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Problem Solving
Algorithms
PSPD Using C Slide 2 of 40
Design
Topic & Structure of the lesson
In this chapter you will learn about:
• Problem Solving
• Algorithm
• Pseudocodes
• Flowcharts
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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
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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
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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 Slide 6 of 40
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 Slide 7 of 40
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 PLANHave 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.
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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?
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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
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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.
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Design
Algorithmic Problem Solving
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.
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Design
Algorithmic Problem Solving
Ingredient
Recipe(software)
Cooking utensils(hardware)
Al-gongBah-kut-the
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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.
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Design
Characteristics of an Algorithm
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.
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Design
Characteristics of an Algorithm
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:
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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?”
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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.
=
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Problem Solving
Input
Processing(Brains)
Output
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Problem Solving
Input Device
Output Device
CPU(Brains)
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Problem Solving
5 10
15
5 + 10 = 15
Input
Processing
OutputLet us assume we are interested in calculating the sum of 5 and 10.
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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.
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Problem Solving
Value1Value2
Sum
Sum = Value1 + Value2
Notice that instead of using specific numbers, variables are used to represent these values.
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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.
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What Are Variables?
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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
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Design
Problem Solving
The next step is to identify the actual processing steps required to convert the input to become the output.
Input Processing Output
Value1
Value2
Sum1) Read Value1, Value2
2) Calculate Sum
3) Display Sum
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Design
Algorithm Development
Once the defining diagram has been developed, the next logical step is to develop the algorithm (which is much more detailed).
Input Processing Output
Value1
Value2
Sum1) Read Value1, Value2
2) Calculate Sum
3) Display Sum
The developed processing steps have to be more detailed in the algorithm.
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Design
Algorithm Development
The basic mathematical operators used in algorithms are as follows:-
+ addition
- subtraction
* multiplication
/ division
= assignment
( ) brackets for grouping calculations
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Design
Algorithm Development
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
Sum = Value1 + Value2
3) Display Sum
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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
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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
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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
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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
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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.
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Decision Making
Example:-
We are looking for a job which pays more than RM4000.
IF (Salary>4000) THENSay "I Will Take The Job!!"
ENDIF
Example of an Expression
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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
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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?
IF (Salary>4000) THENSay “YES!”
ELSESay “NO!”
ENDIF
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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) THENTake Job!!
ENDIF
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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.
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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).
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Decision Making
IF (Salary>4000) And (CreditCard=YES) THENSay “Yes I Will Take The Job!!”
ENDIF
For example, this statement.........
can be represented like this.........IF (Salary>4000) THEN
IF (CreditCard=YES) THENSay “Yes I Will Take The Job!!”
ELSESay “No Credit Card?”Say “Sorry!!”
ENDIFELSE
Say “Not Enough Pay!!”ENDIF
........ whereby more possibilities can be represented.
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Design
Decision Making
For good practice...........
IF (Salary>4000) THENIF (CreditCard=YES) THEN
Say “Yes I Will Take The Job!!”ELSE
Say “No Credit Card?”Say “Sorry!!”
ENDIFELSE
Say “Not Enough Pay!!”ENDIF
........ ensure that statements are properly indented to indicate block of statements which belong together.
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Design
Cont’d
For Example:
if a is greater than b then
print “A is greater”
else
print “B is greater”
end if
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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
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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.
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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.
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Looping Constructs
The looping constructs available in pseudocodes are as follows:-
DOWHILE...ENDDO
FOR…NEXT
REPEAT...UNTIL
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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.
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Design
Looping Constructs
The format of the FOR...NEXT construct is shown below:-
FOR (initialze TO expression) STEP increment:::
ENDDO
Group of statements
An expression which determines whether the loop will continue.
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Design
Looping Constructs
The format of the REPEAT...UNTIL construct is shown below:-
REPEAT:::
UNTIL (expression)
Group of statements
An expression which determines whether the loop will continue.
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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.
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Looping Constructs
Input Processing Output
Salary Total1) Read Salary
2) Calculate Total
3) Display Total
The Defining Diagram
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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
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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
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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).
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Design
Desk Check Table
Identify Data Sets
Input Processing Output
Value1
Value2
Sum1) Read 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.
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Design
Desk Check Table
Identify Expected Results
Input Processing Output
Value1
Value2
Sum1) Read 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.
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Design
Desk Check TableTrace Table - Data Set 1
Read
Value1 Value2
5 3
Sum
Calculate 8
Display
Do the results match the expected results?
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Desk Check Table
Trace Table - Data Set 2
Read
Value1 Value2
8 13
Sum
Calculate 21
Display
Do the results match the expected results?
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Design
Desk Check Table
Trace Table - Data Set 3
Read
Value1 Value2
15 9
Sum
Calculate 24
Display
Do the results match the expected results?
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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.
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Design
Program Flowcharts
The following are the commonly used symbols for drawing program flowcharts.
terminator off-page connector
process storage
decisionmaking
document
input/output connector
arrowheads
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DesignBegin
Read Value1,Value2
Program Flowcharts
CalculateSum = Value1 + Value2
DisplaySum
End
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DesignBegin
Read Amount
Program Flowcharts
End
Amount>20.00?
CalculateActual=Amount * 0.80
CalculateActual=Amount
NOYES
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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.
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Sequence Structure
Pseudocode: Flowchart:
statement_1
statement_2
------------
statement_n
Statement -1
Statement -2
Statement -n
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Selection Structure
Pseudocode: Flowchart:
if condition
then-part
else
else-part
end_if
condition
else-part then-part
truefalse
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Selection Structure
Pseudocode: Flowchart:
if condition
then-part
end_if
condition
then-part
true
false
Y
N
PSPD Using C Slide 69 of 40
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Repetition Structure
Pseudocode: Flowchart:
while condition
loop-body
end-while
condition loop-body
F
TY
N
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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.
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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.
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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 Slide 73 of 40
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.
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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.
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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.
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Follow Up Assignment
• This is an individual piece of work.
• Your source code will be discussed at the end of the next lesson.
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Summary of Main Teaching Points
• Problem Solving
• Pseudocodes• Flowcharts
• Basic control structures
• The sequence structure• The selection structure• The repetition structure