Writing algorithms

Using Algorithms as a Problem Solving Tool
- An Introduction

ICT

Writing Algorithms

In this unit of work you will learn how to design programs that make a
computer perform some simple tasks (or solve some simple problems).

If you sit down in front of a computer and try to write a program to solve
a problem, you will be trying to do four out of five things at once. These
are :

1. ANALYSE THE PROBLEM
2. DESIGN A SOLUTION/PROGRAM
3. CODE/ENTER THE PROGRAM
4. TEST THE PROGRAM
5. EVALUATE THE SOLUTION
[ This comes later]

It is impossible to do four things correctly at the same time, We will
therefore concentrate on each step, one at a time.

1. ANALYSE THE PROBLEM

When you analyse a problem, you look at the problem in front of you and
decide what you need to do to solve the problem.

2. DESIGN A SOLUTION/PROGRAM

Program design is the most important part in producing a computer
program. This is the stage where you decide how your program will work
to meet the decisions you made during analysis.

Program design does not require the use of a computer - you will
carry out your design using pencil and paper.

Approaches To Problem Solving 1 /17

Writing Algorithms

In your design, you will use a method called TOP DOWN DESIGN.
In using this method, you simply write down the steps in the correct
order, that you are required to perform, to solve the problem.

When all these steps are put together you have what is called an
ALGORITHM.

Algorithm:
A step-by-step set of instructions for solving a problem in a limited
number of steps. The instructions for each step are exact and precise
and can be carried out by a computer.

Creating an Algorithm
To begin with we will look at three methods used in creating an algorithm,
these are
STEPPING, LOOPING and CHOOSING.

STEPPING OUT

First of all we will look at a method of creating an algorithm called
STEPPING. This is where all the instructions needed to solve our problem
are set out one after the other. Here are some examples.

PROBLEM: To find the sum of two numbers.
ALGORITHM: 1 add the two numbers together
2 write down the answer.

PROBLEM: To change the temperature in Fahrenheit to Centigrade.
ALGORITHM: 1 subtract 32
2 multiply the result in (1) by 5
3 divide the result in (2) by 9

Both of these examples list the algorithm in an ordered set of steps. Now
it's your turn to try a few.


Writing Algorithms

EXERCISE:
In your workbook, write down an algorithm for each of the following
problems:-

1) Find the average of four numbers.

2) Change the time in seconds to minutes.

3) Find the product of two numbers (this means to multiply the two
numbers).

4) Change a volume in pints to litres (there are 2.2 pints in every litre).

5) Find the difference between two numbers.

All of the problems you have just worked on are fairly simple. Now we will
look at some slightly more complicated problems.

To write an algorithm to solve a more complicated problem we will have to
use a bit more brain power. We will need to have a bit of knowledge and
may have to find out some more information. This information may be
found from a few different sources, for example a textbook, the library
or from your teacher.

As an example, let's work through a problem together:-

PROBLEM: Find the volume of a cone given its diameter and height.

In this problem we know what the diameter and height are of the
cone and we are asked to find its volume. To solve this problem, we
must find out the mathematical formula that allows us to calculate the
volume of the cone. Where could we find this formula if we don't
already know it? - We could look in a mathematics textbook or we could
even try asking our teacher.


Writing Algorithms

Our kind teacher has told us that the formula we need is:

π ⋅r2 ⋅h
Volume = which in plain English means
3
Volume = 3.14 × radius × radius × height ÷ 3

We still have a bit of a problem here, we don't know how to find the
radius of the cone, so again we ask our friendly teacher who tells us that
the radius is half of the diameter.
So given this information we can now write our algorithm:-

ALGORITHM: 1 divide the diameter by 2 to give the radius
2 multiply 3.14 by the radius
3 multiply the result in (2) by the radius
4 multiply the result in (3) by the height
5 divide the result in (4) by 3 to give the volume

This gives the volume of the cone ~ fairly straight forward!

Another example is:-

PROBLEM: Heat up a can of soup

ALGORITHM: 1 open can using can opener
2 pour contents of can into saucepan
3 place saucepan on ring of cooker
4 turn on correct cooker ring
5 stir soup until warm

This may seem a bit of a silly example but it does show us that the order
of the events is important since we cannot pour the contents of the can
into the saucepan before we open the can.


Writing Algorithms

EXERCISE:
In your jotters write down an algorithm for each of the following
problems (remember you may not have all of the knowledge
you need to solve some of these problems ~ ask for help):-

1) To find the average speed of a car given the journey time and the
distance travelled.

2) To find the volume of a cube given the length of a side.

3) To find the volume of a pyramid, given the length and breadth of its
base and its height.

GOING LOOPY ! [LOOPING]

So far, all of the problems we have solved used an algorithm with the set
of instructions in a set order that we refer to as stepping.
What if you have to repeat an instruction or a set of instructions a
number of times to find your solution? In this case you can use loops.
We will look at three different types of loops:-

i. the REPEAT UNTIL loop
ii. the WHILE loop
iii. and the FOR loop

now we will look at each of these a little closer....

i. REPEAT UNTIL LOOP
This type of loop keeps on carrying out a command or commands UNTIL a
given condition is satisfied, the condition is given with the UNTIL
command, for example:-

PROBLEM: To wash a car
ALGORITHM: 1 REPEAT
2 wash with warm soapy water
3 UNTIL the whole car is clean


Writing Algorithms

EXERCISE:
problems
(All of these problems can be solved by using REPEAT UNTIL loops):-

1) To keep delivering newspapers until your paper bag is empty

2) To paint a wall

3) To complete a set of multiple choice questions

ii. WHILE LOOP
In this type of loop the condition is given along with the WHILE command
and the loop keeps on carrying out a command or commands until an END
WHILE command is given, for example:-

PROBLEM: To ask for a number more than 10, then stop when such a
number is given
ALGORITHM: 1 WHILE number given is less than 10
2 ask for a number more than 10
3 END WHILE

EXERCISE:
problems
(All of these problems can be solved by using WHILE loops):-

4) To keep asking for a number less than 5 and stop when a
number less than 5 is given.

5) To keep asking for a password, and to give the message
"accepted" when the correct password is given.

6) To ask for the length of one side of a square, then keep asking for
guesses for the area of the square until the correct area is given
(think about stepping and looping).

iii. FOR LOOP

Writing Algorithms

A FOR loop keeps on carrying out a command or commands, FOR a given
number of times. In this type of loop the number of times it is repeated
must be known. The commands to be repeated are sandwiched between
the FOR and END FOR commands, for example :-

PROBLEM: To print the numbers from 10 to 20
ALGORITHM: 1 FOR number = 10 to 20
2 Print number
3 END FOR

NOTE:
In this loop, the value of number starts at 1 and goes up to 11. Its value
increases by one each time it goes through the loop until it reaches 11.
Since the value of number changes or varies, number is called a variable.
A variable can be given any name provided the name remains the same
throughout your program. We will use the word variable many times in
this work.

VARIABLE :
A quantity or thing, which throughout a calculation, will change in
value. Its name should describe what it is representing e.g. number or
litre or weight etc.


PROBLEM: To print the 13 times table from 1 x 13 to 10 x 13
ALGORITHM: 1 FOR z = 1 to 10
2 Print 13 x z
3 END FOR

In this loop our variable is z, who’s value starts at one and then increases
in value by 1 each time through the loop until z has the value of 10.
Line (2) of this algorithm prints the value of the variable z multiplied by
13.


Writing Algorithms

EXERCISE:
In your jotters write down an algorithm for each of the
following problems:
(All of these problems can be solved by using FOR loops):-

1) To print the 9 times table from 1 x 9 to 12 x 9.

2) To print a message of your choice 4 times.

3) To print a table giving the price of petrol from 1 litre to 25 litres,
given that the price of petrol is 69.5p per litre.

4) To print the values of a number squared from 2 to 20.

5) To print a table showing the area of circles with radii from 10cm to
20cm (ask if you are not sure how to find the area of a circle).

GOING LOOPY ! - WHICH ONE TO USE ?

REVIEW EXERCISE:
following problems:
(All of these problems can be solved by using a loop):-








Writing Algorithms





CHOOSING [IFs, THENs AND ELSEs]

So far we have come across the method of stepping commands and looping
commands. Now we will look at a method for making a choice or a decision.
This technique is called CHOOSING, and uses the commands IF, THEN
and sometimes (but not always) ELSE.
With this type of command a condition is given with the IF command
followed by an action to be taken. If the condition is satisfied, we follow
it by the THEN command. All a bit complicated? Well here are a couple
of examples which should make things a little clearer:-

PROBLEM: To decide if a fire alarm should be sounded
ALGORITHM: 1 IF fire is detected condition
2 THEN sound fire alarm action

PROBLEM: To decide whether or not to go to school
ALGORITHM: 1 IF it is a weekday AND it is not a holiday
2 THEN go to school
3 ELSE stay at home
In this example another command, AND, was used. This command is used
to allow for two or more conditions that have to be satisfied. You will
notice that we have also used the ELSE command in this example where
we are stating an action that must be followed if the conditions are not
met.


Writing Algorithms

EXERCISE:
following problems (All of these problems can be solved by
using the choosing method):-

1) To decide whether or not to wash your hands.

2) To decide whether or not it is time to make lunch.

3) To print the largest of two given numbers.

4) To decide if a number is between 10 and 15, if it is print the number.

ALL TOGETHER NOW..

When you are programming you will find very few problems that can be
solved using just stepping, looping or choosing. In fact most problems will
probably need a combination of all three techniques. These examples
combine STEPPING, LOOPING and CHOOSING to find a solution to the
problems.

PROBLEM: To find the biggest number in a large set of numbers.
ALGORITHM:
1. largest = 0
2. WHILE still numbers to check
3. Read number Looping
Stepping
4. IF number is bigger than largest Choosing
5. THEN largest = number
6. END WHILE
7. Print largest


Writing Algorithms

PROBLEM: To count the number of red boxes in a set of red, white
and blue boxes.
ALGORITHM:
1. number = 0
2. WHILE still boxes to check
3. Read colour
4. IF colour is red
5. THEN number = number +1
6. ELSE number = number
7. END WHILE

Now its your turn to try out all this new found knowledge in the writing of
ALGORITHMS using STEPPING, LOOPING with VARIABLES and CHOOSING.


Writing Algorithms

EXERCISE:
following problems (Stepping, looping and choosing will have
to be used in different combinations for each problem):-

1) To print the smallest number in a large set of numbers.

2) To print the average of a large set of numbers.

3) To check a list of job applicants and reject all those who either smoke
or drink.

4) To ask for a number, less than 50, and then keep adding 1 to it until 50
is reached.


Writing Algorithms

PROBLEMS PROBLEMS PROBLEMS ! !

If you are asked to find a solution to a major problem, it can sometimes
be very difficult to deal with the complete problem all at the same time.
For example building a car is a major problem and no-one knows how to
make every single part of a car. A number of different people are
involved in building a car, each responsible for their own bit of the car’s
manufacture. The problem of making the car is thus broken down into
smaller manageable tasks. Each task can then be further broken down
until we are left with a number of step-by-step sets of instructions in a
limited number of steps. The instructions for each step are exact and
precise.

Top Down Design uses the same method to break a programming problem
down into manageable steps. First of all we break the problem down into
smaller steps and then produce a Top Down Design for each step. In this
way sub-problems are produced which can be refined into manageable
steps.

An example of this is:-

PROBLEM: Ask for the length, breadth and height of a room.
Then calculate and display the volume of the room.

ALGORITHM: 1 ask for the dimensions
2 calculate the volume
3 display the volume

Step 1: 1. Ask for the dimensions
Refinement: 1.1 get the length
1.2 get the breadth
1.3 get the height

Step 2: 2. Calculate the volume
Refinement: 2.1 volume = length x breadth x height


Writing Algorithms

Step 3 does not need any further refinement, so the design is now
complete.

This was a fairly straightforward problem and design. Another, slightly
more complicated example of Top Down Design is explained below:-

PROBLEM: To repair a puncture on a bike wheel.
ALGORITHM: 1. remove the tyre
2. repair the puncture
3. replace the tyre

Step 1: 1. Remove the tyre
Refinement: 1.1 turn bike upside down
1.2 lever off one side of the tyre
1.3 remove the tube from inside the tyre

Step 2: 2. Repair the puncture
Refinement: 2.1 find the position of the hole in the tube
2.2 clean the area around the hole
2.3 apply glue and patch

Step 3: 3. Replace the tyre
Refinement: 3.1 push tube back inside tyre
3.2 replace tyre back onto wheel
3.3 blow up tyre
3.4 turn bike correct way up

Sometimes refinements may be required to some of the sub-problems,
for example if we cannot find the hole in the tube, the following
refinement can be made to 2.1:-


Writing Algorithms

Step 2.1: 2.1 Find the position of the hole in the tube
Refinement: 2.1.1 WHILE hole cannot be found
2.1.2 Dip tube in water
2.1.3 END WHILE

If we now put all of these refined steps together we are left with
the complete algorithm needed to solve our problem.

1. Remove the tyre
2. Repair the puncture
3. Replace the tyre

1. Remove the tyre
1.1 turn bike upside down
1.2 lever off one side of the tyre
1.3 remove the tube from inside the tyre

2. Repair the puncture
2.1 find the position of the hole in the tube
2.1.1 WHILE hole cannot be found
2.1.2 Dip tube in water
2.1.3 END WHILE
2.2 clean the area around the hole
2.3 apply glue and patch

3. Replace the tyre
3.1 push tube back inside tyre
3.2 replace tyre back onto wheel
3.3 blow up tyre
3.4 turn bike correct way up


Writing Algorithms

EXERCISE:
In your jotters write down a Top Down Design for each of the
following problems (Show your initial algorithm and refined
sub-problems as shown in the above example):-

1) To make a butter and jam sandwich.

2) To ask for the length of all the walls in a room, ask for the height of
the room, calculate and then display the total area of the room.

3) To calculate an employee’s wages using these conditions:
Ask for the employee’s name and how many hours they worked.
Up to 40 hours are paid at £4.00 per hour, all hours over 40 hours
are paid at “time and a half”
Display the employee’s name, their basic rate pay, their overtime pay
and their total pay.


Writing algorithms

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