phone number;
ELSE get next entry;
THEN write done entry;
ELSE get next entry;
……………

WHILE Loop
• We may rewrite this using a WHILE Loop:

WHILE Loop
Get first entry;
Call this entry N;
WHILE (N is NOT the required entry)
DO Get next entry;
Call this entry N;
ENDWHILE;

WHILE Loop
PROGRAM SearchForEntry:
Get first entry;
Call this entry N;
WHILE (N is NOT the required entry)
DO Get next entry;
Call this entry N;
ENDWHILE;
END.

WHILE Loop
• Or, in general:
WHILE (<CONDITION>)
DO <Statements>;
ENDWHILE;

WHILE Loop
– Print out the numbers from 1 to 5

WHILE Loop
PROGRAM Print1to5:
A <- 1;
WHILE (A != 6)
DO Print A;
A <- A + 1;
ENDWHILE;
END.

WHILE Loop
START
END
Is A==6?
No
A = 1
Yes
Print A
A = A + 1

WHILE Loop
– Add up the numbers 1 to 5 and print out the result

WHILE Loop
PROGRAM PrintSum1to5:
Total <- 0;
A <- 1;
WHILE (A != 6)
DO Total <- Total + A;
A <- A + 1;
ENDWHILE;
Print Total;
END.

WHILE Loop
– Calculate the factorial of any value

WHILE Loop
– Calculate the factorial of any value
– Remember:
– 5! = 5*4*3*2*1
– 7! = 7*6 *5*4*3*2*1
– N! = N*(N-1)*(N-2)*…*2*1

WHILE Loop
PROGRAM Factorial:
Get Value;
Total <- 1;
WHILE (Value != 0)
DO Total <- Value * Total;
Value <- Value - 1;
ENDWHILE;
Print Total;
END.

Iteration:
FOR, DO, LOOP Loop
Damian Gordon

FOR Loop
• The FOR loop does the same thing as a WHILE loop but is
easier if you are using the loop to do a countdown (or
countup).

FOR Loop
• Can be expressed as:

FOR Loop
PROGRAM Print1to5:
FOR A IN 1 TO 5
DO Print A;
ENDFOR;
END.

FOR Loop
• Or, in general:
FOR Variable IN Range
DO <Statements>;
ENDFOR;

DO Loop
• The WHILE loop can execute any number of times,
including zero times.
• If we are writing a program, and we know that the loop
we are using will be executed at least once, we could
consider using a DO loop instead.

DO Loop
PROGRAM MenuOptions:
DO
Print “****** MENU OPTIONS ******”;
Print “1) Input Data”;
Print “2) Delete Data”;
Print “3) Print Report”;
Print “9) Exit”;
Get Value;
WHILE (Value != 9)
END.

DO Loop
• Or, in general:
DO
<Statements>;
WHILE (<Condition>)

LOOP Loop
• The LOOP loop is one that has no condition, so it is an
infinite loop. But it does include an EXIT command to
break out of the loop if needed.

LOOP Loop
PROGRAM Print1to5:
A <- 1;
LOOP
Print A;
IF (A = 6)
THEN EXIT;
ENDIF;
A <- A + 1;
ENDLOOP;
END.

LOOP Loop
• Or, in general:
LOOP
<Statements>;
IF (<Condition>)
THEN EXIT;
ENDIF;
<Statements>;
ENDLOOP;

Prime Numbers
– Read in a number and check if it’s a prime number.

Prime Numbers
– What’s a prime number?

Prime Numbers
– A number that’s only divisible by itself and 1, e.g. 7.

Prime Numbers
– Or to put it another way, every number other than itself and 1 gives a remainder, e.g. For
7, if 6, 5, 4, 3, and 2 give a remainder then 7 is prime.

Prime Numbers
– Or to put it another way, every number other than itself and 1 gives a remainder, e.g. For
7, if 6, 5, 4, 3, and 2 give a remainder then 7 is prime.
– So all we need to do is divide 7 by all numbers less than it but greater than one, and if
any of them have no remainder, we know it’s not prime.

Prime Numbers
• So,
• If the number is 7, as long as 6, 5, 4, 3, and 2 give a
remainder, 7 is prime.
• If the number is 9, we know that 8, 7, 6, 5, and 4, all give
remainders, but 3 does not give a remainder, it goes
evenly into 9 so we can say 9 is not prime

Prime Numbers
• So remember,
– if the number is 7, as long as 6, 5, 4, 3, and 2 give a remainder,
7 is prime.
• So, in general,
– if the number is A, as long as A-1, A-2, A-3, A-4, ... 2 give a
remainder, A is prime.

Prime Numbers
• First Draft:
PROGRAM CheckPrime:
READ A;
B <- A-1;
WHILE (B != 1)
DO {KEEP CHECKING IF A/B DIVIDES EVENLY}
ENDWHILE;
IF (ANY TIME THE DIVISION WAS EVEN)
THEN Print “It is not prime”;
ELSE Print “It is prime”;
ENDIF;
END.

Prime Numbers
PROGRAM CheckPrime:
Read A;
B <- A - 1;
IsPrime <- TRUE;
WHILE (B != 1)
DO IF (A/B gives no remainder)
THEN IsPrime <- FALSE;
ENDIF;
B <- B – 1;
ENDWHILE;
IF (IsPrime = FALSE)
THEN Print “Not Prime”;
ELSE Print “Prime”;
ENDIF;
END.

Fibonacci Numbers
Damian Gordon

Fibonacci Numbers
• As seen in the Da Vinci Code:

Fibonacci Numbers
• The Fibonacci numbers are
numbers where the next number
in the sequence is the sum of the
previous two.
• The sequence starts with 1, 1,
• And then it’s 2
• Then 3
• Then 5
• Then 8
• Then 13

Leonardo Bonacci (aka Fibonacci)
• Born 1170.
• Born in Pisa, Italy
• Died 1250.
• An Italian mathematician, considered
to be "the most talented Western
mathematician of the Middle Ages".
• Introduced the sequence of Fibonacci
numbers which he used as an example
in Liber Abaci.

Fibonacci Numbers
PROGRAM FibonacciNumbers:
READ A;
FirstNum <- 1;
SecondNum <- 1;
WHILE (A != 2)
DO Total <- SecondNum + FirstNum;
FirstNum <- SecondNum;
SecondNum <- Total;
A <- A – 1;
ENDWHILE;
Print Total;
END.

• Rather than have to store every character in a file (e.g. an MP3
file), it would be great if we could find a way of reducing the
length of the file to allow it to be stored in a smaller space.
Data Compression

• Also Rather than have to send every character in a message, it
would be great if we could find a way of reducing the length of
the message to allow it to be transmitted quicker.
Data Compression

• Let’s look at an example.
The rain in Spain lies mainly in the plain
Data Compression

Data Compression
• The a total of 42 characters (including 8 spaces)

Data Compression
• Lets replace the word “the” with the number 1.

Data Compression
1 rain in Spain lies mainly in 1 plain
the =1

Data Compression
• We’ve reduced the of characters to 38.
the =1

Data Compression
• Lets replace the letters “ain” with the number 2.
the =1

Data Compression
• Lets replace the letters “ain” with the number 2.
1 r2 in Sp2 lies m2ly in 1 pl2
the =1
ain =2

Data Compression
• Lets replace the letters “in” with the number 3.
1 r2 in Sp2 lies m2ly in 1 pl2
the =1
ain =2

Data Compression
• Lets replace the letters “in” with the number 3.
1 r2 3 Sp2 lies m2ly 3 1 pl2
the =1
ain =2
in = 3

Data Compression
• Now lets say 1 means “the ”, so it’s “the” and a space
1 r2 3 Sp2 lies m2ly 3 1 pl2
the =1
ain =2
in = 3

Data Compression
• Now lets say 1 means “the ”, so it’s “the” and a space
1r2 3 Sp2 lies m2ly 3 1pl2
the =1
ain =2
in = 3

Data Compression
• Now lets say 3 means “in ”, so it’s “in” and a space
1r2 3 Sp2 lies m2ly 3 1pl2
the =1
ain =2
in = 3

Data Compression
• Now lets say 3 means “in ”, so it’s “in” and a space
1r2 3Sp2 lies m2ly 31pl2
the =1
ain =2
in = 3

Data Compression
• So that’s 24 characters for a 42 character message, not bad.
1r2 3Sp2 lies m2ly 31pl2
the =1
ain =2
in = 3

Data Compression
• Let’s try a different example.

Data Compression
• Let’s try a different example. Let’s say we are sending a list of
jobs, with each item on the list is 10 characters long.
• Bookkeeper
• Teacher---
• Porter----
• Nurse-----
• Doctor----

Data Compression
• Rather than sending the spaces we could just say how long
they are:
• Bookkeeper
• Teacher---
• Porter----
• Nurse-----
• Doctor----

Data Compression
• Rather than sending the spaces we could just say how long
they are:
• Bookkeeper
• Teacher---
• Porter----
• Nurse-----
• Doctor----
• Bookkeeper
• Teacher3-
• Porter4-
• Nurse5-
• Doctor4-

Data Compression
• We’ve gone from 50 to 42 characters:
• Bookkeeper
• Teacher---
• Porter----
• Nurse-----
• Doctor----
• Bookkeeper
• Teacher3-
• Porter4-
• Nurse5-
• Doctor4-

PROGRAM CompressExample:
Get Current Character;
WHILE (NOT End_of_Line)
DO Get Next Character;
IF (Current Character != Next Character)
THEN Get next char, and set current to next;
Write out Current Character;
ELSE
Keep looping while the characters match;
Keep counting;
Get next char, and set current to next;
When finished write out Counter;
Write out Current Character;
Reset Counter;
ENDIF;
ENDWHILE;
END.

PROGRAM CompressExample:
char Current_Char, Next_char;
Current_Char <- Get_char();
WHILE (NOT End_of_Line)
DO Next_Char <- Get_char();
IF (Current_Char != Next_char)
THEN Current_Char <- Next_Char;
Next_Char <- Get_char();
Write out Current_Char;
ELSE
WHILE (Current_Char = Next_char)
DO Counter <- Counter + 1;
Current_Char <- Next_Char;
Next_Char <- Get_char();
ENDWHILE;
Write out Counter, Current_Char;
Counter <- 0;
ENDIF;
ENDWHILE;
END.

Data Compression
• Or let’s imagine we are sending a list of house prices.
• 350000
• 600000
• 550000
• 2100000
• 3000000

Data Compression
• Now let’s use the # to indicate number of zeros:
• 350000
• 600000
• 550000
• 2100000
• 3000000

Data Compression
• Now let’s use the # to indicate number of zeros:
• 350000
• 600000
• 550000
• 2100000
• 3000000
• 35#4
• 6#5
• 55#4
• 21#5
• 3#6

Data Compression
• We’ve gone from 32 characters to 18 characters:
• 350000
• 600000
• 550000
• 2100000
• 3000000
• 35#4
• 6#5
• 55#4
• 21#5
• 3#6

Data Compression
• Let’s think about images.
• Let’s say we are trying to display the letter ‘A’

Data Compression
• We could encode this as:
• WWWBBWWW
• WWBWWBWW
• WBWWWWBW
• WBWWWWBW
• WBBBBBBW
• WBWWWWBW
• WBWWWWBW
• WWWWWWWW

Data Compression
• We could compress this to:
• WWWBBWWW
• WWBWWBWW
• WBWWWWBW
• WBWWWWBW
• WBBBBBBW
• WBWWWWBW
• WBWWWWBW
• WWWWWWWW

Data Compression
• We could compress this to:
• WWWBBWWW
• WWBWWBWW
• WBWWWWBW
• WBWWWWBW
• WBBBBBBW
• WBWWWWBW
• WBWWWWBW
• WWWWWWWW
• 3W2B3W
• 2WB2WB2W
• WB4WBW
• WB4WBW
• W6BW
• WB4WBW
• WB4WBW
• 8W

Data Compression
• From 64 characters to 44 characters:
• WWWBBWWW
• WWBWWBWW
• WBWWWWBW
• WBWWWWBW
• WBBBBBBW
• WBWWWWBW
• WBWWWWBW
• WWWWWWWW
• 3W2B3W
• 2WB2WB2W
• WB4WBW
• WB4WBW
• W6BW
• WB4WBW
• WB4WBW
• 8W

Data Compression
• We call this “run-length encoding” or RLE.

Data Compression
• Now let’s add one more rule.

Data Compression
• Now let’s add one more rule.
• Let’s imagine if we send the number ‘0’ it means repeat the
previous line.

Data Compression
• So now we had:
• WWWBBWWW
• WWBWWBWW
• WBWWWWBW
• WBWWWWBW
• WBBBBBBW
• WBWWWWBW
• WBWWWWBW
• WWWWWWWW
• 3W2B3W
• 2WB2WB2W
• WB4WBW
• WB4WBW
• W6BW
• WB4WBW
• WB4WBW
• 8W

Data Compression
• And we get:
• WWWBBWWW
• WWBWWBWW
• WBWWWWBW
• WBWWWWBW
• WBBBBBBW
• WBWWWWBW
• WBWWWWBW
• WWWWWWWW
• 3W2B3W
• 2WB2WB2W
• WB4WBW
• WB4WBW
• W6BW
• WB4WBW
• WB4WBW
• 8W
• 3W2B3W
• 2WB2WB2W
• WB4WBW
• 0
• W6BW
• WB4WBW
• 0
• 8W

Data Compression
• Going from 64 to 44 to 34 characters:
• WWWBBWWW
• WWBWWBWW
• WBWWWWBW
• WBWWWWBW
• WBBBBBBW
• WBWWWWBW
• WBWWWWBW
• WWWWWWWW
• 3W2B3W
• 2WB2WB2W
• WB4WBW
• WB4WBW
• W6BW
• WB4WBW
• WB4WBW
• 8W
• 3W2B3W
• 2WB2WB2W
• WB4WBW
• 0
• W6BW
• WB4WBW
• 0
• 8W

Data Compression
• For most images, the lines are repeated frequently, so you can
get massive savings from RLE.

Modularisation
• Let’s imagine we had code as follows:

Modularisation
# Python program to mail merger
# Names are in the file names.txt
# Body of the mail is in body.txt
# open names.txt for reading
with open("names.txt",'r',encoding = 'utf-8') as names_file:
# open body.txt for reading
with open("body.txt",'r',encoding = 'utf-8') as body_file:
# read entire content of the body
body = body_file.read()
# iterate over names
for name in names_file:
mail = "Hello "+name+body
# write the mails to individual files
with open(name.strip()+".txt",'w',encoding = 'utf-8') as mail_file:
mail_file.write(mail)
# Python program to mail merger
# Names are in the file names.txt
# Body of the mail is in body.txt
# open names.txt for reading
with open("names.txt",'r',encoding = 'utf-8') as names_file:
# open body.txt for reading
with open("body.txt",'r',encoding = 'utf-8') as body_file:
# read entire content of the body
body = body_file.read()
# iterate over names
for name in names_file:
mail = "Hello "+name+body
# write the mails to individual files
with open(name.strip()+".txt",'w',encoding = 'utf-8') as mail_file:
mail_file.write(mail)

Modularisation
• And some bits of the code are repeated a few times

Modularisation
• It would be good if there was some way we could wrap
up frequently used commands into a single package, and
instead of having to rewrite the same code over and over
again, we could just call the package name.
• We can call these packages methods or functions
• (or subroutines or procedures)

Modularisation
• Let’s revisit our prime number algorithm again:

Modularisation
PROGRAM CheckPrime:
Read A;
B <- A - 1;
IsPrime <- TRUE;
WHILE (B != 1)
ENDIF;
B <- B – 1;
ENDWHILE;
IF (IsPrime = FALSE)
ENDIF;
END.

Modularisation
• There’s two parts to the program:

Modularisation
• The first part checks if it’s prime…
• The second part just prints out the result…

Modularisation
• So we can create a module from the checking bit:

Modularisation
MODULE PrimeChecker:
Read A;
B <- A - 1;
IsPrime <- TRUE;
WHILE (B != 1)
ENDIF;
B <- B – 1;
ENDWHILE;
RETURN IsPrime;
END.

Modularisation
• Let’s remind ourselves of what the algorithm was initially.

Modularisation
• Now that we have a module to do the check we can
rewrite as follows:

Modularisation
PROGRAM CheckPrime:
IF (PrimeChecker = FALSE)
ENDIF;
END.

Modularisation
• Modularisation make life easier for a lot of reasons:
– It easier for someone else to understand how the code works
– It makes team programming a lot easier, different programmers
can work on different methods
– Can improve the quality of the code
– Can reuse the same code over and over again (“don’t reinvent
the wheel”).

Modularisation
• If we were writing programs about primes, it would be
useful to have a pre-packaged prime test, e.g.
• If we were writing a program to explore Goldbach's
conjecture, that all even integers are sums of two primes,
if would be useful.
• Also if we were exploring twin primes, which are prime
numbers that has a gap of two, (3, 5), (5, 7), (11, 13), (17,
19), (29, 31), (41, 43), (59, 61), (71, 73), (101, 103), (107,
109), (137, 139), it would be useful.

Software Testing
Damian Gordon

• Why do pilots bother doing pre-flight checks when
the chances are that the plane is working fine?
Question

• Software testing is an investigate process to measure the quality of
software.
• Test techniques include, but are not limited to, the process of
executing a program or application with the intent of finding
software bugs.
Software Testing

Software Testing
• How is a software system built?
– Customer contacts an I.T. Company and requests that a software
system be created
– The customer works with an analyst to define a design of the
software system
– The design is given to developers to build the software system
– The developed system is given to software testers to check if it is OK
– The system is handed over to the customers

• The IBM Automatic Sequence
Controlled Calculator (ASCC), called
the Mark I by Harvard University was
an electro-mechanical computer.
• It was devised by Howard H. Aiken,
built at IBM and shipped to Harvard in
February 1944.
• It began computations for the U.S.
Navy Bureau of Ships in May and was
officially presented to the university
on August 7, 1944.
• It was very reliable, much more so
than early electronic computers.
Harvard Mark I

• Howard Hathaway Aiken
• Born March 8, 1900
• Died March 14, 1973
• Born in Hoboken, New Jersey
• He envisioned an electro-
mechanical computing device that
could do much of the tedious work
for him.
• With help from Grace Hopper and
funding from IBM, the machine
was completed in 1944.
Howard H. Aiken

• Rear Admiral Grace Murray
Hopper
• Born December 9, 1906
• Died January 1, 1992
• Born in New York City, New York
• Computer pioneer who
developed the first compiler for
a computer programming
language
Grace Hopper

• Grace Hopper served at the Bureau of Ships Computation
Project at Harvard University working on the computer
programming staff.
• A moth was found trapped between points at Relay #70, Panel
F, of the IBM Harvard Mark II Aiken Relay Calculator while it
was being tested at Harvard University, 9 September 1945.
The First Bug

• The operators affixed the moth to the computer log, with the
entry: "First actual case of bug being found".
• Grace Hopper said that they "debugged" the machine, thus
introducing the term "debugging a computer program".
The First Bug

Bugs a.k.a. …
• Defect
• Fault
• Problem
• Error
• Incident
• Anomaly
• Variance
• Failure
• Inconsistency
• Product Anomaly
• Product Incidence

Eras of Testing
Years Era Description
1945-1956 Debugging orientated In this era, there was no clear difference between testing and
debugging.
1957-1978 Demonstration orientated In this era, debugging and testing are distinguished now - in
this period it was shown, that software satisfies the
requirements.
1979-1982 Destruction orientated In this era, the goal was to find errors.
1983-1987 Evaluation orientated In this era, the intention here is that during the software
lifecycle a product evaluation is provided and measuring
quality.
1988- Prevention orientated In the current era, tests are used to demonstrate that
software satisfies its specification, to detect faults and to
prevent faults.

• Black box testing treats the software as a "black box"—without any
knowledge of internal implementation.
• Black box testing methods include:
– equivalence partitioning,
– boundary value analysis,
– all-pairs testing,
– fuzz testing,
– model-based testing,
– exploratory testing and
– specification-based testing.
Black Box Testing

• White box testing is when the tester has access to the internal
data structures and algorithms including the code that
implement these.
• White box testing methods include:
– API testing (application programming interface) - testing of the
application using public and private APIs
– Code coverage - creating tests to satisfy some criteria of code
coverage (e.g., the test designer can create tests to cause all
statements in the program to be executed at least once)
– Fault injection methods - improving the coverage of a test by
introducing faults to test code paths
– Mutation testing methods
– Static testing - White box testing includes all static testing
White Box Testing

• Grey Box Testing involves having knowledge of internal
data structures and algorithms for purposes of
designing the test cases, but testing at the user, or
black-box level.
• The tester is not required to have a full access to the
software's source code.
• Grey box testing may also include reverse engineering
to determine, for instance, boundary values or error
messages.
Grey Box Testing

• Lowest level functions and procedures in isolation
• Each logic path in the component specifications
Unit Testing

• Tests the interaction of all the related components of a module
• Tests the module as a stand-alone entity
Module Testing

• Tests the interfaces between the modules
• Scenarios are employed to test module interaction
Subsystem Testing

• Tests interactions between sub-systems and components
• System performance
• Stress
• Volume
Integration Testing

• Tests the whole system with live data
• Establishes the ‘validity’ of the system
Acceptance Testing

• Program testing and fault detection can be aided significantly by
testing tools and debuggers. Testing/debug tools include features
such as:
– Program monitors, permitting full or partial monitoring of program code
(more on the next slide).
– Formatted dump or symbolic debugging, tools allowing inspection of
program variables on error or at chosen points.
– Automated functional GUI testing tools are used to repeat system-level
tests through the GUI.
– Benchmarks, allowing run-time performance comparisons to be made.
– Performance analysis (or profiling tools) that can help to highlight hot
spots and resource usage.
Testing Tools

• Program monitors, permitting full or partial monitoring of
program code including:
– Instruction set simulator, permitting complete instruction level
monitoring and trace facilities
– Program animation, permitting step-by-step execution and
conditional breakpoint at source level or in machine code
– Code coverage reports
Testing Tools

Data Structures:
Arrays
Damian Gordon

Arrays
• Imagine we had to record the age of everyone in the class, we
could do it declaring a variable for each person.

Arrays
• Imagine we had to record the age of everyone in the class, we
could do it declaring a variable for each person.
• E.g.
– Integer Age1;
– Integer Age2;
– Integer Age3;
– Integer Age4;
– Integer Age5;
– etc.

Arrays
• But if there was a way to collect them all together, and declare
a single special variable for all of them, that would be quicker.
• We can, and the special variable is called an ARRAY.

Arrays
• We declare an array as follows:
• Integer Age[40];

Arrays
• Which means we declare 40 integer variables, all can be
accessed using the Age name.
……..…

Arrays
• Which means we declare 40 integer variables, all can be
accessed using the Age name.
0 1 2 3 4 5 6 397 ……..… 38

Arrays
44 23 42 33 16 - - 34 8218 ……..… 34
0 1 2 3 4 5 6 7 38 39

Arrays
44 23 42 33 16 - - 34 8218 ……..… 34
0 1 2 3 4 5 6 7 38 39
• So if I do:
• PRINT Age[0];
• We will get:
• 44

Arrays
44 23 42 33 16 - - 34 8218 ……..… 34
0 1 2 3 4 5 6 7 38 39
• So if I do:
• PRINT Age[2];
• We will get:
• 42

Arrays
44 23 42 33 16 - - 34 8218 ……..… 34
0 1 2 3 4 5 6 7 38 39
• So if I do:
• PRINT Age[39];
• We will get:
• 82

Arrays
44 23 42 33 16 - - 34 8218 ……..… 34
0 1 2 3 4 5 6 7 38 39
• So if I do:
• PRINT Age[40];
• We will get:
• Array Out of Bounds Exception

Arrays
44 23 42 33 16 - - 34 8218 ……..… 34
0 1 2 3 4 5 6 7 38 39
• We notice that Age[5] is blank.
• If I want to put a value into it (e.g. 54), I do:
• Age[5] <- 54;

Arrays
44 23 42 33 16 54 34 8218 ……..… 34
0 1 2 3 4 5 6 7 38 39
• We notice that Age[5] is blank.
• If I want to put a value into it (e.g. 54), I do:
• Age[5] <- 54;

Arrays
• We can think of an array as a series of pigeon-holes:

Array
9
10
11
12
13
14
15
16
18
19
1 2
3 4
5
6
7 8
0
17
20

Arrays
• If we look at our array again:
44 23 42 33 16 54 34 8218 ……..… 34
0 1 2 3 4 5 6 7 38 39

Arrays
• If we wanted to add 1 to everyone’s age:
44 23 42 33 16 54 34 8218 ……..… 34
0 1 2 3 4 5 6 7 38 39
+1 +1 +1 +1 +1 +1 +1 +1 +1 +1

Arrays
• If we wanted to add 1 to everyone’s age:
45 24 43 34 17 55 35 8319 ……..… 35
0 1 2 3 4 5 6 7 38 39

Arrays
• We could do it like this:
PROGRAM Add1ToAge:
Age[0] <- Age[0] + 1;
Age[1] <- Age[1] + 1;
Age[2] <- Age[2] + 1;
Age[3] <- Age[3] + 1;
Age[4] <- Age[4] + 1;
Age[5] <- Age[5] + 1;
………………………………………………………
Age[38] <- Age[38] + 1;
Age[39] <- Age[39] + 1;
END.

Arrays
• An easier way of doing it is:
PROGRAM Add1ToAge:
N <- 0;
WHILE (N != 40)
DO Age[N] <- Age[N] + 1;
N <- N + 1;
ENDWHILE;
END.

Arrays
• Or:
PROGRAM Add1ToAge:
FOR N IN 0 TO 39
DO Age[N] <- Age[N] + 1;
ENDFOR;
END.

Arrays
• If we want to add up all the values in the array:

Arrays
• If we want to add up all the values in the array:
PROGRAM TotalOfArray:
integer Total <- 0;
FOR N IN 0 TO 39
DO Total <- Total + Age[N];
ENDFOR;
END.

Arrays
• So the average age is:

Arrays
• So the average age is:
PROGRAM AverageOfArray:
integer Total <- 0;
FOR N IN 0 TO 39
ENDFOR;
PRINT Total/40;
END.

Arrays
• We can add another variable:
integer Total <- 0;
integer ArraySize <- 40;
FOR N IN 0 TO 39
ENDFOR;
PRINT Total/40;
END.

Arrays
integer Total <- 0;
FOR N IN 0 TO 39
ENDFOR;
PRINT Total/ArraySize;
END.

Arrays
integer Total <- 0;
FOR N IN 0 TO ArraySize-1
ENDFOR;
END.

• So now if the Array size changes, we just need to change the value
of one variable (ArraySize).
integer Total <- 0;
ENDFOR;
END.
Arrays

Arrays
• We can also have an array of real numbers:

Arrays
• We can also have an array of real numbers:
22.00
0
65.50
1
-2.20
2
78.80 54.00 -3.33 0.00 47.65
3 4 5 6 7

• What if we wanted to check who has a balance less than zero :
PROGRAM LessThanZeroBalance:
DO IF BankBalance[N] < 0
THEN PRINT “User” N “is in debt”;
ENDIF;
ENDFOR;
END.
Arrays

Arrays
• We can also have an array of characters:

Arrays
• We can also have an array of characters:
G A T T C C A AG ……..… A
0 1 2 3 4 5 6 7 38 39

• What if we wanted to count all the ‘G’ in the Gene Array:
Arrays
G A T T C C A AG ……..… A
0 1 2 3 4 5 6 7 38 39

• What if we wanted to count all the ‘G’ in the Gene Array:
integer G-Count <- 0;
DO IF Gene[N] = ‘G’
THEN G-Count <- G-Count + 1;
ENDIF;
ENDFOR;
PRINT “The total G count is:” G-Count;
END.
Arrays

• What if we wanted to count all the ‘A’ in the Gene Array:
integer A-Count <- 0;
DO IF Gene[N] = ‘A’
THEN A-Count <- A-Count + 1;
ENDIF;
ENDFOR;
PRINT “The total A count is:” A-Count;
END.
Arrays

Arrays
• We can also have an array of strings:

Arrays
• We can also have an array of strings:
Dog
0
Cat
1
Dog
2
Bird Fish Fish Cat Cat
3 4 5 6 7

Arrays
• We can also have an array of booleans:

Arrays
• We can also have an array of booleans:
TRUE
0
TRUE
1
FALSE
2
TRUE FALSE TRUE FALSE FALSE
3 4 5 6 7

Google Search Algorithm
• First Draft:
PROGRAM GoogleCollect:
NextLink <- random website;
WHILE (NextLink != NULL)
DO IF (No copy of this page in google collection)
THEN copy this page into google collection;
ENDIF;
NextLink <- Next link on this page;
ENDWHILE;
END.

Google Search Algorithm
• First Draft:
PROGRAM GoogleSearch:
READ SearchString;
Get First Webpage from collection;
WHILE (Webpages Left to Search)
DO IF (SearchString IN Current-Web-Page)
THEN Put this page on the list;
ENDIF;
Get Next Webpage;
ENDWHILE;
Order the list according to PageRank;
END.

Database Searching
Damian Gordon

Searching
• Oracle
• DB2
• MySQL
• SQL Server
• PostgreSQL

Searching
• Let’s remember our integer array from before:

Searching
44 23 42 33 16 54 34 8218 ……..… 34
0 1 2 3 4 5 6 7 38 39

Searching
• Let’s say we want to find everyone who is aged 18:

Searching: Sequential Search
• This is a SEQUENTIAL SEARCH.
• If the array is 40 characters long, it will take 40 checks to
complete. If the array is 1000 characters long, it will take 1000
checks to complete.

• Here’s how we could do it:
PROGRAM SequentialSearch:
integer SearchValue <- 18;
DO IF Age[N] = SearchValue
THEN PRINT “User “ N “is 18”;
ENDIF;
ENDFOR;
END.
Searching: Sequential Search

Searching: Binary Search
• If the data is sorted, we can do a BINARY SEARCH

16 18 23 23 33 33 34 8243 ……..… 78
0 1 2 3 4 5 6 7 38 39

• This means we jump to the middle of the array, if the value
being searched for is less than the middle value, all we have to
do is search the first half of that array.

• This means we jump to the middle of the array, if the value
being searched for is less than the middle value, all we have to
do is search the first half of that array.
• We search the first half of the array in the same way, jumping
to the middle of it, and repeat this.

• The BINARY SEARCH just takes five checks to find the right
value in an array of 40 elements. For an array of 1000 elements
it will take 11 checks.
• This is much faster than if we searched through all the values.

PROGRAM BinarySearch:
integer First <- 0;
integer Last <- 40;
boolean IsFound <- FALSE;
WHILE First <= Last AND IsFound = FALSE
DO Index = (First + Last)/2;
IF Age[Index] = SearchValue
THEN IsFound <- TRUE;
ELSE IF Age[Index] > SearchValue
THEN Last <- Index-1;
ELSE First <- Index+1;
ENDIF;
ENDIF;
ENDWHILE;
END.

Simple Statistics on Arrays
Damian Gordon

Minimum Value in Array
– Find the minimum value in an array

PROGRAM MinimumValue:
MinValSoFar <- Age[0];
DO IF MinValSoFar > Age[N]
THEN MinValSoFar <- Age[N];
ENDIF;
ENDFOR;
PRINT MinValSoFar;
END.
Minimum Value in Array

Maximum Value in Array
– Find the maximum value in an array

PROGRAM MaximumValue:
MaxValSoFar <- Age[0];
DO IF MaxValSoFar < Age[N]
THEN MaxValSoFar <- Age[N];
ENDIF;
ENDFOR;
PRINT MaxValSoFar;
END.
Maximum Value in Array

Average Value in Array
– Find the average value of an array

PROGRAM AverageValue:
Integer Total <- 0;
ENDFOR;
END.
Average Value in Array

Standard Deviation of an Array
– Find the standard deviation of an array

• First Draft
PROGRAM StandardDeviationValue:
GET AVERAGE OF ARRAY;
TotalSDNum <- 0;
DO SDNum <-(Age[N]-ArrayAvg)*(Age[N]-ArrayAvg)
TotalSDNum <- TotalSDNum + SDNum;
ENDFOR;
Print SquareRoot(TotalSDNum/ArraySize-1);
END.

• Here’s the final version:
PROGRAM StandardDeviationValue:
Integer TotalAvg <- 0;
DO TotalAvg <- TotalAvg + Age[N];
ENDFOR;
AverageValue <- TotalAvg/ArraySize;
TotalSDNum <- 0;
DO SDNum <-(Age[N]-AverageValue)*(Age[N]- AverageValue)
TotalSDNum <- TotalSDNum + SDNum;
ENDFOR;
Print SquareRoot(TotalSDNum/ArraySize-1);
END.

Sorting
• Let’s remember our integer array from before:

Sorting
44 23 42 33 16 54 34 18
0 1 2 3 4 5 6 7

Sorting
44 23 42 33 16 54 34 18
0 1 2 3 4 5 6 7
• How do we sort the data, in other words, get it into this order:

Sorting
44 23 42 33 16 54 34 18
0 1 2 3 4 5 6 7
• How do we sort the data, in other words, get it into this order:
16 18 23 33 34 42 44 54
0 1 2 3 4 5 6 7

Sorting
• As humans, we can sort the array just by inspection (just be
looking at it), but if the array was 100,000 elements long it
would be more of a challenge for us.

Sorting: Bubble Sort
• The simplest algorithm for sort an array is called BUBBLE SORT.

• It works as follows:

• It works as follows for an array of size N:
– Look at the first and second element
• Are they in order?
• If so, do nothing
• If not, swap them around
– Look at the second and third element
• Do the same
– Keep doing this until you get to the end of the array
– Go back to the start again keep doing this whole process for N times.

• Lets look at the swapping bit
– if I wanted to swap two values, the following won’t work:
Age[0] <- Age[1];
Age[1] <- Age[0];
– Why not?

• Lets assume Age[0]=44, and Age[1]=23, if we do the following:
Age[0] <- Age[1];
Age[1] <- Age[0];
– What happens is:
Age[0] <- Age[1];
Age[1] <- Age[0];

Age[0] <- Age[1];
Age[1] <- Age[0];
Age[0] <- Age[1];
Age[1] <- Age[0];
23

Age[0] <- Age[1];
Age[1] <- Age[0];
Age[0] <- Age[1];
Age[1] <- Age[0];
2323

Age[0] <- Age[1];
Age[1] <- Age[0];
Age[0] <- Age[1];
Age[1] <- Age[0];
2323
23

Age[0] <- Age[1];
Age[1] <- Age[0];
Age[0] <- Age[1];
Age[1] <- Age[0];
2323
2323

• We need an extra variable to make this work:

• Lets call it Temp_Value.

Temp_Value <- Age[1];

Age[1] <- Age[0];

Age[1] <- Age[0];
Age[0] <- Temp_Value;

Age[1] <- Age[0];
23

Age[1] <- Age[0];
2323

Age[1] <- Age[0];
2323
44

Age[1] <- Age[0];
2323
4444

Age[1] <- Age[0];
2323
4444
23

Age[1] <- Age[0];
2323
4444
2323

• Let’s wrap an IF statement around this:
IF (Age[1] < Age[0])
THEN Temp_Value <- Age[1];
Age[1] <- Age[0];
ENDIF;

• And in general:
IF (Age[N+1] < Age[N])
THEN Temp_Value <- Age[N+1];
Age[N+1] <- Age[N];
Age[N] <- Temp_Value;
ENDIF;

• Let’s replace “N” with “Index”
IF (Age[Index+1] < Age[Index])
THEN Temp_Value <- Age[Index+1];
Age[Index+1] <- Age[Index];
Age[Index] <- Temp_Value;
ENDIF;

• To get from one end of the array to another:
FOR Index IN 0 TO N-2
DO IF (Age[Index+1] < Age[Index])
ENDIF;
ENDFOR;

• Does this mean we have the array sorted?

• Does this mean we have the array sorted?
• No

44 23 42 33 16 54 34 18
0 1 2 3 4 5 6 7

23 44 42 33 16 54 34 18
0 1 2 3 4 5 6 7

23 42 44 33 16 54 34 18
0 1 2 3 4 5 6 7

23 42 33 44 16 54 34 18
0 1 2 3 4 5 6 7

23 42 33 16 44 54 34 18
0 1 2 3 4 5 6 7

23 42 33 16 44 34 54 18
0 1 2 3 4 5 6 7

23 42 33 16 44 34 18 54
0 1 2 3 4 5 6 7

23 42 33 16 44 34 18 54
0 1 2 3 4 5 6 7
• So what happened?

23 42 33 16 44 34 18 54
0 1 2 3 4 5 6 7
• We have moved the largest value (54) into the correct position.

• Let’s do it again:

23 42 16 33 44 34 18 54
0 1 2 3 4 5 6 7

23 42 16 33 34 44 18 54
0 1 2 3 4 5 6 7

23 42 16 33 34 18 44 54
0 1 2 3 4 5 6 7

• We have moved the second largest value (44) into the correct
position.
23 42 16 33 34 18 44 54
0 1 2 3 4 5 6 7

23 16 42 33 34 18 44 54
0 1 2 3 4 5 6 7

23 16 33 42 34 18 44 54
0 1 2 3 4 5 6 7

23 16 33 34 42 18 44 54
0 1 2 3 4 5 6 7

23 16 33 34 18 42 44 54
0 1 2 3 4 5 6 7

23 16 33 34 18 42 44 54
0 1 2 3 4 5 6 7
• We have moved the third largest value (42) into the correct
position.

16 23 33 34 18 42 44 54
0 1 2 3 4 5 6 7

16 23 33 18 34 42 44 54
0 1 2 3 4 5 6 7

16 23 33 18 34 42 44 54
0 1 2 3 4 5 6 7
• We have moved the fourth largest value (34) into the correct
position.

16 23 18 33 34 42 44 54
0 1 2 3 4 5 6 7

16 23 18 33 34 42 44 54
0 1 2 3 4 5 6 7
• We have moved the fifth largest value (33) into the correct
position.

16 18 23 33 34 42 44 54
0 1 2 3 4 5 6 7

16 18 23 33 34 42 44 54
0 1 2 3 4 5 6 7
• We have moved the sixth largest value (23) into the correct
position.

• Let’s not bother!

• Let’s not bother!
• It’s sorted!

• So we need two loops:

• So we need two loops:
FOR Outer-Index IN 0 TO N-1
DO FOR Index IN 0 TO N-2
ENDIF;
ENDFOR;
ENDFOR;

PROGRAM BubbleSort:
Integer Age[8] <- {44,23,42,33,16,54,34,18};
DO FOR Index IN 0 TO N-2
ENDIF;
ENDFOR;
ENDFOR;
END.

Sorting:
Optimising Bubblesort
Damian Gordon

• If we look at the bubble sort algorithm again:

• The bubble sort pushes the largest values up to the top of the
array.

• So each time around the loop the amount of the array that is
sorted is increased, and we don’t have to check for swaps in
the locations that have already been sorted.
• So we reduce the checking of swaps by one each time we do a
pass of the array.

PROGRAM BubbleSort:
Integer Age[8] <- {44,23,42,33,16,54,34,18};
ReducingIndex <- N-2;
DO FOR Index IN 0 TO ReducingIndex
ENDIF;
ENDFOR;
ReducingIndex <- ReducingIndex – 1;
ENDFOR;
END.

• Also, what if the data is already sorted?
• We should check if the program has done no swaps in one
pass, and if t doesn’t that means the data is sorted.
• So even if the data started unsorted, as soon as the data gets
sorted we want to exit the program.

Sorting: Bubble SortPROGRAM BubbleSort:
Integer Age[8] <- {44,23,42,33,16,54,34,18};
DidSwap <- FALSE;
DidSwap <- TRUE;
ENDIF;
ENDFOR;
IF (DidSwap = FALSE)
THEN EXIT;
ENDIF;
ENDFOR;
END.

PROGRAM BubbleSort:
Integer Age[8] <- {44,23,42,33,16,54,34,18};
DidSwap <- FALSE;
DidSwap <- TRUE;
ENDIF;
ENDFOR;
IF (DidSwap = FALSE)
THEN EXIT;
ENDIF;
ENDFOR;
END.

• The Swap function is very useful so we should have that as a
method as follows:

MODULE SWAP[A,B]:
Integer Temp_Value
Temp_Value <- B;
B <- A;
A <- Temp_Value;
RETURN A, B;
END.

A complete course in Program Design using Pseudocode

A complete course in Program Design using Pseudocode

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