ProblemSolving Part 1 Algorithms and Pseudo Coding

7/30/2019 ProblemSolving Part 1 Algorithms and Pseudo Coding

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Problem SolvingPart 1

Algorithms

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Topic & Structure of the lesson

In this chapter you will learn about:

Problem Solving

Algorithm Pseudocodes

Flowcharts

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Key Terms you must be able to use

If you have mastered this topic, you should beable to use the following terms correctly in your assignments and exams :

program

pseudocode

flowchart

algorithm5/9/2013


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Problem Solving Techniques

In this chapter you will learn about:

What problem solving is

The software development method of problem solving using computersBasic algorithm control structures

The sequence structure

The selection structureThe repetition structure

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Problem Solving Techniques

By the time you have completed this chapter,you willhave acquired the ability to:

Apply the software development method to solveproblems

Difference between the Algorithm & theFlowchart

Knowing about the control structures

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Problem Solving

A great discovery solves a great problem but there is a grain of discovery in the solution of any problem. Your problem may bemodest; but if it challenges your curiosity and brings into play

your inventive faculties, and if you solve it by your own means,you may experience the tension and enjoy the triumph of discovery. Such experiences at a susceptible age may create ataste for mental work and leave their imprint on mind and character for a lifetime.

George Polya

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Problem Solving

First:

You have tounderstand theproblem.

UNDERSTANDING THE PROBLEM

What is the unknown? What are the data?Whatis the condition?Is it possible to satisfy the condition?Is thecondition sufficient to determine the unknown?Or is it sufficient?Or Redundant? Or Contradictory?Draw a figure.Introduce suitablenotation.Separate the various parts of thecondition.Can you write them down?


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Problem Solving

Second:Find the connectionbetween the data andthe unknown.

Auxiliary problemsmay be devised if needed.

You should obtaineventually a plan of the solution.

DEVISING A PLANHave you seen it before? Or have youseen the same problem in slightly differentform?Do you know a related problem?Look at the unknown! Try to think of afamiliar problem having the same or similar unknown. Split the problem into smaller,

simple sub-problems. If you cannot solvethe proposed problem try to solve firstsome related problem. Or solve moregeneral problem. Or special case of theproblem. Or solve the part of the problem.


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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 iscorrect? Can you prove that it is correct?

Fourth:

Examine thesolutionobtained.

LOOKING BACK

Can you check the result? Can you derivethe result differently? Can you use theresult, or the method, for some other problem?


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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 aset of instructions , that takes some value or set of values,as input , and produces some value or set of values, asoutput.

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Derived from the name of Mohammed al-khowarizmi, aPersian mathematician in the ninth century.

Al-khowarizmi--Algorismus(in Latin)--Algorithm

An algorithm is like a recipe, that converts theingredients into some culinary dish.

The formal written version is a program.Algorithms/programs are the software .The machinethat runs the programs is the hardware .

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Ingredient

Recipe(software)

Cooking utensils(hardware)

Al-gongBah-kut-the

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Characteristics of an Algorithm

Each step of an algorithm must be exact,preciously and ambiguously described.

It must terminate, i.e. it contains a finitenumber of steps.

It must be effective, i.e.., produce the correctoutput.

It must be general, i.e.. to solve everyinstance of the problem.

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An Algorithm is implemented in some p r o g r a m m i n g language.

prog ram = Algo r i thm + Data St ruc tu res .

Data Struc tures refer to the types of data used andhow the data are organized in the program.

An algorithm is usually presented in the form of somepseudo-code , which is a mixture of Englishstatement,some mathematical notations,and selectedkeywords from a programming language.

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PROBLEM:

You are required to design a completesystem which will enable the sum of twovalues to be calculated.

An Algorithm should emphasize theWHAT s and not the HOWs . Consider theproblem below:

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Problem Solving

To grapple with this problem, we have tounderstand the problem from the human

perspective. A question to ask yourself is this,

How Would You Calculate the Sum of TwoValues?

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Problem Solving

As the computer is also a device similar to the wayin which the human brain functions, the process of calculating the sum of two values can also be easily

performed by the computer.

=5/9/2013


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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 10.5/9/2013


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Problem Solving

As shown previously, the example values (5 and10) have been specified explicitly .

As the brain is flexible enough in calculating awide range of numbers , the two input valueshave 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.5/9/2013


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What Are Variables?

Variables are memory locations within the computer whichallows 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 storethings.

Data (for example, name,age, salary) can be stored in

these containers.5/9/2013


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What Are Variables?

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Problem Solving

Now that we have an exact idea about how theproblem is solved, let us represent this in a clearer manner, using the defining diagram .

Input Processing Output

Value1

Value2

Sum

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Problem Solving

The next step is to identify the actual processing steps required to convert the input to become theoutput .


Value1

Value2

Sum1) Read Value1, Value2

2) Calculate Sum

3) Display Sum

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Algorithm Development

Once the defining diagram has beendeveloped, the next logical step is to developthe algorithm (which is much more detailed).


Value1

Value2

Sum1) Read Value1, Value2

2) Calculate Sum

3) Display Sum

The developed processing steps have to be more

detailed in the algorithm.5/9/2013


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Algorithm Development

Example of an algorithm (using pseudocodes) whichcan be used to carry out the tasks outlined in the

defining diagram is as follows:-

1) Read Value1, Value2

2) CalculateSum = Value1 + Value2

3) Display Sum5/9/2013


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Pseudo Coding

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Pseudocoding

A Pseudocode language is semiformal, English-like language with a limited vocabulary that can beused 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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Pseudocode for the Control Structures

The Sequence Control Structure:

The sequence co n t ro l s t ruc tu re is a series of stepsor statements that are executed in the order in whichthey are written in an algorithm.For Example:

read taxable inc om e

read f i l ing s ta tus com pute incom e tax

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Contd

The Selection Control Structure:The se lec t ion co nt ro l s t ruc ture defines two courses of action, depending on the outcome of a condition. Acondition is an expression that, when evaluated, computesto either true or false.

Syntax is: i f cond i t ion

then-par t

else

else-part

end-if

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Decision Making

Being able to mimic the way the human brainworks, the computer also has the ability to makedecisions .

Decision making can be represented inpseudocodes using the IF...THEN construct.

IF ( expression ) THEN::

ENDIF5/9/2013


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Decision Making

IF ( expression ) THEN:

:ENDIF

The expression is a comparison betweentwo values which evaluates to either true of false .

Statements are

placed here.5/9/2013


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Decision Making

Example:-

We are looking for a job which pays more thanRM4000.

IF (Salary>4000 ) THENSay "I Will Take The Job!!"

ENDIF

Example of anExpression

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Decision Making

Commonly used relational operators in expressions :-

> Greater Than

< Less Than

= Equals To

< > Not Equals To

>= Greater Than or Equals To


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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 thespot) about the job offer with a salary of RM2000. Your decision would be to only take a job worth more thanRM4000. What would you say?

IF (Salary>4000 ) THENSay YES!

ELSESay NO!

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Decision Making

Certain conditions may give rise to more thanone expression being evaluated. These areknown as compound expressions .

Example:-

You are interested in taking up a job which paysmore than RM4000 and that the company must

also provide a credit card .IF (Salary>4000) And (CreditCard=YES) THEN

Take Job!!ENDIF

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Decision Making

Compound expressions can be representedusing the following operators :-

AND Every expression must evaluate to be

true in order for the whole expression tobe true.

OR As long as any one of the expression

can be true, the entire IF statement willbe true.

NOT The inverse (opposite ) of the entireexpression.

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Decision Making

IF statements can be nested , that is, placedwithin another IF statement.

This is used in situations when the expressionis more complex than the simple decisions (asseen 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) THENIF (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.5/9/2013


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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 properlyindented to indicate block of statements

which belong together.5/9/2013


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Contd

For Example:

i f a i s g reater than b then

p r in t A is greater

e lse

p r in t B is greater

end i f

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Contd

Repetition Control Structure:

The repet i t ion co nt ro l s t ruc tu re specifies a block of one or more statements that are repeatedly executeduntil a condition is satisfied.

Syntax is:

wh i le cond i t ion

loop-body

end-while

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Looping Constructs

Looping constructs (also known as repetition or iteration constructs) are a kind of construct foundin pseudocodes which allows statements (or a

group of statements) to be repeated .The main reason why looping constructs areprovided 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 thepayroll applies the same calculations for each employee to produce the pay slip .

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Looping Constructs

The looping constructs available in pseudocodesare as follows:-

DOWHILE...ENDDO

FOR NEXT

REPEAT...UNTIL

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Looping Constructs

The format of theDOWHILE...ENDDO construct isshown below:-

DOWHILE ( expression )::

:ENDDO

Group of statements

An expression which determineswhether the loop will continue.

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Looping Constructs

The format of the FOR...NEXTconstruct is shown below:-

FOR (initialze TO expression) STEP increment::

:ENDDO

Group of statements


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Looping Constructs

The format of theREPEAT...UNTIL construct isshown below:-

REPEAT::

:UNTIL ( expression )

Group of statements


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Looping Constructs

Take a look at the following example:-

You are required to develop a complete system

which will allow the total payroll to becalculated.

The system is required to read in the amount to

be paid for each employee .The moment the system receives an inputvalue of -99, the system is required to stop anddisplay the total payroll .

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Looping Constructs


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 = ", Total5/9/2013


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Contd

Example:

Dowhile (income is less than 50000) print Enter taxable income;should begreater than or equal to 50000 read income

Enddo

Documents

ProblemSolving Part 1 Algorithms and Pseudo Coding