Contents
Section 2: Problem-solving and program design ....................................................................................... 2
Objective 2.1:
Outline the steps in problem solving. ........................................................................... 2
Objective 2.2:
Decompose a simple problem into its significant parts. ............................................... 2
Objective 2.3:
Distinguish between variables and constants............................................................... 4
Objective 2.4:
Use appropriate data types........................................................................................... 4
Objective 2.5:
Explain the concept of algorithms ............................................................................... 7
Objective 2.6:
Identify ways of representing algorithms .................................................................... 7
Objective 2.7:
Develop algorithms to solve simple problems ............................................................. 7
Objective 2.8
Test algorithms for correctness ................................................................................. 23
Section 2:
Problem-solving and program design
Objective 2.1:
Outline the steps in problem solving.
Objective 2.2:
Decompose a simple problem into its significant parts.
Content
Definition of the problem; propose and evaluate solutions; Determination of the
most efficient solution; develop and represent algorithm; test and validate the
solution; decompose a problem into input, processing, output and storage.
The steps in problem solving
The steps in problem solving are:
1. Definition of the problem
2. Propose and evaluate solutions
3. Determination of the most efficient solution
4. Develop and represent algorithm
5. Test and validate the solution
Definition of the problem
Defining the problem is the first step towards solving a problem. It is the most important step
since it leads to a clearer understanding of what is given and what is required. If the
programmer does not fully understand what is required, then he/she cannot produce the
desired solution. This step involves decomposing the problem into three key components:
1. Inputs: what is given (source data)
2. Outputs: the expected results
3. Processing: the tasks/actions that must be performed
To do this, a defining diagram is used. A defining diagram is a table with three columns labeled
to represent the components.
Inputs can be identified by the keywords that precede them. These are: GIVEN, ENTER, READ,
or ACCEPT.
Outputs can be identified by the keywords: PRINT, DISPLAY, FIND, PRODUCE, or OUTPUT.
Processing can be determined by asking;
“What do I have to do with the inputs in order to produce the desired output?” The
actions/tasks determined must be listed in a logical sequential order.
Example:
Given two numbers find and print their product.
Defining diagram:
INPUT
2 numbers say num1, num2
PROCESSING
1. Read two numbers
OUTPUT
PRODUCT
2. Find the product
3. Print the product
Proposing and Evaluating Solutions
Proposing a solution
The second step in solving a problem is ‘Proposing and Evaluating Solutions’. After defining the
problem, you would know what needs to be done. In this step, you figure out how to do it,
bearing in mind that a problem can have many different solutions. Initially, go through each
step of the solution manually (by hand) using sample input data to see if the solution provides
the desired outcome. Then review it to see how you can make it more efficient. After
completing the manual solution to the problem the next step is to write the solution as a
sequence of instructions.
Example:
Start
Read first number, call it num1
Read second number, call it num2
Multiply num1 by num2
Print product
Stop
Objective 2.3:
Distinguish between variables and constants
Variables
In processing data, values that are manipulated need to be stored in a memory location.
Because of the large number of storage location in memory, we need to have an identifier to
label each location. Depending on if the value changes during the execution of the instructions,
it is called a variable. If the value does not change it is called a constant.
Choosing Identifier Names
Choose names that reflect the kind of data that is being stored. It helps any reader to
understand the solution better, if the identifier reflects what they store. For example, the
variable name product indicates that the value stored in that memory location is a product. If
instead, X was used, this does not convey the contents of that memory location to the reader of
the solution, and it will make debugging and program maintenance more difficult. Most
programming languages have strict rules regarding identifier names, for example, in Pascal,
they must begin with a letter or underscore; they can be a combination of letters and digits or
underscore and the length cannot exceed 31 characters.
Objective 2.4:
Use appropriate data types
Each piece of data stored in memory is of a specific data type. In programming there are five (5)
basic data types.
Data Type
Description
Examples
Integer
Positive and negative whole numbers including zero
23,-45, 0
Real
All numbers including fractions
15.7, -19.25, 8
Character
Any key on the keyboard
‘A’, ‘z’, ‘8’, ‘?’
String
Characters put together
‘Hello world’, ‘Marcus’
Boolean
True or False
TRUE or FALSE
Evaluating solutions
There are many ways to solve some problems. Usually, the initial solution may not be the most
efficient solution. As such, in solving any problem you must explore alternative solutions to
come up with the best (most efficient) solution.
Some points to consider when developing alternative solutions are:
 Can the result be derived differently?
 Can the solution be made more general? E.g. Would it work if there were more inputs –
100 numbers instead of 3 numbers?
 Can the solution be used for a similar problem? E.g. To find the average mark in the
results from a test or average temperature for the month.
 Can you reduce the number of steps and still maintain the logic?
 Can you make it more robust? Would it work properly if incorrect data is entered?
E.g. Given three numbers find and print their average.
Initial solution:
Start
Get first number, call it num1
Get second number, call it num2
Get third number, call it num3
Add num1 to num2 to num3, storing in sum
Divide sum by 3, storing in average
Print average
Stop
First alternative solution:
Start
Get num1, num2, num3
Sum = num1 + num2 + num3
Average = Sum ÷ 3
Print average
Stop
N.B. two steps were removed but the logic is maintained.
Second alternative solution:
Start
Get num1, num2, num3
Average = (num1 + num2 + num3) ÷ 3
Print average
Stop
N.B. One more step and a variable is removed but the logic is maintained. The solution is more
efficient since less memory is required, less CPU time is required and the program executes
faster since there are fewer instructions to be executed.
Third alternative solution:
Start
N= 3
Sum = 0
Repeat N times
Get number
Add number to sum
End Repeat
Average = sum ÷ N
Print Average
Stop
N.B. This solution is more general. It can easily be adapted to find the average of any amount of
numbers by changing the value of N. It utilizes less memory since a single variable is used to
hold every number that will be entered.
Initializing variables
In the last solution given above, the variable sum was given the value 0. This is referred to as
initialization. This means giving the variable an initial or starting value. Sometimes it is
necessary to give variables a starting value. This ensures that any data previously stored in that
memory location, from a previous operation, is erased and not used mistakenly in a new
operation.
Initialization is also necessary whenever a value needs to be incremented (added to by a value,
usually one). For example in adding the numbers entered in the solution above. The statement
“Add number to sum” is translated to the computer as “sum = sum + num” therefore if the
variable sum has a value stored from a previous operation, the resultant value of sum would be
incorrect.
Use the following rule to determine when to initialize a variable:
If a variable appears on the right hand side of an assignment statement before a value
is assigned to it, then it must be assigned an initial value before the assignment
statement is executed.
Determining the Most Efficient Solution
After evaluating and refining the solution, the next step is to choose the most efficient solution.
Use the following attributes to determine the most efficient solution:
1. It should be maintainable (i.e. easy to read and upgrade, if necessary).
2. Should use memory efficiently
3. Should be robust (be able to check for invalid input data)
Objective 2.5:
Explain the concept of algorithms
Objective 2.6:
Identify ways of representing algorithms
Objective 2.7:
Develop algorithms to solve simple problems
Develop and represent the solution as an algorithm
An algorithm is a sequence of precise instructions which, if followed, produces a solution to a
given problem in a finite amount of time.
Algorithms can be represented using pseudocode or a flowchart. It cannot be executed by the
computer. Pseudocode uses English–like statements that models or resembles a programming
language. A flowchart uses geometrical objects.
Algorithmic Structure
Terminator:
Declaration:
Body:
Terminator:
Start of statement(s)
Initialization of variables, if necessary
Sequence of steps
End of statement(s)
E.g.
Start
{terminator}
sum = 0
{Declaration}
count = 0
Repeat
Read num
count = count + 1
{Body}
sum = sum + num
Until count > 10
Print sum
Stop
{terminator}
Control Structures
In programming, control structures are used to represent logic. There are different types of
control structures: sequential, selection and loop (repetition). Just like a program, the body of
an algorithm is made up of various control structures.
Sequential structures include:
 Input statements: these accept data entered into the computer and store the value in
the location with the given variable name e.g.
input name
get num1, num2
read price and tax_rate
accept option
 Output statements: these display/output data that is in the computer’s memory e.g.
Output Sum
Print total_cost
Display “ Enter student’s name”
Write sum, average
 Assignment statements: gives the value on the right of the assignment operator (equal
sign) to the variable on the left of the assignment operator e.g.


N= 100
Count = 0
Answer = “END”
Calculation statements: uses the values on the right of the assignment operator and
performs mathematical operations, then assigns the result of the calculation to the
variable on the left of assignment operator e.g.
Sum = num1 + num2
Difference = Payment – bill
Average = sum ÷ 3
Prompting statements: these are used with input statements to request or notify the
user to enter data into the computer. These statements are displayed on the screen.
Prompting statements precede input instructions. E.g.
Print “Enter student name: “
Read name
Prompting statement
Selection structures include the IF-THEN or IF-THEN-ELSE statements: They perform
comparisons between values and make a decision based on the result of the comparison e.g.
 IF ( A > B) THEN
Display A
ENDIF
or

IF( age >= 50) THEN
Print “Old”
ELSE
Print “Young”
ENDIF
N.B. If the decision consists of more than one instruction statement. These statements must be
enclosed in a BEGIN and an END e.g.

IF (A > B) THEN
BEGIN
C=A+B
Print C
END
ENDIF
Comparisons are made using a condition/decision statement. A condition/decision statement is
an expression that when evaluated gives a Boolean result i.e. either TRUE or FALSE. Condition
statements use relational operators between two variables e.g.
 A>B
or between a variable and a constant e.g.

age >= 50
Relational Operators
=
Meaning
Equal to
<> or ≠
Not equal to
>
Greater than
<
Less than
>=
Greater than or equal to
<=
Less than or equal to
Boolean Operators
These are also called logical operators. They are used when a selection is based upon one or
more decisions being TRUE or FALSE. The decisions are combined using Boolean operators: OR,
AND and NOT.
If the AND operator is used both conditions must be met, in order for the total expression to be
TRUE or FALSE.
E.g.
IF (day = ‘Friday’) AND (date = 13) THEN
PRINT ‘Today is a Black Friday’
If the OR operator is used, either conditions must be met, in order for the total expression to be
TRUE or FALSE.
E.g.
IF (qualifications = ‘degree’) OR (workExperience = 5) Then
PRINT ‘Application approved’
To determine the outcome of Boolean operations, truth tables can be used. A truth table lists
all possible combinations of operands, and, for each combination, gives the value of the
expression.
E.g.
A AND B
There are two operands, A and B. Since each operand can have up to two values, there are four
combinations of A and B:
A
B
1. False
False
2. False
True
3. True
True
4. True
False
The truth table for A AND B is:
A
B
A AND B
False False
False
False
True
False
True
True
True
True
False
False
The truth table for A OR B is:
A
B
A OR B
False False
False
False
True
True
True
True
True
True
False
True
The truth table for NOT is different because it takes only one operand and has only two
combinations:
A
NOT A
False
True
True
False
Activity:
Given that t= 10, u = -3 and s = 4
If A = t > 5, B= 6 >= s, C= 0 <= u and D = s > t, evaluate
i.
A AND B = TRUE
ii.
A OR B = TRUE
iii.
D AND C = FALSE
iv.
A OR C = TRUE
v.
B OR D = TRUE
vi.
NOT A = FALSE
vii.
NOT D = TRUE
viii.
NOT C = TRUE
ix.
NOT B AND C = FALSE
x.
(NOT A) AND (NOT C) = FALSE
Loop structures include the FOR loop, WHILE loop or REPEAT loop: They allow statements to be
repeated a fixed number of times or until a condition becomes TRUE or FALSE e.g.
 FOR count = 1 to 5 DO
Print count
END FOR

WHILE (noOfItems <= 5) DO
BEGIN
Read price
noOfItems = noOfItems + 1
Total =Total + price
END
END WHILE

REPEAT
Print “I love programming”
count = count + 1
UNTIL count > 10
For each loop example given above, the number of times the instructions have to be repeated
is known. As such, it is necessary to keep track of how many times the instructions are
repeated. This is done by counting or iteration, which involves increasing the value of a counter
variable by a fixed number every time the instructions are repeated. This counter can be part of
a condition as in the FOR loop.
e.g.
FOR count = 1 to 5 DO
Print count
END FOR
Or within the body of the loop e.g. in WHILE loop and REPEAT UNTIL loop.
e.g.
WHILE (noOfItems <= 5) DO
BEGIN
Read price
noOfItems = noOfItems + 1
Total =Total + price
END
END WHILE
REPEAT
Print “I love programming”
count = count + 1
UNTIL count >= 10
In both cases, the instructions stop repeating when the value of the counter becomes equal to
a certain value. N.B. Counter variables in the WHILE and REPEAT_UNTIL loops MUST be
initialized before the counter variable is incremented (increased).
E.g.
cars = 0
counter variable is initialized to zero
WHILE cars <=10 DO
BEGIN
PRINT “ENTER model of car: “
INPUT model
cars = cars + 1
PRINT “Model # “, cars, “is “, model
END
ENDWHILE
When the number of times the instructions has to be repeated is NOT known, only the WHILE
loop or REPEAT_UNTIL loop can be used. These loops can allow instructions to be repeated
until a terminating value or sentinel value is inputted. The sentinel value causes the loop to
stop. It is a dummy value that signals the end of the data to be entered for processing.
E.g.
PRINT “ENTER model of car: “
INPUT model
WHILE model ≠ “End” DO
BEGIN
cars = cars + 1
PRINT “ENTER another model: “
INPUT model
END
ENDWHILE
PRINT “Number of cars entered is “, cars
E.g.
REPEAT
PRINT “ENTER another model: “
INPUT model
cars = cars + 1
UNTIL model = “End”
PRINT “Number of cars entered is “, cars
N.B. The sentinel or terminating value used is the string “End”.
Using the FOR loop
In this construct the counter variable is initialized when the loop is first executed and is
increased by a fixed value each time the set of instructions is executed. The syntax for the FOR
loop can be either of the following depending on the problem given:

FOR (<counter variable> = <start value> TO <end value>) DO
BEGIN
Lines of code;
END
ENDFOR
E.g.

FOR (count = 1 TO 20) DO
Writeln (count);
ENDFOR
(To make a FOR loop go in descending order)
FOR<counter variable> = <start value> DOWNTO <end value> DO
BEGIN
Lines of code;
END
ENDFOR
E.g.
FOR (count = 10 DOWNTO 1) DO
Write (count);
ENDFOR

(To make a FOR loop increment by an amount different to 1)
FOR (<counter variable> = <start value> TO <end value> STEP <incremental value>) DO
BEGIN
Lines of code;
END
ENDFOR
E.g.
FOR (count = 1 TO 21 STEP 2) DO
Write (count);
ENDFOR
Using the WHILE loop
In this construct, the condition is tested at the start of the loop. If it is TRUE, the instruction
within the WHILE and ENDWHILE are executed until the condition becomes FALSE and the loop
is exited. Statements before and after the loop are carried out once. If the condition in the
WHILE loop is FALSE, the computer skips the instructions within the loop and continues with
statements after the loop.
Using the REPEAT_UNTIL loop
In this construct, the condition is tested at the end of the loop. The instructions within the
REPEAT and UNTIL are executed until the condition becomes TRUE and the loop is exited. The
instructions within the REPEAT and UNTIL are always executed at least once. Just like the WHILE
loop, statements before and after the loop are carried out once. If after the first execution of
instructions within the REPEAT_UNTIL loop, the condition is FALSE, the computer exits the loop
and continues with statements after the loop. N.B. The REPEAT_UNTIL loop does not need the
BEGIN and END to enclose multiple statements.
FLOWCHARTS
A flowchart represents the steps in an algorithm using geometric symbols and arrows. The symbols
contain the instructions and the arrows show the order in which the instructions should be executed to
solve the problem.
FLOWCHART SYMBOLS
Start
Stop
Decision
Connector
Terminators or terminals
Input or Output
Process
Rules for flowcharts
1. The main symbols used in a flowchart are the Decision, Process and Terminal symbols.
2. Every flowchart must have a START and a STOP symbol.
3. Lines with arrow-heads indicate the flow of sequence.
4. Processes have only one entry point and one exit point.
5. Decisions have only one entry point, one TRUE exit point and one FALSE exit point.
6. The REPEAT loop has a process before the decision, since it always executes the process at least
once.
7. The WHILE loop has a decision before the process.
8. Use arrow-heads on connectors where the direction of flow may not be obvious.
Examples of a flowchart:
Problem 1:
Read in three marks and display their average.
Flowchart diagram showing sequenced instructions
Start
Enter the marks
totalMarks = mark1 + mark2 +mark3
avgMark = totalMark/noOfMarks
Display avgMark
Stop
Problem 2:
Ask the user to enter two numbers then display the greater number.
Flowchart diagram showing selection
Start
Enter num 1, num 2
Yes
num1 > num2?
No
Display num 1
Stop
Display num 2
Problem 3:
Print the number 1 to 5.
Flowchart diagram showing FOR loop
Start
num = 1
Yes
num < 5?
No
Stop
Display num
Problem 4:
Read the marks of students terminated by 999. Find and print the highest mark.
Flowchart diagram showing WHILE loop
Start
Highest = 0
Read mark
No
Read mark
mark <> 999?
Yes
mark > highest?
Yes
Highest = mark
Print Highest
Stop
No
Problem 5:
Print the numbers 1 to 5.
Flowchart diagram showing REPEAT loop
Start
number = 1
Display number
number = number + 1
number > 5?
No
Stop
Yes
Objective 2.8
Test algorithms for correctness
Manual testing/dry running
This is also called desk-checking. It allows the user to detect any logic errors by
tracing through the program. Dry-running involves executing the program
manually by using input values for variables and recording what takes place after
each instruction is executed. This method uses a trace table which is completed
upon manual execution of the program to record and determine what the
program is doing. To create a trace table, you must record all variables found in
the program as headings, as well as the heading ‘OUTPUT’ to represent what is
printed.
E.g.
What is printed by the following algorithm?
count = 0
WHILE count <= 10 DO
count = count + 2
PRINT count
ENDWHILE
Count OUTPUT
0
Count is set to 0; count < 10
2
2
2 is added to count and 2 is printed; count <10
4
4
2 is added to count and 4 is printed; count <10
6
6
2 is added to count and 6 is printed; count <10
8
8
2 is added to count and 8 is printed; count <10
10
10
2 is added to count and 10 is printed;
12
12
2 is added to count and 12 is printed; count not less than 10
so loop is exited.
Objective 2.9
Use the top-down design approach to problem
solving.
Top-down Design
This is a technique used in programming whereby a given problem is broken
down into smaller problems and each sub-problem is broken down into a set of
tasks, which a further broken down into a set of actions that collectively solve the
original problem.
Calculate and print wages
Get data
Get rate
Calculate wages
Get hours
worked
Multiply rate by hours worked
Print wages
This technique is called top-down design because the division of problems starts
at the top level and you work your way down.
The process of breaking down the problem into sub-problems and the subproblems into tasks and the tasks into actions is referred to as stepwise
refinement.