8.1 alogorithm & prolem solving

PSPD Using C
Design
Topic & Structure of the lesson
In this chapter you will learn about:
• Problem Solving
• Algorithm
• Pseudocodes
• Flowcharts

PSPD Using C
Design
Key Terms you must be able to use
If you have mastered this topic, you should be
able to use the following terms correctly in your
assignments and exams:
• program
• pseudocode
• flowchart
• algorithm

PSPD Using C
Design
Problem Solving Techniques
In this chapter you will learn about:
 What problem solving is
 The software development method of
problem solving using computers
 Basic algorithm control structures
 The sequence structure
 The selection structure
 The repetition structure

PSPD Using C
Design
Problem Solving Techniques
By the time you have completed this chapter,you
will have acquired the ability to:
 Apply the software development method to
solve problems
 Difference between the Algorithm & the
Flowchart
 Knowing about the control structures

PSPD Using C
Design
Problem Solving
First:
You have to
understand the
problem.
UNDERSTANDING THE PROBLEM
What is the unknown? What are the data?What
is the condition?
Is it possible to satisfy the condition?Is the
condition sufficient to determine the unknown?Or
is it sufficient?Or Redundant? Or Contradictory?
Draw a figure.Introduce suitable
notation.Separate the various parts of the
condition.Can you write them down?

PSPD Using C
Design
Problem Solving
Second:
Find the connection
between the data and
the unknown.
Auxiliary problems
may be devised if
needed.
You should obtain
eventually a plan of
the solution.
DEVISING A PLAN
Have you seen it before? Or have you
seen the same problem in slightly different
form?
Do you know a related problem?
Look at the unknown! Try to think of a
familiar problem having the same or similar
unknown. Split the problem into smaller,
simple sub-problems. If you cannot solve
the proposed problem try to solve first
some related problem. Or solve more
general problem. Or special case of the
problem. Or solve the part of the problem.

PSPD Using C
Design
Problem Solving
Third:
Carry out your
plan.
CARRYING OUT THE PLAN
Carrying out your plan of the solution,check
each step. Can you see clearly that step is
correct? Can you prove that it is correct?
Fourth:
Examine the
solution
obtained.
LOOKING BACK
Can you check the result? Can you derive
the result differently? Can you use the
result, or the method, for some other
problem?

PSPD Using C
Design
Problem Solving
The software development method
The software development method consists of the
following steps:
 Requirements specification
 Analysis
 Design
 Implementation
 Testing and verification
 Documentation

PSPD Using C
Design
Algorithmic Problem Solving
Algorithmic problem:
Any problem whose solution can be expressed as a
set of executable instructions.
Algorithm:
A well defined computational procedure consisting of
a set of instructions, that takes some value or set of
values, as input, and produces some value or set of
values, as output.

PSPD Using C
Design
Derived from the name of Mohammed al-
khowarizmi, a Persian mathematician in the ninth
century.
Al-khowarizmi--Algorismus(in Latin)--Algorithm
 An algorithm is like a recipe, that converts the
ingredients into some culinary dish.
 The formal written version is a program.
 Algorithms/programs are the software.The machine
that runs the programs is the hardware.

PSPD Using C
Design
Ingredient
Recipe
(software)
Cooking utensils
(hardware)
Al-gong
Bah-kut-the

PSPD Using C
Design
Characteristics of an Algorithm
 Each step of an algorithm must be exact,
preciously and ambiguously described.
 It must terminate, i.e. it contains a finite
number of steps.
 It must be effective, i.e.., produce the correct
output.
 It must be general, i.e.. to solve every
instance of the problem.

PSPD Using C
Design
 An Algorithm is implemented in some programming
language.
program = Algorithm + Data Structures.
 Data Structures refer to the types of data used and
how the data are organized in the program.
 An algorithm is usually presented in the form of some
pseudo-code, which is a mixture of English
statement,some mathematical notations,and selected
keywords from a programming language.

PSPD Using C
Design
PROBLEM:
You are required to design a complete
system which will enable the sum of two
values to be calculated.
 An Algorithm should emphasize the
WHAT’s and not the HOW’s. Consider
the problem below:

PSPD Using C
Design
Problem Solving
To grapple with this problem, we have to
understand the problem from the human
perspective.
A question to ask yourself is this,
“How Would You Calculate the Sum of Two
Values?”

PSPD Using C
Design
Problem Solving
As the computer is also a device similar to the way
in which the human brain functions, the process of
calculating the sum of two values can also be easily
performed by the computer.
=

PSPD Using C
Design
Problem Solving
Input
Processing
(Brains)
Output

PSPD Using C
Design
Problem Solving
Input Device
Output Device
CPU
(Brains)

PSPD Using C
Design
Problem Solving
5 10
15
5 + 10 = 15
Input
Processing
Output
Let us assume we are interested in calculating the sum of 5
and 10.

PSPD Using C
Design
Problem Solving
As shown previously, the example values (5 and
10) have been specified explicitly.
As the brain is flexible enough in calculating a
wide range of numbers, the two input values
have to be generalised.

PSPD Using C
Design
Problem Solving
Value1
Value2
Sum
Sum = Value1 + Value2
Notice that instead of using specific numbers,
variables are used to represent these values.

PSPD Using C
Design
What Are Variables?
Variables are memory locations within the computer which
allows pieces of data to be stored.
The word variable comes from the word vary, which means
that whatever you place within a variable can be changed.
A variable can be viewed as a container used to store
things.
Data (for example, name,
age, salary) can be stored in
these containers.

PSPD Using C
Design
What Are Variables?

PSPD Using C
Design
Problem Solving
Now that we have an exact idea about how the
problem is solved, let us represent this in a clearer
manner, using the defining diagram.
Input Processing Output
Value1
Value2
Sum

PSPD Using C
Design
Problem Solving
The next step is to identify the actual processing
steps required to convert the input to become the
output.
Value1
Value2
Sum1) Read Value1, Value2
2) Calculate Sum
3) Display Sum

PSPD Using C
Design
Algorithm Development
Once the defining diagram has been
developed, the next logical step is to develop
the algorithm (which is much more detailed).
Value1
Value2
2) Calculate Sum
3) Display Sum
The developed processing steps have to be more
detailed in the algorithm.

PSPD Using C
Design
The basic mathematical operators used in algorithms
are as follows:-
+ addition
- subtraction
* multiplication
/ division
= assignment
( ) brackets for grouping calculations

PSPD Using C
Design
Example of an algorithm (using pseudocodes) which
can be used to carry out the tasks outlined in the
defining diagram is as follows:-
1) Read Value1, Value2
2) Calculate
3) Display Sum

PSPD Using C
Design
Pseudocoding
A Pseudocode language is semiformal, English-
like language with a limited vocabulary that can be
used to design and describe algorithms.
The pseudocode language can be used for:
 Designing algorithms
 Communicating algorithms as programs
 Implementing algorithms as programs
 Debugging logic errors in program

PSPD Using C
Design
Pseudocode for the Control Structures
The Sequence Control Structure:
The sequence control structure is a series of steps
or statements that are executed in the order in which
they are written in an algorithm.
For Example:
read taxable income
read filing status
compute income tax

PSPD Using C
Design
Cont’d
The Selection Control Structure:
The selection control structure defines two courses of
action, depending on the outcome of a condition. A
condition is an expression that, when evaluated, computes
to either true or false.
Syntax is: if condition
then-part
else
else-part
end-if

PSPD Using C
Design
Decision Making
Being able to mimic the way the human brain
works, the computer also has the ability to make
decisions.
Decision making can be represented in
pseudocodes using the IF...THEN construct.
IF (expression) THEN
:
:
ENDIF

PSPD Using C
Design
Decision Making
IF (expression) THEN
:
:
ENDIF
The expression is a comparison between
two values which evaluates to either true of
false.
Statements are
placed here.

PSPD Using C
Design
Decision Making
Example:-
We are looking for a job which pays more than
RM4000.
IF (Salary>4000) THEN
Say "I Will Take The Job!!"
ENDIF
Example of an
Expression

PSPD Using C
Design
Decision Making
Commonly used relational operators in expressions:-
> Greater Than
< Less Than
= Equals To
< > Not Equals To
>= Greater Than or Equals To
<= Less Than or Equals To
( ) Brackets used for prioritising certain calculations

PSPD Using C
Design
Decision Making
Since all expressions works out to be either true or false,
what the IF..THEN statement represents is a two-state
condition.
For example,
A potential employer is waiting for you to give a reply (on the
spot) about the job offer with a salary of RM2000. Your
decision would be to only take a job worth more than
RM4000. What would you say?
Say “YES!”
ELSE
Say “NO!”
ENDIF

PSPD Using C
Design
Decision Making
Certain conditions may give rise to more than
one expression being evaluated. These are
known as compound expressions.
Example:-
You are interested in taking up a job which pays
more than RM4000 and that the company must
also provide a credit card.
IF (Salary>4000) And (CreditCard=YES) THEN
Take Job!!
ENDIF

PSPD Using C
Design
Decision Making
Compound expressions can be represented
using the following operators:-
AND Every expression must evaluate to be
true in order for the whole expression to
be true.
OR As long as any one of the expression
can be true, the entire IF statement will
be true.
NOT The inverse (opposite) of the entire
expression.

PSPD Using C
Design
Decision Making
IF statements can be nested, that is, placed
within another IF statement.
This is used in situations when the expression
is more complex than the simple decisions (as
seen earlier).

PSPD Using C
Design
Decision Making
IF (Salary>4000) And (CreditCard=YES) THEN
Say “Yes I Will Take The Job!!”
ENDIF
For example, this statement.........
can be represented like this.........
IF (CreditCard=YES) THEN
ELSE
Say “No Credit Card?”
Say “Sorry!!”
ENDIF
ELSE
Say “Not Enough Pay!!”
ENDIF
........ whereby more possibilities can be represented.

PSPD Using C
Design
Decision Making
For good practice...........
IF (CreditCard=YES) THEN
ELSE
Say “No Credit Card?”
Say “Sorry!!”
ENDIF
ELSE
Say “Not Enough Pay!!”
ENDIF
........ ensure that statements are properly
indented to indicate block of statements
which belong together.

PSPD Using C
Design
Cont’d
For Example:
if a is greater than b then
print “A is greater”
else
print “B is greater”
end if

PSPD Using C
Design
Cont’d
Repetition Control Structure:
The repetition control structure specifies a block of
one or more statements that are repeatedly executed
until a condition is satisfied.
Syntax is:
while condition
loop-body
end-while

PSPD Using C
Design
Looping Constructs
Looping constructs (also known as repetition or
iteration constructs) are a kind of construct found
in pseudocodes which allows statements (or a
group of statements) to be repeated.
The main reason why looping constructs are
provided is because most of the problems which
we encounter everyday requires some degree of
repetition.

PSPD Using C
Design
Looping Constructs
An example of a process which is iterative:-
Payroll processing is very much an iterative
process as the person processing the
payroll applies the same calculations for
each employee to produce the pay slip.

PSPD Using C
Design
Looping Constructs
The looping constructs available in pseudocodes
are as follows:-
DOWHILE...ENDDO
FOR…NEXT
REPEAT...UNTIL

PSPD Using C
Design
Looping Constructs
The format of the
DOWHILE...ENDDO construct is
shown below:-
DOWHILE (expression)
:
:
:
ENDDO
Group of
statements
An expression which determines
whether the loop will continue.

PSPD Using C
Design
Looping Constructs
The format of the FOR...NEXT
construct is shown below:-
FOR (initialze TO expression) STEP increment
:
:
:
ENDDO
Group of
statements

PSPD Using C
Design
Looping Constructs
The format of the
REPEAT...UNTIL construct is
shown below:-
REPEAT
:
:
:
UNTIL (expression)
Group of
statements

PSPD Using C
Design
Looping Constructs
Take a look at the following example:-
You are required to develop a complete system
which will allow the total payroll to be
calculated.
The system is required to read in the amount to
be paid for each employee.
The moment the system receives an input
value of -99, the system is required to stop and
display the total payroll.

PSPD Using C
Design
Looping Constructs
Salary Total1) Read Salary
2) Calculate Total
3) Display Total
The Defining Diagram

PSPD Using C
Design
Looping Constructs
Algorithm (Using Pseudocodes)
1) Display "Enter Salary"
2) Read Salary
3) Total = 0
4) DOWHILE (Salary<>-99)
Total = Total + Salary
Display "Enter Salary"
Read Salary
ENDDO
5) Display "Total Payroll = ", Total

PSPD Using C
Design
Cont’d
Example:
Dowhile (income is less than 50000)
print “Enter taxable income;should be
greater than or equal to 50000”
read income
Enddo

PSPD Using C
Design
Desk Check Table
A desk check table is used to verify the correctness of the
design. This is to ensure that the program which will
eventually be developed is going to produce the answer
which is required.
The desk check table is developed based on the following
steps:-
1) Identify the data sets.
2) Identify the expected results.
3) Trace through the algorithm with the data sets using
a trace table.
4) Analyse & compare the results produced in step (3)
and the expected results in step (2).

PSPD Using C
Design
Desk Check Table
Identify Data Sets
Value1
Value2
2) Calculate Sum
3) Display Sum
Focus on the input section of the defining diagram and
identify some possible values (data sets) which can be
used to test the system.

PSPD Using C
Design
Desk Check Table
Identify Expected Results
Value1
Value2
2) Calculate Sum
3) Display Sum
Focus on the output section of the defining diagram and
identify some possible values which the system will
produce based on the data sets.

PSPD Using C
Design
Desk Check Table
Trace Table - Data Set 1
Read
Value1 Value2
5 3
Sum
Calculate 8
Display 
Do the results match the expected
results?

PSPD Using C
Design
Desk Check Table
Read
Value1 Value2
8 13
Sum
Calculate 21
Display 
results?

PSPD Using C
Design
Desk Check Table
Read
Value1 Value2
15 9
Sum
Calculate 24
Display 
results?

PSPD Using C
Design
Program Flowcharts
As humans are more inclined towards
understanding diagrams and pictures rather
than words, pseudocodes tends to become
tedious to understand if too lengthy.
Program flowcharts, because they are
represented graphically, makes understanding
easier.

PSPD Using C
Design
Program Flowcharts
The following are the commonly used
symbols for drawing program flowcharts.
terminator off-page
connector
process storage
decision
making
document
input/output connector
arrowheads

PSPD Using C
DesignBegin
Read Value1,
Value2
Program Flowcharts
Calculate
Display
Sum
End

PSPD Using C
DesignBegin
Read Amount
Program Flowcharts
End
Amount>20.00?
Calculate
Actual=Amount * 0.80
Calculate
Actual=Amount
NOYES

PSPD Using C
Design
Flowcharting

 Another technique used in designing and representing
algorithms.
 Alternative to pseudocoing
 A pseudocode description is verbal, a flowchart is
graphical in nature.
Definition:
 A flowchart is a graph consisting of geometrical shapes
that are connected by flow lines.

PSPD Using C
Design
Sequence Structure

Pseudocode: Flowchart:
statement_1
statement_2
------------
statement_n
Statement -1
Statement -2
Statement -n

PSPD Using C
Design
Selection Structure

if condition
then-part
else
else-part
end_if
condition
else-part then-part
truefalse

PSPD Using C
Design
Selection Structure

if condition
then-part
end_if condition
then-part
true
false
Y
N

PSPD Using C
Design
Repetition Structure
while condition
loop-body
end-while
condition loop-body
F
T
Y
N

PSPD Using C
Design
Summary
 Problem Solving– the process of transforming the
description of a problem to its solution.
 To Solve complex problems, we use computers as a
tool and develop computer programs that give us
solutions.
 A commonly used method for problem solving using
computers is the software development method,which
consists of six steps.

PSPD Using C
Design
Summary
1. The Requirements specification, provides us with
a precise definition of the problem.
2. In the analysis phase we identify problem
inputs,outputs,special constraints, and formulas and
equations to be used.
3. The design phase is concerned with developing an
algorithm for the solution of the problem.

PSPD Using C
Design
Summary
4. The implementation of an algorithm is a computer
program.When executed, it should produce the solution to
the problem.
5. Program Verification is the process of ensuring that a
program meets user requirements.
6. Program testing, on the other hand, is the process of
executing a program to demonstrate its correctness.
7. Program Documentation facilitates the use of the
program,future program maintenance efforts,and program
debugging.

PSPD Using C
Design
Summary
 An algorithm is a sequence of a finite number of steps
arranged in a specific logical order that, when executed,
produce the solution for a problem.
 A pseudocode language is a semiformal,English-like
language with a limited vocabulary that can be used to
design and describe algorithms.

PSPD Using C
Design
Summary
 Any algorithm can be described in terms of three basic
control structures.They are the sequence,selection and
repetition structures.
 The top-down stepwise refinement of algorithms is a
fundamental problem-solving strategy.
 A Flowchart is a graphical representation of an
algorithm.

PSPD Using C
Design
Quick Review Question
1. State the difference between the Dowhile –
Enddo structure and the
Repeat – Until structure.
2. Write an algorithm that will display the first
hundred even numbers
using the Do-While loop.

PSPD Using C
Design
Follow Up Assignment
• This is an individual piece of work.
• Your source code will be discussed at the
end of the next lesson.

PSPD Using C
Design
Summary of Main Teaching Points
• Problem Solving
• Pseudocodes
• Flowcharts
• Basic control structures
• The sequence structure
• The selection structure
• The repetition structure

8.1 alogorithm & prolem solving

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