Pseudocode and Algorithms. Definition An algorithm is a series of actions placed in the order they are to be executed in order to solve a particular problem.

Pseudocode and AlgorithmsPseudocode and Algorithms

DefinitionDefinition

• An algorithm is a series of actions placed in the order they are to be executed in order to solve a particular problem.

• So getting ready for work in the morning might be:– Get out of bed

– Take shower

– Get dressed

– Eat breakfast

– Go to work

• You may have the actions correct but the order might be wrong.

– Get dressed

– Take shower

– Go to work ………… Wet!

In the practical exercises for Topic One (Data

Representation and Manipulation) we followed step-by-

step instructions to convert decimal numbers to binary

The step-by-step instructions were an example of an

algorithm

In the practical exercises for Topic Two we developed a

number of short Pascal programs based on algorithms

We will now begin to consider how to develop longer,

more sophisticated algorithms as a means of designing

computer programs

Algorithms involve combination ofAlgorithms involve combination of

Sequence

English imperative sentences, doing one thing after

another

Procedure

a mini-algorithm, that is a part of a bigger algorithm

Selection

choice of action depending on a comparison or test.

This uses the IF..THEN..ELSE statement

Repetition

Doing the same thing over and over again. There are

two statements to use here - While..Do and

For...Do

Algorithm involving SelectionAlgorithm involving Selection

get up

if it is a weekday

and you don’t cultivate a beard

and you have stubble on your chin

then

find a razor

shave

endif

Calculating Pension Rights - Algorithm Calculating Pension Rights - Algorithm involving Selectioninvolving Selection

If age > 60 then

calculate pension payable

endif

To make this algorithm easy to understand we use a procedure with a clear name.

The logic of this procedure is described in another (mini) algorithm

A Mini Algorithm (or Procedure)A Mini Algorithm (or Procedure)

Calculate Pension Payable

if gender is female then

calculate woman’s pension

else

check for man’s pension

endif

More Procedures!

Another ProcedureAnother Procedure

Check for Man’s Pension

if age > 65 then

pay man’s pension

endif

And so on…

Procedures in PascalProcedures in Pascal

• The following is the main body of a Pascal program that uses procedures to do something simple!

The Two ProceduresThe Two Procedures

We will look at this again in the tutorial and practical sessions

Procedures help us to write readable Procedures help us to write readable programsprograms

• We can break complex programs up into simple procedures

• Ideally procedures should be functionally cohesive

• i.e. they should do just one thing and it should be clear what that thing is from their name

• If a procedure has to do anything complex it can be broken down into other procedures

• So we might create a program that has a main body that looks like a high-level algorithm.

• For example:

Using indentsUsing indents

If DrinkType = Coffee then

If CoffeeType = “Latte” then

Cost = £2.15

Else

Cost = £1.75

EndIf

Else

Cost = £0.75

EndIf

If DrinkType = Coffee then

If CoffeeType = “Latte” then

Cost = £2.15

Else

Cost = “£1.75

EndIf

Else

Cost = £0.75

EndIf

Using indents in pseudocode helps to show the program structure and can be useful in checking for programming errors. In the example shown here you can see where one structure has been nested within another and where the control is passed back to the original structure

An algorithm that finds the average of two numbers

Input: Two numbersAdd the two numbersDivide the result by 2Return the result

End

Easier to read than Pascal.

Easy to translate into Pascal.

An algorithm to change a numeric exam result to a pass/no pass grade.

Input: One number

if the number is greater than or equal to 40

thenSet the grade to “pass”

elseSet the grade to “fail”

End ifReturn the grade

End

An algorithm to change a numeric exam result to a letter grade.

Input: One number if the number is between 70 and 100 then

Set the grade to “A”if the number is between 50 and 69 then

Set the grade to “B”

if the number is between 40 and 59 then Set the grade to “C”

Return GradeEnd

An algorithm to find the largest of a set of numbers when you do not know the number of numbers.

Input: A list of positive integers

Set Largest to 0while (more integers)

if (the integer is greater than Largest) then

Set largest to the value of the integer End if

End while Return Largest

End

An algorithm to find the largest of 1000 numbers.

Input: 1000 positive integersSet Largest to 0Set Counter to 0while (Counter less than 1000) if the integer is greater than Largest

then Set Largest to the value of the integer End if Increment Counter

End whileReturn Largest

End

Find largest number using a procedure

Input: A list of positive integers

Set Largest to 0while (more integers)

FindLargerEnd whileReturn Largest

End

Procedure: Find larger

Input: Largest and current integer

if (the integer is greater than Largest)then

Set Largest to the value of the integerEnd if

End

How to use PseudocodeHow to use Pseudocode

Before you start typing your program on the computer, sit down and think about what you want to do.

Run through in your head the steps you think you need and then write them down.

THIS is what your pseudocode is.

Control loopsControl loops

The For/Next/Step Loop

Probably the simplest form of looping.

You specify a start and end number and the size of the step. For example if we start at two and move towards the end number of eight in steps of two we will have:

2 4 6 8 Four stages.

Example

We want to print four number 7s

For Times = 2 to 8 step 2

Print “7”

Next

A Problem in Need of a For LoopA Problem in Need of a For Loop

• Find the first 20 Fibonacci numbers. The Fibonacci sequence starts with two numbers:

1 1

• Each subsequent number is formed by adding the two numbers before it. 1+1=2, 1+2=3, 2+3=5, etc. This forms the following sequence:

1 1 2 3 5 8 13 21 34 55 89 144 ...

Algorithm Algorithm

FibonacciNum1 := 0;

FibonacciNum2 := 1;

For count := 1 to 20 do

Display Fibonacci2

temp := Fibonacci2;

Fibonacci2 := Fibonacci1 + Fibonacci2;

Fibonacci1 := Temp

End ForThis algorithm seems to solve

the problem.

To test it I need to translate it into Pascal

Pascal CodePascal Code

• First I need to declare the variables:

Then I can code up the solution:

Pascal CodePascal Code

Output from the ProgramOutput from the Program

If we enter this program into Free Pascal then Compile and Run it – we see the following output

It works!

While loopsWhile loops

• This loop repeats as long as (While) a stated

condition is met.

• In the next example, the variable Counter has to be

less than or equal to 10 in order for the looping to

continue.

• Note a While/Loop structure will not execute even

once if the While condition is violated (False) the first

time through.

While loopsWhile loops

While/Loop Example:

Counter = 1

While Counter <= 10

Print Counter

Counter = Counter + 1

Loop

What this does is print the value Counter over and over

for values starting at 1 and ending at 9.

A Problem in Need of a While LoopA Problem in Need of a While Loop

• Display all powers of 2 that are less than 50000.

• Display the list in a properly formatted manner, with commas between the numbers.

• Display five numbers per line. The output should look like this:

1, 2, 4, 8, 16,

32, 64, 128, 256, 512,

1024, 2048, 4096, 8192, 16384

Pascal Code for this ProblemPascal Code for this Problem while number <= 20000 do

Begin linecount := linecount + 1;

(* Print a comma and space unless this is the first number on the line *) if linecount > 1 then write (', '); (* Display the number *) write (number); (* Print a comma and go to the next line if this is the last number on the line UNLESS it is the last number of the series *) if (linecount = numperline) and not (number * 2 > 20000) then begin writeln (','); linecount := 0 end; (* Increment number *) number := number * 2; end; (* while *) writeln;

Note how helpful the comments

are!

Output from this ProgramOutput from this Program

Repeat Until/Loop Example:Repeat Until/Loop Example:

This loop repeats Until the Counter variable exceeds 10.

Note a Do Until/Loop structure will not be entered if the

Until condition is already True on the first encounter.

Counter = 1

Repeat

Print Counter

Counter = Counter + 1

Loop Until Counter > 10

WARNING!!WARNING!!

If you fail to provide:

• a condition in a While structure which fails to become False or

• a condition in an Until structure which fails to become True

Then

The structure will never terminate and will result in

an error called an “Infinite Loop”

GuidelinesGuidelines

Note that although the pseudocode does not use exact

programming language syntax, it does use loops or

If/Then/Else statements, where needed.

You should not use exact syntax in your pseudocode,

because someone should be able to look at your

pseudocode and from that write a program in ANY

language.

GuidelinesGuidelines

It should be specific enough, though, to give an idea of

what type of program-flow you are thinking of.

Note also that comments can help explain parts.

In general, your pseudocode shouldn't need comments to

explain it, but sometimes it helps!

Practicals and Tutorial QuestionsPracticals and Tutorial Questions

• Time to develop some algorithms and translate them into code

• Have a look at the tutorial and practical questions for this topic before moving on to the review questions

Review QuestionsReview Questions

• What is conditional looping? How does it differ from unconditional looping?

• What is the maximum number of times a While-Do structure will be executed?

• What is the maximum number of times a Repeat-Until structure will be executed?

• What is the maximum number of times a For-To structure will be executed?

• Do we need three different types of loop structure in a programming language?

• Can one type of control structure be nested inside another?