Problem-solving and program design
1. Outline the steps in problem-solving
If you research the topic of Problem Solving by using either the internet or any reputable text
book, most likely you will see the number of procedures range from probably four (4) to seven
(7) steps. For example, you may come across the following seven (7) main steps when trying to
solve a problem:
Step 1. Define the Problem
Step 2. Analyze the Problem
Step 3. Identifying Possible Solutions
Step 4. Selecting the Best Solutions
Step 5. Evaluating Solutions
Step 6. Develop an Action Plan
Step 7. Implement the Solution
The above seven steps above may be merged into four steps as follows:
Step 1. Define the Problem
State the problem clearly.
* Try to state the problem in your own words
* Write down what are you trying to find out or supposed to do
* Describe what data is input and what information is output
* Draw an INPUT-PROCESSING-OUTPUT (IPO) diagram
* Describe what calculations are needed that use the input to produce the output
Step 2. Identify and evaluate possible solutions
This involves selecting the best solutions
* Look for a pattern.
* Examine related problems, and determine if the same technique can be applied.
* Examine a simpler or special case of the problem to gain insight into the solution of the
original problem.
Step 3. Develop and represent the algorithm
Develop a solution that is general in nature.
* Make a table.
* Make a diagram (such as an algorithm).
* Work backward.
* Work the problem by hand (with a calculator or a using a trace table) for a specific set of data.
Step 4. Test the solution with a variety of data to validate that you are solution correct to the
problem given.
Ensure that you include error messages for data that is not expected on input or in processing
that may cause the program to crash
Here is another set of steps on the phases. Can you place the following three steps into the four
step above?
Problem-Solving Phase
1. Analysis and specification.(Define problem and what solution must do.)
2. General solution (algorithm).(Develop logical sequence of steps to solve problem.)
3. Verify.(follow steps - by hand.)
Implementation Phase
1. Specific solution (program).(Translate algorithm to code.)
2. Test.(Check computed results manually.)
Maintenance Phase
1. Use the program.
2. Maintain.(Modify to meet changed requirements or to correct errors.)
2. Decompose a simple problem into its significant parts
Input, Process, Output, Storage
Input
Entering data from an external source into the system can be achieved either:
1. Manually using keyboards which are often used to enter data into a system, or
2. Automatically, where data can be entered into the system using hardware such as OMR, microphone,
or sensors.
Processing
Once this data is entered, it can be processed, meaning you can:
– Search
– Sort, and
– Perform Calculations on the data
Processing data is important as it leads to useful output from the system.
Output
After the data is processed into information, it can be presented in different ways for the user, such as:
– Printed to an output device such as a printer or fax (Hardcopy)
– Printed on the screen (softcopy)
– Sound (such as the sounds from ATMs when you are making a transaction or the sound from the cash
register)
– Light, (flashing lights on an ambulance; a flashing light to take your money or card from the ATM)
– Can you think of any more ways to output information?
Output essentially deals with any data that is leaving the system.
Storage
If data doesn’t need to be output immediately after processing it may be saved for later use on a storage
medium such as a hard drive.
Also, stored data may be accessed to be processed with new data to output more information.
Note the unique qualities of storage mediums such as CDs and Disk Drives. They can be input devices
when data is being stored on them, but they become output devices when data is required from these
devices.
3. Distinguish between variables and constants
Variables and Constants
The ability to manipulate variables is one of the most powerful features of a programming
language.
Let's explain variables and constants by first understanding something that you are hopefully
familiar with.
Suppose each week Janus and Kikiyo go to a particular room in a building for a meeting. The
room is the same location with the same furniture and may even have a name, such as Room
LT4.
Each week when they go to the meeting, Janus may or may not sit in the same seat since Kikiyo
or someone else who got there earlier may have taken that seat, so Janus sits somewhere else.
SO! The room LT4 is a constant. It is located in the same place for the duration of your meeting.
While, where Janus, Kikiyo and the other sit varies. Their seats are variable each week when
they go to the meeting. Sometimes Janus or Kikiyo or someone else may miss the meeting.
Janus, Kikiyo and the other people have names but their seat location in the weekly meeting is
what varies.
In Pascal terms, the syllabus states that :
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a variable is an area of storage whose value can change during processing. In our
example the variable is the seat location
a constant can contain a value that never changes during the processing of the program.
In our example the constant is the room.
Variables
Programmers generally choose names for the variables that are meaningful. That is, the
programmer uses a variable that indicates what the variable is used for. It is good programming
practice to use meaningful variable names that suggest what they represent, since this makes the
program more readable and easier to understand.
For example:
Tax, FirstName, DeptCode, SeatNo, HoursWorked, and so on.
The assignment statement creates a new variable and assigns them values. For example, in Pascal
the following assignment statements are valid:
SeatNo := 'Janus';
HoursWorked := 35;
Please note the following in every assignment statement:
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the variable to be assigned a value must appear on the left of the assignment operator
the assignment operator is :=
a legal expression (value to be assigned) must appear on the right
Constants
A constant represents a value that does not change for the duration of the program. So, for
example, in Pascal , a value of 25% or .25 will be assigned to the variable Tax. However, Tax
cannot change to any other percentage while the program is being run.
Const Tax = 0.25; {to represent 25 %}
Note the use of the equal sign for the Constant Declaration.
4. Use appropriate data types
Problem 1
Write an algorithm and draw a flowchart that reads two values, determines the largest value and
prints the largest value with an identifying message.
ALGORITHM
Step 1:
Input VALUE1, VALUE2
Step 2: if (VALUE1 > VALUE2) then
MAX = VALUE1
else
MAX = VALUE2
endif
Step 3: Print “The largest value is”, MAX
Flowchart
Problem 2
Write an algorithm and draw a flowchart to convert the length in feet to centimeter.
Algorithm
Input the length in feet (Len_FT)
Calculate the length in cm (Lcm) by multiplying Len_FT by 30
Print length in cm (Len_CM)
Pseudocode:
Step 1: Input Len_FT
Step 2: Len_CM Step 3: Print Len_CM
Flowchart
Problem 3
Write an algorithm and draw a flowchart that will read the two sides of a rectangle and calculate
its area.
Algorithm
Input the width (W) and Length (L) of a rectangle
Calculate the area (Area) by multiplying L with W
Print Area
Pseudocode
Step 1: Input W, L
Step 2: Area = W * L
Step 3: Print Area
Flowchart
5. Explain the concept of algorithms
Algorithms and flowcharts
Using our steps in problem solving, a typical programming task can be divided into two phases:
1. Problem solving phase

This phase is where you produce an algorithm ( an ordered sequence of steps) that
describe solution of problem
2. Implementation phase

This phase is where you implement the program in some programming language, in this
case, Pascal.
Steps in Problem Solving
First produce a general algorithm
An algorithm as a set or list of instructions for carrying out some process step by step until it
reaches the end of the algorithm.
A recipe in a cookbook is an excellent example of an algorithm. So, the recipe includes the
ingredients and the method of cooking until you (hopefully) end up with a nice dish!
An example of an algorithm people use would be a recipe:
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4 extra large eggs, beaten
1&1/2 C. stock
1/2 teaspoon salt
1 onion, minced
1 C. tuna flakes
1 t. soy sauce
1 Tablespoon oil
1.
2.
3.
4.
5.
Mix all the ingredients, except the oil, in a deep bowl
Put 1" water in wide pot, then place deep bowl of batter inside the pot
Cover pot tightly and steam 15 min.
Heat oil very hot and pour over custard
Steam 5 more min.
Serves 4 people
Examples of Algorithms
Algorithms can be represented as:
1. Pseudocode - English like words that specify the sequence of steps in an algorithm
2. Flowcharts - a graphical tool using standard symbols to show the sequence of steps in an
algorithm
So whether you use pseudocode or flowcharts to expand your algorithm, here is why algorithm
are so useful:
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Every algorithm must have an end, so there must be a set of steps followed in that
algortihm to reach the end. For example, you follow the steps of the recipe to reach the
end which is your dish that is ready to eat!
Every instruction should therefore be clear, with short instructions and easily understood
The instructions should be in a sequence from top to bottom. Using the example recipe
above, you follow the instructions from step 1 to step 5.
To illustrate how we use algorithms (pseudocode and flowcharts) to a programming problem, let
us use an example:
Example 1:
Write an algorithm to determine a student’s final grade and indicate whether the student
has passed or failed. The final grade is calculated as the average of four marks.
Pseudocode
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
Remember, pseudocode is very similar to everyday English, which helps programmers
develop their algorithms.
Refine the pseudocode successively to get step by step detailed statements that are easy to
understand
Pseudocode: First try
List the tasks that need to be performed. You can also use an IPO chart to help you:
INPUT
PROCESSING
OUTPUT
calculate GRADE (average)
M1, M2, M3, M4
as (M1+M2+M3+M4)/4
Print Message FAIL or PASS
Compare GRADE (less than 50)
Input a set of 4 marks
Calculate their average by summing and dividing by 4
if average is below 50
Print “FAIL”
else
Print “PASS”
Detailed Pseudocode
Input M1,M2,M3,M4
GRADE = (M1+M2+M3+M4)/4
If (GRADE < 50)
Then
Print “FAIL”
Else
Print “PASS”
Endif
Flowcharts
Now we can also transform the pseudocode to a flowchart.
A flowchart is a graphical representation of the algorithm (again, a sequence of instructions that
reach an end). Different symbols are used to draw each type of flowchart.
Flowcharts show how data flows from the input of data through the computer to final output or
storage (note the IPOS diagram in a previous section).
A Flowchart
shows logic of an algorithm emphasizes individual steps and flow of data from one action to the
next
Flowcharting guidelines
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The flowchart should flow from top to bottom
Each symbol is connecting by lines that have arrows (not lines alone)
Avoid having flow lines crossing each other
Each symbol has at least one flow line entering it and another one leaving it, except for
the START and STOP symbols.
The decision symbol has two exit points; these can be on the sides or the bottom and one
side (See the decision above for 'Is Grade < 50?')
Use meaningful phrases in the symbols
6. Identify ways of representing algorithms
Representation of algorithms

Represent of Algorithms as Pseudocode and Flow Charts
Design an algorithm and the corresponding flowchart for adding the test scores as given below:
29, 38, 97, 85, 52, 55
Pseudocode
1. Start
2. Total = 0
3. Get the first testscore
4. Add first testscore to Total
5. Get the second testscore
6. Add to Total
7. Get the third testscore
8. Add to Total
9. Get the Forth testscore
10. Add to Total
11. Get the fifth testscore
12. Add to Total
13. Get the sixth testscore
14. Add to Total
15. Output the Total
16. Stop
Related Flow chart
The example 1, algorithms (pseudocode and flowchart) illustrate the steps for solving the
problem of adding six testscores. Where one testscore is added to Total at a time.
Note that the flowchart should have a Start step at the beginning and at least one stop step at the
end.
Since we want the sum of six testscores, then we should have a variable to store the
resulting sum after each addition. In this example, the container is called Total and we make sure
that Total should start with a zero value by step 2.
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LOOPS
For loop
Since we know that there are six testscores, we can can use a FOR loop. Here is the
flowchart that uses a FOR loop:
Pseudocode
1. Start
2. Total = 0
3. Count = 0 (to count the six testscores)
4. If the Count = 6, go to step 7
5. Get a testscore
6. Add the testscore to Total (Total = Total + testscore)
7. Add 1 to the Count
8. Go to step 4 to get next testscore
7. Output the Total
8. Stop
Flowchart
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While Loop
Here is another way, we need to add a last number to the list of numbers given. This
number should be special, so unique so that each time we get a testscore, we test it to see
if we have reached that special, unique number. Common numbers are -1, or 99. In this
example, since we are using testscores, it may not be wise to use 99 as the unique number
to stop the program.
Pseudocode
1. Start
2. Total = 0
3. Get a testscore
4. If the testscore is equal to -1, go to step 7
5. Add to testscore ( Total = Total + testscore)
6. Go to step 3 to get next testscore
7. Output the Total
8. Stop
Flowchart
In this flowchart we use a While loop. While we have not entered that special unique
testscore of -1, the user is prompted to enter another testscore.
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TRUTH TABLES
Boolean Operators: AND
When using the AND Operator, both expressions must be TRUE for the compound
expression to be true.
If (expression1) AND (expression2)
THEN
Output (‘Both expressions are true’);
So if a is 4 and b is 2
Then
(a <= 2) AND (b = 2)
Evaluates to
(4 <= 2) AND (2 = 2)
FALSE AND TRUE
FALSE
Boolean Operators: OR
When using the OR Operator, either one expression or both expressions can be TRUE for
the compound expression to be true.
If (expression1) OR (expression2)
THEN
Output (‘One or both expressions are true’);
So if a is 4 and b is 2
Then
(a <= 2) OR (b = 2)
(4 <= 2) OR (2 = 2)
FALSE OR TRUE
TRUE
Boolean Operators: NOT
The NOT Operator simply reverses the boolean value of the boolean expression that
appears immediately to its right.
If NOT (expression)
THEN writeln(‘This expression is FALSE’);
So if a is 4 and b is 2
Then
NOT ((a <= 2) OR (b = 2) ) will evaluate to
NOT (4 <= 2) OR (2 = 2))
NOT (FALSE OR TRUE)
NOT (TRUE)
to FALSE.
Precedence of Arithmetic Operators
Priority
Operator(s)
1st
NOT
2nd
AND, *, /
3rd
OR, +, -
4th
=, <>, >, <, >=, <=
Truth Tables
Negation
~
p
F
T
T
F

AND
Here both statements are true
p
AND
q
p AND q
T
T
T
T
F
F
F
T
F
F
F
F
Conditional Statement
Relational Operators compare two values. Let us assume that the values A and B contain
two numbers. We can compare the two values as follows:
NAME
SYMBOL MEANING
Greater than
A>B
"A" is greater than B
Greater-than or equal A >= B
"A" is Greater-than or equal to "B"
Equals
A=B
"A" equals B
not-equals
"A" <> "B" "A" does not equal "B"
Less-than
"A" < "B"
Less-equal
"A" <= "B" "A" is less than or equal to "B"
"A" is Less than "B"
Making decisions
Conditional Statements are used to help with decisions that can be made based on the
results of comparing two values. For example, the expression A>B is a logical
expression. It describes a condition we want to test.
So:
if A>B is true (if A is greater than B) we take one action, such as print the value of A
if A>B is false (if A is not greater than B) we take another action, such as print the value
of B
The algorithm for conditional statements are shown below:
If condition then
true alternative
else
false alternative
endif
An algorithm for the conditional statement is:
If A>B then
print A
else
print B
endif
IF-THEN Statement
IF (Boolean expression) THEN
STATEMENT;
•In evaluating the Boolean expression, If it is TRUE then the STATEMENT is
executed. If it is FALSE then the STATEMENT is skipped.
IF-THEN-ELSE Statement
IF (Boolean expression) THEN
STATEMENT1
ELSE
STATEMENT2;
In evaluating the Boolean expression, If it is TRUE then STATEMENT1 is executed. If
it is FALSE then STATEMENT2 is executed.
7. Develop algorithms to solve simple problems;
Solving Simple problems
Problem 1
Write an algorithm and draw a flowchart that reads two values, determines the largest
value and prints the largest value with an identifying message.
ALGORITHM
Step 1:
Input VALUE1, VALUE2
Step 2: if (VALUE1 > VALUE2) then
MAX = VALUE1
else
MAX = VALUE2
endif
Step 3: Print “The largest value is”, MAX
Flowchart
Problem 2
Write an algorithm and draw a flowchart to convert the length in feet to centimeter.
Algorithm
Input the length in feet (Len_FT)
Calculate the length in cm (Lcm) by multiplying Len_FT by 30
Print length in cm (Len_CM)
Pseudocode:
Step 1: Input Len_FT
Step 2: Len_CM Step 3: Print Len_CM
Flowchart
Problem 3
Write an algorithm and draw a flowchart that will read the two sides of a rectangle and
calculate its area.
Algorithm
Input the width (W) and Length (L) of a rectangle
Calculate the area (Area) by multiplying L with W
Print Area
Pseudocode
Step 1: Input W, L
Step 2: Area = W * L
Step 3: Print Area
Flowchart
8. Test Algorithm for correctness
Trace tables
A trace table is a useful technique used to test an algorithm with data to make sure that program
does what it is supposed to do and no logical errors occur
The best way to use a trace table is through manual tracing or a dry run of the program
statements.
Advantages of using a trace table include:
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Checking the sequence of steps of the program algorithm or code before you execute the
code
locate errors in your algorithm or program code
Let us use some program code below along with a trace table for all the variables and outputs.
Program Code
y=3
For x =1to4
y=y+x
Loop
Print (y)
Trace Table
x
y
output
1 3
2 4
3 6
4 9
4 13 13
Many times a question on trace tables will ask you to complete the table which will include
headings and some values to use as input with sometimes a few values as output.
Note the variables in the headings will also be found in the fragment of code given
Fill in all values that are input to the variables in the columns
Fill in all outputs from the statements
Go through EACH LINE of the program
9. Use the top down approach to problem solving.
Top-down Design Approach
A problem may seem impossible to solve because at first glance it can be very complex.
Complex problems can be solved using top-down design, also called stepwise refinement, where
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We divide the problem into sub-problems (smaller parts)
Then break those sub-problems into smaller parts
Soon, it is easy to solve the small easy problems
Then the program as a whole will be solved
Advantages of Top-Down Design
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Sub-dividing the problem into parts helps clarify what needs to be done.
At each step of refinement, the new sub-tasks become less complicated and, therefore, easier to
program.
Parts of the solution may turn out to be used in other parts of the program
Subdividing the problem into sub-parts allows more than one person to work on the solution.
Example of Top-Down Design
Problem:

Make some bakes
Unfortunately, stating the problem isn't enough to actually make any bakes, we need to break the task down:

Make some bakes
1. Organise Kitchen
2. Make bakes
3. Serve
Each of these tasks can then be broken down further:
1. Organise Kitchen
1. Clean surfaces
2. Get out mixing bowl, whisk, spoon, sieve
3. Get out flour, sugar, salt, eggs, milk, butter
4. Put on apron
2. Make bakes
1. Sift salt and flour into bowl
2. Add sugar
3. Mix dry ingredients
4. cream butter into dry ingredients until the mixture resembles breadcrumbs
5. Add water (milk is optional)
6. Mix well. Add flour so that the batter is not too sticky
7. Cook
8. Serve
And each of these tasks can be broken down further, let us take a look at the Cook:

Fry Bakes
1.
2.
3.
4.
5.
6.
Heat pan to right temperature
Scoop tablespoon of batter
Spoon scoops of batter into pan
When brown, flip bakes
Remove, when both sides are brown
Place bakes on paper towels or on rack
We can break down some of these tasks even further.
So starting at a single point, making bakes, we have broken down the task into it individual parts.