4.1 Algorithms

4 Algorithms and flowcharts

4.1 Algorithms

Before we look at how to write or edit an algorithm, let us consider what is

meant by an algorithm. In computer science, information technology and

mathematics, an algorithm is a set of instructions sequenced to solve a problem

or to represent a calculation. Some would say that an algorithm is basically a data

program flowchart without the boxes. It is actually a list of precise steps.

The order in which these steps are carried out is always crucial to the way an

algorithm works. We start at the first line of the algorithm and work downwards

to the final instruction. When an algorithm is created to produce information,

data is input, processed, then the result is output. An algorithm must be carefully

designed. It must be written in a way that caters for all possible scenarios. Any

steps that rely on decisions being made must be dealt with in sequence and

the conditions must be clear and unambiguous. Depending on the way the

algorithm is written, not all instructions are carried out for a particular scenario,

but they still have to be written in a way that allows for all possible scenarios.

Algorithms can be written in many different ways, including everyday natural

language,

pseudocode, flowcharts or programming languages. Natural

language can sometimes lead to instructions which are open to interpretation

and so tends not to be used in very complex algorithms. Pseudocode and

flowcharts are structured ways of writing algorithms and we will concentrate on

these approaches. Programming languages are primarily intended for converting

algorithms to a form that can be understood and executed by a computer.

When solving problems in this chapter, the algorithms will be written in

pseudocode. Pseudocode is independent of any programming language. Once

the pseudocode is written and checked to make sure that it solves the problem,

In this chapter you will learn how to:

+ write a basic algorithm that demonstrates a

decision-making process

+ use conditional branching within an

algorithm

+ use loops within an algorithm

+ use nested loops within an algorithm

+ include procedures/subroutines within an

algorithm

+ edit a given algorithm

+ writeanalgorithmtosolveagivenproblem

+ editagivenflowchart

+ drawabasicprogramflowchartthat

demonstrates a decision-making process

+ drawaprogramflowcharttosolveagiven

problem

+ identify errors in an algorithm or program

flowchart for a given scenario.

Before starting this chapter you should understand the:

+ comparison operators >, <,=

+ arithmeticoperators+,-,*,/

+ orderofarithmeticaloperationsinanequation.

4 ALGORITHMS AND FLOWCHARTS

it would be fairly straightforward to translate it into any programming language

we were familiar with.

Any algorithm consists of statements which have linear progression, that is the

result of one statement is used in the statements that follow. It may also contain

conditional branching, such as IF…THEN…ELSE or CASE…ENDCASE,

which results in a decision being made between two or more courses of actions.

It will probably also involve the use of

loops such as WHILE…ENDWHILE

or REPEAT…UNTIL. A loop is a sequence of statements that are repeated a

number of times.

Here are some key actions that are performed and the common terms used in

pseudocode:

» inputting data: INPUT or READ

outputting data: WRITE or PRINT

» calculation: +, -, *, /

» comparison: >, <, =, <>

» setting values:

←

Do not worry if you have not met some of these before as we will be going into

much greater detail when we begin to write our own algorithms.

4.1.1 Writing an algorithm

By the end of this chapter, you will be able to write a basic algorithm that

demonstrates a decision-making process. In order for you to be able to do this

you will need to become familiar with a number of pseudocode terms. One of

the most basic units of an algorithm is a variable. It is best to think of a variable

as an area of the computer’s memory that stores one item of data, such as a

number. The algorithm designer is able to choose the names of the variables,

making writing an algorithm easier, and also it is possible to write an algorithm

where we can change the values each time we work the algorithm. Assigning

a value to a variable name can be done using an arrow symbol,

←. The variable

name is to the left of the sign and the value is to the right, for example:

X ← 42

means we want to store the number 42 in X.

We can also assign calculations and other types of processing this way, for

example:

Z ← W + X + Y

This assigns the result of adding the contents of W, X and Y together and stores

the result of this calculation in Z.

Input and output

Consider your use of calculators. When you want to do a calculation such as

42× 36, three things have to happen. First of all, you have to type in the numbers,

then the calculator’s internal computer calculates the answer and finally it outputs

the answer on the screen. The last two occur so quickly that you probably do not

realise that the calculation occurs before the answer appears on the screen.

4.1 Algorithms

If we were writing an algorithm to describe this calculation it would simply be:

INPUT X, Y // input two numbers, one is X, the

other is Y

Z ← X*Y // multiply the two numbers and call

the answer Z

PRINT Z // output the answer Z

It is written like this so that X and Y represent any two numbers.

We can think of Z as somewhere we store the result of X multiplied by Y.

The last line causes the answer (Z) to be output.

Notice we have used // to make comments. This just helps us to see what is

going on but is not part of an instruction to be carried out.

If we use 42 and 36 as our numbers, Z would be 42*36, which is 1512.

We could use any letters or words instead of X, Y and Z.

We could have written:

INPUT firstnumber, secondnumber

answer ← firstnumber*secondnumber

PRINT answer

This is an example of how writing an algorithm can be made simpler just by

using variable names that make sense and result in the algorithm being easier

to follow. Always try to use variable names which give a clue to what they are

storing.

The last statement could also be written as:

PRINT "The answer is", answer

This would result, using our calculation, in the following output:

The answer is 1512

Conditional branching

This is sometimes referred to as selection. Conditional branching means that

certain statements are carried out depending on the value stored within a

particular variable name. There are generally considered to be two types, which

are IF…THEN…ELSE and CASE…ENDCASE.

IF…THEN…ELSE

From now on, whenever you see words within angle brackets, this is just an

explanation of what you will be typing in and not the exact words themselves,

for example <statement> would mean that a statement must go here, such as:

A ← B+C

4 ALGORITHMS AND FLOWCHARTS

Sometimes, IF statements do not have an ELSE part, such as in this sequence of

instructions:

IF <condition>

THEN

ENDIF

An example of this type is:

INPUT number1, number2

X ← number1/number2

IF number2 > number1

THEN

X ← number2/number1

ENDIF

PRINT X

Here, two numbers are input and the first number is divided by the second

number, with the result being stored in X. The IF condition checks to see if

the second number is bigger than the first. If it is, then the second number

is divided by the first number and that result is stored in X, overwriting the

previous result. If it is not, then X remains unchanged. The value in X is then

output.

It is important to note that IF statements are slightly indented. It does not

matter how much the indentation is, as long as you are consistent and use the

same amount of indentation for each IF.

THEN statements are further indented and again, you just need to be

consistent. The statement after THEN is further indented. ENDIF must always

be in line with the IF statement. Any statements that come after ENDIF are not

indented.

IF statements with an ELSE clause are written as follows:

IF <condition>

THEN

<statement or list of statements to be carried

out>

ELSE

<alternative statement or list of alternative

statements to

be carried out>

ENDIF

4.1 Algorithms

Using our example above, a better way of writing the algorithm would be:

INPUT number1, number2

IF number2 > number1

THEN

X ← number2/number1

ELSE

X ← number1/number2

ENDIF

PRINT X

Here, as before, the value of X is the bigger of the two numbers divided by the

smaller number.

The algorithm inputs two numbers. It checks to see if the second number is

bigger than the first and if it is then it divides the second number by the first

number, storing the answer in X. If it is not bigger (ELSE) it divides the first

number by the second number, storing the answer in X.

Again, it is important to note the indents and the fact that ELSE is immediately in line

with THEN. The statement below THEN is in line with the statement below ELSE.

Sometimes it is necessary to have what are called nested IF statements. This is an

IF condition within another IF. You will have met these when using spreadsheet

software during your practical lessons.

Let us consider an exam system where if a student gains 75 or more marks they are

awarded a distinction; if they get between 60 and 74 marks they are awarded a merit;

between 40 and 59 marks the student is awarded a pass; otherwise they fail the course.

This is the type of problem which requires nested IF statements to solve it. One

solution is as follows:

1INPUT mark

2 IF mark <75

3 THEN

4 IF mark <60

5 THEN

6 IF mark <40

7 THEN

8 PRINT "Sorry you have failed"

9 ELSE

10 PRINT "You have passed"

11 ENDIF

12 ELSE

13 PRINT "Well done. You have been awarded a merit"

14 ENDIF

15 ELSE

16 PRINT "Congratulations you have been awarded a distinction"

17 E N DIF

4 ALGORITHMS AND FLOWCHARTS

Each line of pseudocode is numbered. This does not normally tend to be the

casebut it has been done here to make the explanation of this algorithm easier

tofollow.

Consider marks of 34, 45, 62 and 78. We will work through the algorithm for

eachmark.

With an IF statement we follow the THEN part when the IF statement is true

but we only follow the ELSE part if the IF statement is false.

For the first mark of 34:

Statement 1 will store 34 in the variable name ‘mark’.

Statement 2 is true so we go on to statements 3 and 4.

Statement 4 is true so we go on to statements 5 and 6.

Statement 6 is also true so we move on to statements 7 and 8, which cause the

message ‘Sorry you have failed’ to be printed out.

We can go on to statement 11 as we can ignore statements 9 and 10 which are

only followed if statement 6 was false.

Statement 11 is just there to tell us that statement 6 is now closed.

We can ignore statements 12 and 13 which would only be followed if statement

4 were false.

Statement 14 tells us we have reached the end of the IF in statement 4.

Again, we can ignore statements 15 and 16 as statement 2 is not false, which

brings us to statement 17, which shows us that we have reached the end of the

whole sequence of the nested IF.

Briefly then, for the mark of 45, statements 2 and 4 are true, so we reach

statement 6 which is false. As a result, we jump to the ELSE statement 9 and

reach statement 10 which causes the message ‘You have passed’ to be printed

out. We then ignore all the remaining ELSE statements.

For the mark of 62, statement 2 is true but statement 4 is false, so we jump to

the corresponding ELSE statement to the line 5 THEN statement, which is

line 12. That causes us to go on to line 13, which causes the message ‘Well

done. You have been awarded a merit’ to be printed out.

For the mark of 78, line 2 is false so we jump straight to the corresponding

ELSE statement in line 15 which leads to line 16 being printed out

‘Congratulations you have been awarded a distinction’ and then we reach

line 17.

Always make sure that the number of ENDIFs matches the number of IFs and

that they are indented to match. Always make sure the ELSEs are in line with

theTHENs.

CASE…ENDCASE

With this type of condition, depending on the value input, the algorithm carries

out one of a number of statements. The condition can be phrased differently

but we shall use CASE <identifier> OF, though some would use CASE OF

<identifier>. Whichever you choose to use, just be consistent.

The value input is usually a number which then determines which statement will

be carried out.

4.1 Algorithms

CASE <identifier> OF

OTHERWISE : <statement or list of statements>

ENDCASE

Depending on the value entered, either one statement or several statements can

be carried out. For example:

INPUT grade

CASE grade OF

'distinction': X ← 75

Y ← 100

'merit': X ← 60

Y ← 74

'pass': X ← 40

Y ← 59

'fail': X ← 0

Y ← 39

ENDCASE

PRINT "Your mark must have been between ",X, " and ",Y

This algorithm allows you to type in your grade as a word. The values of

X and Y are set accordingly depending on the word you type in. The range

of marks that your mark must have been within is then printed out after

the phrase ‘Your mark must have been between’. Note the comma after the

quotation marks. Commas are used to separate variable names from the

words that are printed out.

For example, if ‘distinction’ is typed in, then X is set to 75 and Y is set to 100

and the algorithm jumps immediately to ENDCASE and then prints out the

message: ‘Your mark must have been between 75 and 100’.

Notice neither the quotes nor the commas are printed out.

If the word ‘merit’ had been typed in then the first case (‘distinction’) is ignored

and the second case is carried out, then it jumps to ENDCASE and prints out

the appropriate message. With ‘pass’, it goes straight to the third case then

ENDCASE before printing the message, and with ‘fail’, it goes to the fourth

case then ENDCASE and prints out the message.

It is quite common for CASE…ENDCASE to have numbers input and the

appropriately numbered CASE statement to be carried out. Here is an example

which includes an OTHERWISE statement.

4 ALGORITHMS AND FLOWCHARTS

INPUT number

CASE number OF

1 : PRINT "This is the number 1"

2 : PRINT "This is the number 2"

OTHERWISE: PRINT "You have entered an

unacceptable number"

ENDCASE

The OTHERWISE case must always be the last case statement.

There are a number of variations of the CASE…ENDCASE statement but you

will need to be consistent with your use of any variation to the method given

above.

Activity 4a

1 Write an algorithm using IF…THEN which will input a number, then print out

the number multiplied by 8 if it is less than 3, multiplied by 4 if it is between 3

and 5, and multiplied by 2 if it is any other number.

2 Write an algorithm using CASE…ENDCASE which will input a number,

then print out the number divided by 2 if it is less than 6, divided by 5 if it is

between 6 and 10, and divided by 10 if it is any other number.

Loops

When referring to the writing of computer programs or algorithms, a loop

is a sequence of repeated statements that are carried out a number of times.

This number may be just one or it can be a very large number, depending on

the problem which needs solving. There are two ways a loop operates. One

way is sometimes referred to as a pre-condition loop, meaning the conditional

statement is checked before (pre) any of the sequence of statements is followed.

This is when a condition is checked to see if it is met and if it is, the sequence

of statements is carried out. When the last statement is reached, the conditional

statement is returned to. The condition is checked again and the whole process

is repeated. Once the condition has not been met, it jumps to the last statement

and exits the loop.

The other type of loop is sometimes referred to as a post-condition loop. As its

name suggests, the conditional statement is only checked after the sequence has

been carried out for the first time. If the condition is not met, then the first

statement is returned to. This is repeated until the condition is met, in which

case the next statement after the close of the loop is carried out. The loops

which will be described here are the WHILE…ENDWHILE loop (a pre-

condition loop) and the REPEAT…UNTIL loop (a post-condition loop).

Before describing the different types of loop, the concept of counting within

an algorithm has to be considered. If a loop is to be repeated a certain number

of times, it is usual to set up a counter. This usually involves the initialising of a

variable (setting it to 0). The variable name used is often just ‘count’. It is quite

common for the first statement in any algorithm to be:

count ← 0

4.1 Algorithms

This count is then incremented (increased by 1) every time a sequence of

statements is carried out.

count ← count + 1

The loop can then be set up to be executed an exact number of times. This is

done by basing the conditional statement on whether the count has reached the

number of times we want the loop to be carried out.

WHILE…ENDWHILE

The WHILE…ENDWHILE loop looks like this:

WHILE <condition>

<a statement or a list of statements to be carried

out>

ENDWHILE

Some variations of this loop have the word ‘DO’ after the condition:

WHILE <condition> DO

We will not be using this in this book.

While the condition is met, the statements between the WHILE and

ENDWHILE statements will be carried out. As soon as the conditional

statement stops being true, the loop ends.

An example of a WHILE…ENDWHILE algorithm using a counter would be:

count ← 0

INPUT number

WHILE count < number

count ← count + 1

PRINT count, "x 10 = ", count*10

ENDWHILE

This algorithm takes as input the number of times the loop is to be

executed – ‘number’. It checks whether the count is less than this number

before proceeding with the sequence of statements to be carried out. The

first statement increments the counter so that it goes up by one before the

calculation is performed. This algorithm is printing out the multiplication table

for 10, often called the 10 times table, up to the number that is input. If the

number input was 6 it would calculate 1*10, 2*10, 3*10, 4*10, 5*10 and finally

6*10 before exiting.

REPEAT…UNTIL

Unlike the WHILE…ENDWHILE loop, which tests the condition at the start

of the loop, the REPEAT…UNTIL loop checks the condition at the end of the

loop. It is similar to a WHILE…ENDWHILE loop, except that a REPEAT…

UNTIL loop is executed at least once.

4 ALGORITHMS AND FLOWCHARTS

The REPEAT…UNTIL loop looks like this:

REPEAT

<a statement or a list of statements to be carried

out>

UNTIL <condition>

The statements between the REPEAT and UNTIL are carried out and from

then on, for as long as the UNTIL condition is not met, they will be repeated.

After the first time, they will only be carried out while the conditional

statement is false. As soon as the condition becomes true, the loop ends.

We can convert the example above which uses the WHILE…ENDWHILE loop

into the following:

count ← 0

INPUT number

REPEAT

count ← count + 1

PRINT count, "x 10 = ", count*10

UNTIL count = number

The only difference is that if you did not want anything printed out, you could

type in 0 for the number. With the WHILE…ENDWHILE loop it would print

nothing out. With the REPEAT…UNTIL loop it would print out:

1 x 10 = 10

despite the fact we might not want it to. This is a big disadvantage of the

REPEAT…UNTIL loop, but as long as you want the loop to be executed at

least once, it works well.

Nested loops

A nested loop, as its name suggests, is a loop within a loop. Let us start with an

example. We have already seen an algorithm which can output a multiplication table.

Now we will look at an algorithm which will output several multiplication tables.

count1 ← 0

INPUT number1 // this is the number of multiplication tables

printed out

INPUT number2 // this is the number we want to go up to in

each table

WHILE count1 < number2

count1 ← count1 + 1 // count1 is incremented so we do not

get 0 × 0

count2 ← 0

WHILE count2 < number1

count2 ← count2 + 1 // count2 is incremented so we do not get 1 × 0

PRINT count1, "x ", count2, "= ", count1*count2

ENDWHILE

4.1 Algorithms

The variable number1 is the number of multiplication tables we want and

number2 is how far we want the table to go up to. For example, if 6 is input for

number1, then the 1, 2, 3, 4, 5 and 6 multiplication tables will be printed out,

and if 12 is input for number2 each table will go up to 12×.

Notice that both count1 and count2 are incremented immediately after the loop

starts to prevent the algorithm from printing out 0×1 or 1×0. The WHILE…

statement only checks whether the condition is met before the loop is allowed

to start. When count2 gets to 6, it will have already printed out 1×6 and the

count1 loop will increment then count2 will be set back to 0. This is repeated

until count1 is 12 and count2 is 6.

The final output would be:

1 × 1 = 1 1 × 2 = 2 1 × 3 = 3 1 × 4 = 4 1 × 5 = 5 1 × 6 = 6

2 × 1 = 2 2 × 2 = 4 2 × 3 = 6 2 × 4 = 8 2 × 5 = 10 2 × 6 = 12

3 × 1 = 3 3 × 2 = 6 3 × 3 = 9 3 × 4 = 12 3 × 5 = 15 3 × 6 = 18

4 × 1 = 4 4 × 2 = 8 4 × 3 = 12 4 × 4 = 16 4 × 5 = 20 4 × 6 = 24

5 × 1 = 5 5 × 2 = 10 5 × 3 = 15 5 × 4 = 20 5 × 5 = 25 5 × 6 = 30

6 × 1 = 6 6 × 2 = 12 6 × 3 = 18 6 × 4 = 24 6 × 5 = 30 6 × 6 = 36

7 × 1 = 7 7 × 2 = 14 7 × 3 = 21 7 × 4 = 28 7 × 5 = 35 7 × 6 = 42

8 × 1 = 8 8 × 2 = 16 8 × 3 = 24 8 × 4 = 32 8 × 5 = 40 8 × 6 = 48

9 × 1 = 9 9 × 2 = 18 9 × 3 = 27 9 × 4 = 36 9 × 5 = 45 9 × 6 = 54

10 × 1 = 10 10 × 2 = 20 10 × 3 = 30 10 × 4 = 40 10 × 5 = 50 10 × 6 = 60

11 × 1 = 11 11 × 2 = 22 11 × 3 = 33 11 × 4 = 44 11 × 5 = 55 11 × 6 = 66

12 × 1 = 12 12 × 2 = 24 12 × 3 = 36 12 × 4 = 48 12 × 5 = 60 12 × 6 = 72

The same output would be produced using the following nested REPEAT…

UNTIL loop:

count1 ← 0

INPUT number1

INPUT number2

REPEAT

count1 ← count1 + 1

count2 ← 0

REPEAT

count2 ← count2 + 1

PRINT count1, "x ", count2, "= ", count1*count2

UNTIL count2 = number1

UNTIL count1 = number2

Advice

Common errors

An error sometimes made by people writing algorithms with nested loops is

not matching up the number of WHILE statements with the same number of

ENDWHILEs. The same error can happen with REPEATs and UNTILs. You must

always check this and make sure they are correctly indented.

4 ALGORITHMS AND FLOWCHARTS

An IF statement checks if something is true and if it is, it carries out a matching

statement. As we have seen above, if it is not true, the algorithm will either

carry on or have an alternative statement to carry out which requires an ELSE

statement. Sometimes, people forget to include a matching ELSE statement.

Procedures/subroutines

When writing algorithms, it is often good practice to use subroutines, which

are sometimes called procedures, although technically a procedure is a subset of

subroutines. A subroutine is a sequence of algorithm statements that perform a

specific task. This subroutine can then be used in other algorithms as and when

needed.

The subroutines or procedures follow the following pattern:

PROCEDURE <value>

ENDPROCEDURE

Let us consider a house builder who needs to know the area of the top part

of a brick wall underneath the roof. He or she wants to calculate the number

of bricks to be used. Such a house is shown in the figure below, with the area

which needs to be calculated indicated as a red triangle. The other areas which

would need to be calculated are rectangle shapes. An algorithm can be written

to work out these areas and this could then be used to calculate the number of

bricks needed. This could all be done by using simple subroutines.

The subroutines or procedures could be simply written as:

PROCEDURE triangle(width, height)

area ← width*height*0.5

PRINT area

ENDPROCEDURE

PROCEDURE rectangle(length, width)

area ← length*width

PRINT area

ENDPROCEDURE

4.1 Algorithms

The main algorithm could be:

INPUT width, height // type in the height and width of

the triangle

CALL triangle (width, height) // this would print out the area

INPUT number // type in the number of walls

count ← 0

WHILE count < number

INPUT length, height

count ← count + 1

CALL rectangle (length, height) // this would print out the area of

each wall

ENDWHILE

Notice that although we used length and width as the variable names when we set

up the rectangle procedure, we can use different variable names when we ‘CALL’ it.

As long as we ‘pass’ two numbers to the procedure, it will perform the calculation.

Once the procedure or subroutine is set up, it can be called as many times as we

want.

File handling

There are a number of file-handling functions used in pseudocode, but they are

really outside the scope of this book. However, you will need to demonstrate

an understanding of how file handling works, without necessarily knowing the

technical terms. Let us consider the very basic algorithm that was constructed in

Chapter 1.

1 First record in the transaction file is read

2 First record in the old master file is read

3REPEAT

4 IDs are compared

5 IF IDs do not match, old master file record is

written to new master file

6 IF IDs match transaction is carried out

7 IF transaction is D or C, old master file

record is not written to new master file

8 IF transaction is C, data in transaction file

is written to new master file

9 IF IDs match, next record from transaction file

is read

10 Next record from master file is read

11 UNTIL end of old master file

12 Data in transaction file record is written to

new master file

13 Any remaining records of the transaction file are

written to the master file

4 ALGORITHMS AND FLOWCHARTS

You should now be able to convert it into a properly structured algorithm such

as this (notice we are using command words for the file input – READ and

output – WRITE):

READ first record from the transaction file

READ first record from the old master file

REPEAT

IF ID of old master file record <> ID of transaction file record

THEN

WRITE old master file record to new master file

ELSE

IF transaction = C

THEN

WRITE data in transaction file record to new master file

ENDIF

READ next record from master file

UNTIL end of old master file

WRITE data in transaction file record to new master file

WRITE any remaining transaction file records to the master file

4.1.2 Drawing flowcharts

There is another way of writing an algorithm and that is by using a program

flowchart. A program flowchart is a diagrammatic way of representing an algorithm

used to produce the solution to a problem. A flowchart consists of symbols,

connected to each other by arrows which indicate the path to be followed when

working through the flowchart. Each different shape symbol represents a different

stage in the process. From now on when we mention the word flowchart we are

referring to program flowchart. This is not the same as a system flowchart, which

you will meet in the A2 text book. Below is a list of the more common symbols.

Input/output This shape symbol represents input or output. It is equivalent

to either the INPUT or PRINT statement.

Decision This is a decision box and is equivalent to the IF statement but

is also used in loops.

Terminator

(Start/Stop)

This is the symbol used to show where the flowchart begins

and also where it ends. It is also used at the start and end of a

subroutine.

Process box This symbol represents any calculation or assigning of

variables, usually contains the ← symbol.

Subroutine

This is the symbol used to call a subroutine from the main

flowchart. It is equivalent to CALL.

Flow line

This is the symbol that shows which direction you should follow

when working through the flowchart.

Connector

Sometimes a flowchart can extend over many pages. This

symbol indicates the continuation of the flowchart.

4.1 Algorithms

Sometimes flowcharts are so complex that they occupy more than one page. To

illustrate this, let us imagine that the central heating system flowchart shown in

Chapter 3 has been extended. Here it is, labelled.

Start

Stop

system switched

on?

temperature <

pre-set?

INPUT

temperature

Yes

Send signal

to open valves

Send signal to

close valves

Send signal to

switch pump off

Send signal to

switch pump on

These are connector symbols

These are

terminator symbols

These are

decision

boxes

These are

output boxes

This is an

input box

A B C

V Figure4.1LabelledflowchartfromChapter3

It is possible that this flowchart might have continued on to another page. The

connector symbols have been added to the ends of the flow lines to show how

they would be positioned, if this were the case. Connector symbols A, B and

C would be drawn at the top of the next page with the appropriate flow lines

flowing down to the next symbol(s) if the flowchart continued.

To illustrate how to draw a flowchart, let us consider the earlier algorithms:

PROCEDURE triangle(width, height)

area ← width*height*0.5

PRINT area

ENDPROCEDURE

Triangle (width, height)

area m width*height*0.5

PRINT area

Return

This becomes:

100

4 ALGORITHMS AND FLOWCHARTS

INPUT width, height // type in the height and width of the

triangle

CALL triangle (width, height) // this would print out the area

INPUT number // type in the number of walls

count ← 0

WHILE count <number

INPUT length, height

count ← count + 1

CALL rectangle (length, height)

ENDWHILE

This becomes:

Start

INPUT

width,

height

CALL triangle

(width, height)

Stop

Count < number ?

INPUT

length,

height

Yes

INPUT

number

Count m 0

Rectangle (length, width)

area m length*width

PRINT area

Return

PROCEDURE rectangle(length, width)

area ← length*width

PRINT area

ENDPROCEDURE

This becomes:

101

4.1 Algorithms

CALL rectangle

(length, height)

Count m

count + 1

Notice the use of connector symbols because the flowchart goes over two pages.

As well as being able to increase the value of a counter, it is possible to add up a

set of numbers in the same way, using:

total ← total + number

but you need to initialise the total as you would initialise a count. The flowchart

to add up five numbers would look like this.

Start

Stop

Count < 5 ?

INPUT

number

Yes

Count m 0

Total m 0

PRINT total

Count m count + 1

Total m total + number

Common errors people make when drawing flowcharts and writing algorithms

are:

» failing to initialise a count (leaving out count ← 0)

» failing to initialise a running total (leaving out total ← 0)

» getting the greater than (>) confused with the less than (<) symbol

» In flowcharts, having the yes and no the wrong way around.

Activity 4b

1 Look back at the section on greenhouses in Chapter 3. Refine the algorithms provided for temperature,

moisture and light control to make them more efficient. Consider what should happen if the device is

already switched off or switched on. Include extra statements to replace where the original algorithm has

phrases like ‘or leave on’ and ‘or leave off’.

102

4 ALGORITHMS AND FLOWCHARTS

The sequence of statements needed for this will be similar to the following:

WHILE system switched on

INPUT value

IF value < pre-set

THEN

IF device off

THEN

send signal to device to switch on

ENDIF

ELSE

IF device on

THEN

send signal to device to switch off

ENDIF

ENDWHILE

You will need to change the word ‘device’ to the name of the device being used. You will need to change

‘value’ to the physical variable being measured. Draw program flowcharts for each algorithm so that each

is a subroutine with an appropriate name. You can assume the system is switched on.

2 Draw a simple program flowchart which would check if the system was on and would then call the three

subroutines.

3 Here is a program flowchart to output the sum of eight numbers. Identify the errors in it and suggest

improvements (the yes and no flow lines are positioned correctly).

Start

Stop

Count > 8 ?

INPUT

number

Yes

Count m 0

Count m count + 1

Sum m sum + number

103

4.1 Algorithms

Examination-style questions

1 Write an algorithm using WHILE…ENDWHILE conditions, which would input

10 exam marks and if the mark was greater than 40 the output would be

‘You have passed’. If it was not, then the output would be ‘You have not

reached the pass mark’.

[6]

Write an algorithm using a REPEAT…UNTIL loop which would input

five numbers and would output the largest number.

[4]

Draw a flowchart which will allow the average of six numbers to be

calculated.

[6]

A student wants to output the 10 multiplication (times) table up to a certain

number, which will be input at the start of the algorithm. The student wishes

to make sure that an invalid number is not input.

Identify the errors in this algorithm and suggest improvements.

[5]

count ← 0

WHILE count = 0

INPUT number

IF number < 1

THEN

PRINT "number is invalid"

ENDWHILE

WHILE count < number

PRINT count, "x 10 = ", count*10

ENDWHILE

5 This flowchart inputs an examination

mark and then outputs an appropriate

message. If the mark is 80 or more, the

message is distinction; if it is 60 or

more, it is a merit; if it is 40 or more,

it is a pass; otherwise, it is a fail.

Identify the errors in this flowchart and

suggest how it might be edited

to produce the required output.

[2]

Start

Stop

Mark < = 80 ?

Mark < = 60 ?

Yes

Mark < = 40 ?

INPUT

mark

"Pass"

"Fail"

"Merit"

"Distinction"