Department of
Computing
Science
CS_PAS
Course
Manual
1999/2000
University of Aberdeen
CS_PAS
1999/2000
COURSE MANUAL
Introduction
Welcome to this course. No matter how much programming you may have done in the past - and that
includes none - I hope that you will find the course interesting and instructive. This manual contains the
information you will need to get started.
Much of the material for the course is available on the World Wide Web: lecture notes, slides used in
lectures, solutions to problems, etc. You will be told later in this manual how to access it.
At the end of this course you should understand the basic principles of structured program design and
be able to apply them in writing a simple Pascal program which makes extensive use of library
procedures and functions. It is a pre-requisite for any undergraduate wishing to continue their studies in
Computing Science, and it is also suitable if you wish to develop programming skills to support your
studies in other subject areas.
One of the following books is required for the course:
J Bishop, Turbo Pascal Precisely , Addison-Wesley (1992) paperback.
or
D W Nance, Understanding Turbo Pascal: Programming and Problem Solving, West Publishing
Company (1994).
Most of you taking this course will be doing so in classrooms belonging to the University Computing
Centre.
Some may be taking it at a remote Study Centre; in this case the Centre will have provided suitable
facilities, and you should consult the staff there.
It is possible to use a stand-alone computer at home for working on this course; a Web page will be set
up which will describe how to do this.
In the rest of this document, the following conventions will apply:
 a hollow bullet (like this) indicates that you should take some action
italics will usually describe the response you should get
Copyright: Jim Hunter (September 1998)
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KAREL the Robot
During the first part of this course, you will be writing programs which control a robot called KAREL.
It's too expensive to provide everyone with a real robot, so we have to simulate him on the PC.
Getting to Know KAREL and his World
Your first objective is to get to know KAREL and his world. To this end we have built a version of the
KAREL simulator (we call it a 'manual' version - ManKAREL) which allows you to control KAREL
using the mouse.




If necessary, start up Windows NT.
Open the Science and Engineering folder on the Desktop
Open the Computing Science folder.
Double click on the Mount CS_PAS icon
Note: You should always do this before you start ant work in connection with this course - amongst
other things it mounts the L: drive.
 Double-click on the ManKAREL icon. This will bring up a large window which shows KAREL’s
world, and a smaller window (the Control Panel) which will allow you to get KAREL to do things.
 If necessary, move the Control Panel away from the centre of the screen.
KAREL's World
KAREL lives in a flat world with the standard north, south, east and west compass points; north is to
the top of your screen. He moves around a two-dimensional grid marked by an array of Grid Points
(often referred to simply as Points). KAREL is always positioned on a Grid Point facing north, south,
east or west; he is represented by a black crescent. Grid Points have co-ordinates - an X co-ordinate
(running from left to right) and a Y co-ordinate (running from bottom to top). We'll use the standard
convention to indicate the co-ordinates of a given Grid Point e.g. (3,4) means that the X co-ordinate is 3
and the Y co-ordinate is 4. The Origin is the Point (1,1) - not (0,0) which doesn't exist in KAREL's
world.
We will need to refer to distances in KAREL's world. The basic unit of distance is that between two
neighbouring Points. I will refer to this distance as a block - referring to the American way of describing
the distance between two parallel streets.
KAREL's world is bounded all round by external walls. We can set up different worlds for KAREL to
be in, with different internal walls, but they all have the external walls just described. Internal walls can
be of any length, and are positioned between adjacent Points, blocking KAREL's path from one Point to
the next; walls are represented by blue lines. KAREL can detect walls but can't penetrate them. The
other kind of object in KAREL's world is a beeper. Beepers are small plastic balls that emit a quiet
beeping noise; one beeper is represented by red concentric circle - more than one by a red number.
They are situated on Points and can be picked up, carried or put down by KAREL. The figure on the
next page gives one possible world for KAREL. In this world KAREL starts as shown at Point (3,11).
Different worlds are stored in separate files. The name of the file is the name of the world. Each file
determines where the internal walls are (if any), where KAREL starts from, where any beepers are (if
any) and how many beepers he is carrying to begin with (if any).
KAREL's Capabilities
KAREL can only move in the direction he is facing, one Point at a time. He can also turn, although he
only understands the command to turn left. He carries with him a beeper bag and at any time, if he has
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beepers in his bag, can take one out and place it where he is. If he is on the same Point as a beeper then
he can pick it up and put it in his bag. Finally he can turn himself off. He therefore understands the
following commands:
move
pickbeeper
turnoff
turnleft
putbeeper
Note that turnoff should always be the last command given to KAREL. Certain actions are illegal trying to move through a wall, trying to pick up a beeper that isn't there, or trying to put down a beeper
when his beeper-bag is empty. You will get a message indicating that the action you have attempted is
impossible. The action won't be carried out. It is important to note that when you program KAREL in
Pascal, the program will stop (exit) if an illegal command is given.
Controlling KAREL Using the Mouse
On this occasion, KAREL finds himself in the world shown below; he has five beepers in his bag.
 Click on the various buttons to get the appropriate actions.
 Notice that the last action to be performed is given as a Status Message at the bottom left hand
corner of the window.
If you try to do something illegal, then the Status Message will tell you what has happened.
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KAREL's World Window
A the very top of KAREL's world window you will see the menu bar which lists a number of commands
which are obeyed when the mouse is clicked on them. Some of them will give rise to a drop-down
menu from which you can select an option by clicking the mouse; if you don't want to choose any of the
options click the mouse outside the drop-down menu.
Run
Ultimately, this will start executing the instructions in the program you have written
to control KAREL. Since you have no program at present, it is 'greyed out' to show
that it is not available.
Exit
Stop running your program at whatever point it's at.
World
Load World
Normally KAREL will appear in whatever world you have specified in your program.
In this case I have specified the world which is defined in the file called manual.
However you can put him in different worlds and this command allows you to do so.
It will open up a file select box - pre-existing worlds are stored in
L:\delphi\system\worlds.
Create New World
If you don't like any of the existing worlds, then you can create a new one. Selecting
this command will bring up the World Editor. It’s probably not a good idea to use this
yet - instructions will be given later.
View
Status Window
This pops up a window which will keep a record of the commands that you have
given. It’s not particularly useful at present, but when you come to write programs, it
should help you to understand what’s going on. You may need to move it to a
convenient spot.
Refresh
This redraws the contents of the window, and shouldn’t really be needed.
Pause/Resume
Again, this isn’t any use at present, but when you start running a program, it is useful
to be able to stop it running to see what is going on, and then to resume it again.
Speed
Defined as 1 (slow) .. 6 (fastest). These are the speeds at which KAREL carries out
his actions. Slow speeds are useful when you are running a program and need time to
see what is happening.
Print
Should print out the contents of the window to the printer. Use this fairly sparingly; if
everyone in the room were to print every screen, the printer queue would get full up
and you'd wait a long time for output.
Help
At present, this just brings up the Copyright box.
 What you get KAREL to do in this world is not very important; just familiarise yourself with the
various commands. You might like to get him to set out all the beepers (those he has in his bag plus
the other two) in a straight horizontal line somewhere.
KAREL’s Senses
KAREL has a number of sensory inputs. We won’t use them for a bit, but it seems appropriate to
mention them now. He has three cameras which tell him if there is a wall immediately ahead of him, to
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his right, or to his left - but only for walls that are half the distance between Grid Points away - he is
very short sighted. So he knows the answer TRUE or FALSE to the following questions:
front_is_clear
left_is_clear
right_is_clear
front_is_blocked
left_is_blocked
right_is_blocked
He can hear if he is next to a beeper, but, because beepers are so quiet (and his hearing isn't that good),
only if he and the beeper are on the same Point:
next_to_a_beeper
He can tell whether he has any beepers in his bag, but not how many:
any_beepers_in_beeper_bag
He also has a compass which can tell him which way he is facing:
facing_north
facing_east
facing_south
facing_west
Note that the only way KAREL can find out about the world is through his senses. He doesn't have
direct access to any of the information in the world files but must navigate through the world we have
set up for him using only the capabilities described above.
Finally he can tell which Point he is on. In our programs we can get at these values by using two
functions (don't worry what a function is yet) which give (respectively) his X and Y co-ordinates at the
time:
Karel_X
Karel_Y
Pascal and Delphi
Pascal is the name of the language you will be writing programs in; Delphi is the name of the
development environment. Delphi provides state-of-the-art programming facilities. This has the
disadvantage that it provides far more power than you need at present, but it does allow us to provide
you with a teaching environment which would be difficult to provide in any other way.
Running Your First Program
You are now ready to run your first Pascal program - one that has been already written.
 you should already have copied the file L:\delphi\programs\notmuch.dpr into a suitable directory on
your H: drive; if you haven’t, do so now.
 use Windows Explorer and find your copy of notmuch.dpr.
 double click on it to start Delphi, this may take a little time, especially if you are running on a 486
PC. It is not a good idea to try to run Delphi on any 386 PC.
You should see:
 a menu bar at the top of the screen
 a window on the left hand side of the screen called the Object Inspector.
 You will never need the Object Inspector so close it
 a window with the title NOTMUCH.DPR; this is the window you will use to enter and change your
Pascal code - for this reason it is called the Edit Window. Resize it if necessary.
 It might be a good idea to minimise any other open windows to reduce clutter on your screen.
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The Edit Window should contain the following code:
PROGRAM notmuch;
USES cskarel;
BEGIN
setworld(’notmuch’);
move;
move;
pickbeeper;
move;
turnleft;
move;
move;
putbeeper;
move;
turnoff
END.
The world notmuch is shown below. KAREL's task is to move the beeper from Point (4,2) to Point
(5,4) and to finish at Point (5,5).
We will discuss the structure of this program in lectures.
For the moment you should note that the command:
setworld('notmuch')
ensures that when the program is run, KAREL will find himself in the world notmuch. The general
form of the command is:
setworld('<worldname>')
where <worldname> is the name of a particular world. Note that the names of worlds are always
enclosed by single quotation marks.
You will be working through many problems, and the worldnames to be used are given with each
question. setworld sets up the appropriate world and draws it on the screen, and should always be
the first command in a KAREL program.
 Choose Run, Run or click the dark blue arrow on the tool-bar. This is called (no surprise) Running
the program.
This will bring up KAREL’s world window with KAREL in the world notmuch.
 In this window, choose Run to execute the sequence of statements in the program.
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 Run the program several times, using the commands to pause, change speed, look at the status
window, etc.
 When you have finished, choose File, Close All.
 Exit from Delphi - choose File, Exit.
We can note at this point that there are two further commands you can include in your program:
speed(1), speed(2) ... speed(6)
This determines how fast KAREL moves. You can change this during the simulation by using a
command from the menu (see above) but you can also change it from within your program.
Pause_KAREL
This causes your program to suspend its execution at the point where it is encountered. You resume
execution by clicking on Resume in the menu bar.
Writing Your First Program
 Start Delphi by double clicking the Delphi icon in the Computing Science folder.
Ignore the windows that appear
 Choose File, New… and click on the Projects tab.
 Double click on KAREL
 A window will appear asking you to Select Directory - this is where your program will be saved.
You first need to make sure that the correct drive is selected (drop down menu) and then the correct
directory.
 If you are ever asked to replace the existing file program.dpr, then say YES.
The Edit Window will now contain the following code:
PROGRAM program;
USES cskarel;
BEGIN
{ Save this file with another filename
by choosing File, Save Project As...
DO NOT change the first line of the file (i.e. PROGRAM ...)
Then delete this comment. }
END.
 Save the file by choosing File, Save Project As ...
A suitable name might be first.
You should save it to the appropriate directory in your H: drive.
You can just use the simple filename first - Delphi will save it as first.dpr. All your program files will
have the file extension .dpr.
Notice that the name of the program has been changed to the name of the file.
 Now delete the comment (the text between the curly brackets { ... }) using Editing commands (see
below)
When making changes to the program, the Edit Window must be active. If it isn't, make it active by
clicking the mouse inside the window.
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To delete text inside a program, move the mouse to the end of it, click, and press Backspace or Delete
keys, as required. For deletions of larger sections use the drop-down menu, headed by Edit using the
options Cut, Copy and Delete. For these, a section of text must be highlighted in the Edit Window by
dragging the mouse over it. This is done by dragging the mouse across the area - move the mouse to the
start of the area, press the left button and keep it depressed while moving the mouse to the end of the
area.
Cut
Copy
Paste
removes the highlighted text, but puts it into a temporary area called the clipboard .
leaves the highlighted text in the Edit Window but places a copy of it in the clipboard.
copies the contents of the clipboard (created by the last Copy or Cut ) to the area in the Edit
Window currently selected by the mouse.
Delete removes the highlighted text and does not save it in the clipboard.
For example, you could remove the three lines of text between the { … } by highlighting them and
choosing Edit, Cut.
You are now going to change this program so that KAREL accomplishes a specific task.
KAREL starts in the initial situation illustrated below; his task is to get to the beeper, pick it up, and
then turn himself off.
The following program will accomplish that task:
PROGRAM first;
USES cskarel;
BEGIN
setworld('hiding');
move;
turnleft;
turnleft;
turnleft;
move;
turnleft;
move;
turnleft;
move;
pickbeeper;
turnoff
END.
 Edit the program to include the text between BEGIN and END. To add text inside the program,
move the mouse to the point of entry, click, and type the desired text.
 Run the program as before
You may get some errors before KAREL's world window appears - these are compilation errors; check
that you have entered the program exactly as it appears above. Try to figure it out for yourself - mis-
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spellings, missing semi-colons, etc., but get help if you are stuck. If you haven't encountered such an
error then create one deliberately!
Compilation errors are one kind of error. Other errors are run-time errors which are errors which occur
as the program runs.
 Deliberately create a run time error by removing one of the commands (i.e. move or turnleft)
 Run the program again. KAREL will either run into a wall or will try to pick up a beeper that isn’t
there.
 Alter the program in various ways and run the altered versions; understand what is happening.
 You will spend a most of your time at the terminal in the Editor Window. It is a very good idea to
invest time now in becoming very familiar with it and its capabilities. Your investment will be
repaid in the future!
Saving Your Program
You should make a permanent copy of the correct version of your program; you do this by saving it
again:
 Choose File, Save
Note that you have already saved it once before, so it already has a name
 You might want to get a print-out by choosing File, Print
If you use the Windows Explorer to look in the directory where you are saving your files, you will find
more than you bargained for - i.e. a number of files with the same name but with different extensions.
You can leave these alone, because they are all quite small with the exception of the .exe files. These
can get quite large, and if you run short of file quota, you may want to remove them. There is no harm
in this as they are recreated every time you compile your program.
Important Delphi Commands
Here is a summary of the most important Delphi commands. As we’ve already said, Delphi is a very
complex system, and there are many more commands than you will need in this course.
File
New …
Open
Reopen
Save
Save As ...
Close
Print
Exit
Choose the Project tab. Creates a new program for you to work with. Note that
you can only work on one program (or project) at a time. In the dialogue box that
appears, you would normally select the KAREL project.
Opens an existing project for you to work on
Provides a list of projects that you've worked on recently
Saves the program you are working on to disk. It is a good idea to do this at
frequent intervals.
Saves the program under a different name.
Stop working on the current program.
Get a listing of your program on the printer.
Leave Delphi
Edit
Undo/Redo
Undo (or do again) the effect of the last editing command - useful if you make a
mistake.
Cut, Copy, Paste and Delete
Already described
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Run
Run
Program Reset
Complies and runs your program.
Useful if you really get into trouble and need to stop your program executing.
Help
Delphi has extensive built-in help facilities; much of what is said will be too
complicated, but it’s always worth trying!
Structure of a Complete KAREL Program in Pascal
This is the way it should look; we'll come to procedures soon:
PROGRAM <program_name>;
USES cskarel
{Compulsory}
{Compulsory}
PROCEDURE <new_name_1>;
BEGIN
<statement>;
.
.
<statement>
END;
{Not Compulsory}
.
.
PROCEDURE <new_name_n>;
...
{Not Compulsory}
BEGIN
{Compulsory}
setworld(’worldname’);
{Compulsory for using KAREL}
<statement>;
{This is where KAREL starts executing instructions, either pre-defined,
or defined above}
<statement>
turnoff
{The usual way to end a KAREL program}
END.
{Compulsory}
Example Programs
All of the programs talked about in the lectures, and all of the solutions to problems (where they are
complete programs) are (or will be) available in the directory L:\delphi\programs.
You can copy them into your own directory, run them and modify them as you wish.
The World Editor
KAREL is not restricted to the worlds which have already been defined. You may create your own
worlds for KAREL to explore. Run the KAREL World Editor by clicking Weditor in the Computing
Science folder or by choosing World, Create New World from the KAREL window.
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The World Editor is controlled primarily by using the mouse. Note that if you are using a one-buttoned
mouse then clicking with the right mouse button can be simulated by holding down the <CTRL> key
while pressing the mouse button.
Here is a summary of the functionality of the World Editor.
File
New World
Open World
Save
Creates a new, blank KAREL world
Loads a world from disk
Saves the current world to disk under its current filename; note that you can only
save your new worlds to a directory on your drive (H:).
Save As...
Saves the current world to disk under a new filename
Exit
Exits the World Editor program
Update and Return
This option only exists if you are running the World Editor from a KAREL
program. It will make the KAREL Simulator load the world currently in the
Editor, minimise the Editor and return to the KAREL program.
View
Refresh
Refreshes the screen
Item
Beeper (Single) Places the editor into Single Beeper Mode. In this mode, a left mouse click will
place a single beeper on the Point the cursor is over. A right click will delete a
single beeper. Subsequent left mouse clicks will add one to the number of
beepers on that Point, and subsequent right mouse clicks will subtract one.
Beeper (Multiple)
Places the editor into Multiple Beeper Mode. In this mode, the mouse cursor may
be dragged while pressing either the left mouse button (to place beepers) or the
right mouse button (to delete beepers).
Beeper (Specified)
In this mode, when the left mouse button is clicked over a Point a dialogue box
appears for you to enter the number of beepers you wish to be at this Point.
Wall
Places the editor into Wall Mode. In this mode, you may press the left button and
drag the mouse to create a new wall. Releasing the button finalises the operation.
Clicking on a wall with the right mouse button allows you to delete that wall.
Karel
Once this option is selected, you may click with the left mouse button to place
KAREL in another position in the world. Right-click in order to rotate KAREL.
Beeper Bag
Selecting this option brings up a dialogue in which you may enter the number of
beepers for KAREL’s beeper bag.
World Name
This option allows you to enter a name for KAREL’s world (up to 255
characters). This name then appears at the top of the World Editor as well as any
program using the KAREL World Simulator.
Special FX
Flood Beepers
This allows you to add a number (positive or negative) of beepers to every Point
of the world.
Options
Colours
This option allows you to change the background colour of the World Editor
About
Brings up information about the World Editor’s author
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Interacting with the User
As time goes on, your programs will need to write textual messages to the screen and to take in text and
numbers that the user types in. In much of the course software, the following procedures and functions
will be available. Note that for non-KAREL programs you will have to include IO in your USES
statement.
procedure DisplayStringToUser(MessageString:STRING)
displays the MessageString in a box
function GetStringFromUser(Question:STRING): STRING
displays the Question string and waits for the user to type a string in reply; the function returns
when the user hits Return
function GetIntegerFromUser(Question: STRING): INTEGER
displays the Question string and waits for the user to type an integer in reply; the function
returns when the user hits Return; if a valid integer is not entered, an error message is
displayed and the user has a chance to try again.
function GetRealFromUser(Question: STRING): REAL
as for GetIntegerFromUser but returning a real number.
function YesNoQuestion(Question: STRING): BOOLEAN
pops up a dialogue box with the text Question in it. It has two buttons - Yes and No. If Yes
is clicked, then the function returns TRUE, otherwise FALSE.
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Tutorial Problems
1.
Start KAREL in the initial situation illustrated on the left below and simulate his execution of the
program below. KAREL's task is to get to the beeper, pick it up, and then turn himself off. Say
where KAREL ends up and what error occurs (if any). If an error does occur, explain how you
would correct the program. This program has no lexical or syntactic errors.
PROGRAM getit;
USES cskarel;
BEGIN
setworld('getit');
turnleft;
turnleft;
move;
turnleft;
move; move;
turnleft;
move;
turnleft;
move;
pickbeeper;
turnoff
END.
2.
Every morning KAREL is awakened in bed
when his newspaper, represented by a beeper,
is thrown onto the front porch of his house.
Program KAREL to retrieve his paper and
bring it back to bed with him. The initial
situation is given in Figure 2-5, and the final
situation must have KAREL back in bed (same
Point, same direction) with the newspaper.
Verify that the program is correct by hand
simulating with KAREL in the appropriate
initial situation. (If you want to try this out in
practicals, the world is paper).
3.
The wall sections in Figure 2-6 represent a
mountain (north is up). Program KAREL to
climb the mountain and then plant a flag,
represented by a beeper, on the summit - Point
(5,5); KAREL must then descend the other side
of the mountain to location (8,1). Assume that
he starts with the flag-beeper in his bag.
Remember that KAREL is not a super-robot
who can leap up and down in a single bound.
KAREL must closely follow the mountain's face
on his way up and down, i.e. he must be in
contact with the internal walls at all times. (If
you want to try this out in practicals, the world
is mountain).
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Write appropriate definitions for the following four new instructions:
(i)
turnaround, which turns KAREL around 180;
(ii) move_mile - a mile is eight blocks;
(iii) move_backward, which moves KAREL one block backward but leaves him facing
the same direction;
(iv) move_kilo_mile, which moves KAREL 1000 miles forward.
This last problem is difficult, but a fairly short solution does exist. You may use the move_mile
instruction in this problem without redefining it. Also, which of these four instructions might
cause an error shutoff when it is executed? Which will certainly do so?
5.
(a) KAREL sometimes works as a pin-setter in a
bowling alley. He starts this task in bowling at
Point (5,1) facing north with ten beepers in his
beeper-bag and no beepers set out. Write a program
that instructs him to achieve the final situation as
shown.
(b) Rework your solution to part (a) by defining:
PROCEDURE set_out_a_row
(n : INTEGER);
where n is the number of pins in the row. Use FOR
loops to get the simplest program you can.
6.
Define face_south, a new procedure that faces
KAREL south regardless of the direction he is initially facing. First, do this without using
face_north as a known procedure. Experiment with different forms of the IF/THEN and
IF/THEN/ELSE statements and with the FOR instruction. Next, write face_south assuming
that the procedure face_north has already been defined. Given that face_north is
correct, it should be easy to convince anyone of the correctness of face_south.
7.
Look at the following statement. Is there a simpler statement which has the same effect when it is
executed? If so, write it down; if not, explain why not.
IF NOT next_to_a_beeper
THEN move
ELSE move
8.
Assume that KAREL is on a Point with either one or two beepers. Write a new procedure that
leaves him facing north if he is started on a Point with one beeper and facing south if he is started
on a Point with two beepers. After KAREL has executed this procedure, there must be the same
number of beepers on the Point as were there originally. Write another version of the procedure
in which no beepers are left on the Point.
9.
Write an instruction that turns KAREL off if he is completely surrounded by walls, unable to
move in any direction. If he is not completely surrounded, KAREL should execute this
instruction by leaving himself turned on, and by remaining on the same Point, facing the same
direction in which he started. Hint: To write this instruction correctly, you may need to include a
turnoff inside it. This combination is perfectly legal, but it is the first time that you will have
used a turnoff instruction outside of the main program compound statement.
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10.
1999/2000
COURSE MANUAL
Look back at the 'climbing stairs' example
discussed in the lectures - Figure 3.1(a). The object
is to get KAREL to the top step having picked up
all the beepers. Write a solution using a FOR loop.
Look at all the previous tutorial and practical
examples you have been set, and see where
repeated code could be replaced by a FOR loop.
11.
Write a new instruction for KAREL named
empty_beeper_bag. When KAREL executes this instruction, he should empty his beeperbag on the Point he is standing at.
12.
Write a new instruction called go_to_origin that positions KAREL at Point (1,1) facing
east, regardless of his initial location or the direction he is initially facing. Assume that there are
no internal wall sections present. Hint: Use the south and west external walls as guides.
13.
Study the following program fragments separately. What does each do? For each one, is there a
simpler program fragment that yields the same result when executed? If so, write it down; if not,
explain why not. Hint: The formal properties of REPEAT and WHILE are useful.
(i)
REPEAT
move
UNTIL NOT next_to_a_beeper;
IF next_to_a_beeper
THEN pickbeeper
ELSE turnoff
(ii)
WHILE NOT next_to_a_beeper DO
IF next_to_a_beeper
THEN pickbeeper
ELSE move
14.
Write an instruction that faces KAREL east if he is on a Point with an even number of beepers,
and faces him west if he is on a Point with an odd number of beepers (zero is considered an even
number for this task). KAREL can clear the Point of beepers while he is determining which
direction to face
15.
Which of the following are invalid Pascal identifiers and why?
16.
A1
A1
12A
A1*
JANE'S
scarlet
SCARLET
YO-YO
this_one
FunnyOne
Why do Pascal and certain other languages insist that variables have a pre-declared type?
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17.
1999/2000
COURSE MANUAL
What is the value of the variable result at the end of execution of each of the following
sequences of assignment statements? Can (ii) be simplified and if so, how?
(i)
VAR party, doubles,
singles, result : INTEGER;
BEGIN
party := 27;
doubles := party div 2;
singles := party mod 2;
result := singles + doubles
END
(ii)
VAR a, b, result : INTEGER;
i, j : BOOLEAN;
BEGIN
a:= 12;
b:= 5;
a := a + b;
b := a - b;
i := a > b;
j := a <= b;
IF i OR j
THEN result := a * b
ELSE result := a - b
END
18.
We want to interchange the values of two variables a and b. Explain why the pair of statements
below doesn't do this, and find a way, using just assignment statements, that does. (Hint: use an
extra variable temp).
a := b;
b := a;
19. KAREL finds himself inside a rectangular
box, made up of internal walls. Other than
that he is in the box, he doesn't know where
he is, nor which way he is facing. There are
no other internal walls. His task is, by
making the appropriate moves, to establish
the dimensions of the box. Write a program
which will do this.
Use the
DisplayStringToUser statement to output the
dimensions e.g. for the given example:
The box is 7 by 5 blocks.
If you want to program this, the world is box.
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CS_PAS
20.
1999/2000
COURSE MANUAL
KAREL is at one end of a line of beepers facing along it. Write a procedure which, when it
returns, has the number of beepers in the line stored in a variable number (which will be
declared in the main program):
PROCEDURE count_beepers
KAREL should pick up the beepers as he goes. It is up to you to decide where he ends up, but
you should be clear where it is. Write two versions - one with a WHILE loop, and one with a
REPEAT loop.
21.
What are the essential differences between WHILE and REPEAT loops?
22.
Look at the following Pascal expressions. With the given variable declarations, some are legal
and some are not. Say which is which. For those that are legal state the type of the value of the
expression. For those that are not, say why not.
VAR a, b, c : INTEGER; i, j : BOOLEAN;
(i)
(iv)
(vii)
(x)
23.
a
b
i
a
<= b
AND c
= j
mod b
(ii)
(v)
(viii)
i OR a
i * j
a < b < c
(iii)
(vi)
(ix)
NOT i
a  c
NOT i AND j
k, m and n are all integer variables. What are their values after executing the following
sections of code?
(i)
n:=3; m:=n+2;
IF n<3
THEN
n:=4
ELSE
IF m>4
THEN
k:=5
ELSE
k:=6;
(ii)
n:=4; k:=0;
REPEAT
IF n<>2
THEN k:= k + SQR(n);
n:=n-1
UNTIL n=1;
24.
Why is it advantageous to be able to declare symbolic constants in Pascal programs?
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CS_PAS
25.
1999/2000
COURSE MANUAL
Work out the values of the following expressions, given the initial values for the variables:
VAR a, b : INTEGER;
a=7; b:=4;
(i)
(ii)
(iii)
(vi)
(v)
26.
SQR(a) + SQR(b)
ODD(a-b) OR ODD(a+b)
PRED(PRED(PRED(SUCC(SUCC(SUCC(a))))))
ODD(a mod 2) = ODD(a)
SQR(b) + 2*b + 1 - SQR(SUCC(b))
Write three sections of code each of which ends up with the integer variable sum assigned to the
sum of the fourth powers of the odd integers between 0 and 10:
(i) using a FOR loop;
(ii) using a REPEAT loop.
(iii) using a WHILE loop;
You can get the fourth power by taking the square of the square.
27.
Write the following expressions in Pascal notation:
(i)
(iv)
28.
sin3 + 3 sin cos
xmin  x  x'  xmax
(ii)
ax2 + bx + c
(iii)
1/
(v)
a  1/
(vi)
r2
3 |b|
2x
For each of the following expressions, work out its value when the variables have the values
given. If the parentheses were removed, would the resulting expression be legal. If so what
would be the value? Are any of the parentheses unnecessary? If the resulting expression is not
legal, why not?
a:=3; b:=9; c:=5; i:= TRUE; j:= FALSE; k:= FALSE;
(i) (a+b)*c
(iv) (a*b)/c
29.
(ii) (a<6) AND (b>7)
(v) ((a*b))+(5*c)
Explain why the values of the following expressions may both be different from 13.0. How
significant is the difference in each case?
(i) (13 div 7)*7.0
30.
(iii) NOT((i OR j) AND k)
(vi) (15-b)div(c mod 2)
(ii) (13.0/7.0)*7.0
If day and month are integer variables, and possibly_leap is a Boolean variable, rewrite
the following statement more concisely:
IF (day=29) AND (month=2)
THEN possibly_leap := TRUE
ELSE possibly_leap := FALSE
31.
If two rabbits produce a litter of four babies every three months, and if rabbits are capable of
reproduction when they are three months old, write a piece of code which will work out how
long it will take to generate more than 500 rabbits starting from 2 babies.
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CS_PAS
32.
1999/2000
COURSE MANUAL
Write a program that repeatedly prompts for a string, reads it in, and outputs the string and its
length, until the user enters the word end.
Enter the string: Hi there
The string
Hi there
has 8 characters
Enter the string: What a load of rubbish!
The string
What a load of rubbish!
has 23 characters
Enter the string: end
Bye bye
33.
Write a program that reads in two integers a and b where a < b, calculates the sum of all integers
i such that a  i  b and i is not exactly divisible by 5 or by 7.
Enter the lower integer: 20
Enter the upper integer: 30
The sum is: 151
34.
Write a program that reads in two temperatures T low and Thigh which are temperatures in
degrees Centigrade, and writes out a conversion table at intervals of 0.3 degree Centigrade from
Centigrade to Fahrenheit. Temperatures in Centigrade should be given to one decimal place,
those in Fahrenheit to two decimal places. To convert a temperature in degrees Centigrade (T c)
to one in degrees Fahrenheit (T f ) use the formula:
T f = 9 T c /5 + 32
Enter the lower temperature: 45
Enter the higher temperature: 48
35.
Centigrade
Fahrenheit
45.0
45.3
45.6
45.9
...
48.0
113.00
113.54
114.08
114.62
118.40
The following are the various procedures than can be called for an external text file used for
input. Assuming the declarations:
VAR input_data: TEXT; n: INTEGER;
what do they accomplish?
AssignFile(input_data, 'myfile.txt');
Reset(input_data);
READLN(input_data, n);
CloseFile(input_data);
What are the corresponding procedures for an external text file used for output?
What built-in function do you know which takes an input text file as its parameter, and returns a
Boolean? Under what circumstances does the function return TRUE?
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COURSE MANUAL
36.
What is meant by an (n+1/2) times loop? How can it arise in a program with a loop to handle an
input data stream where a marker indicates the end of the data? How does the use of the EOF
function simplify the loop?
37.
Write a program that
i)
ii)
prompts the user for the name of a text file;
copies the contents of that file to the screen; every 20 lines it should pause and say to
the user:
Press <RETURN> to continue
and wait until RETURN is pressed before doing so. Note that the procedure
READLN without any parameters will complete execution when the RETURN key
alone is pressed.
38.
Use the squared grid below to show what the output would be from the following code, assuming
that the constants have the values as given:
CONST
a =
b =
c =
d =
e =
f =
-56.2345;
0.000348;
-591;
't';
'Merry Christmas';
'
'; {three spaces}
WRITELN('123456789012345678901234567890');
WRITELN(a);
WRITE(b, f, c);
WRITELN;
WRITELN(a:13);
WRITELN(b:11);
WRITELN(a:10:2, f,
b:10:2);
WRITELN(c:8);
WRITELN;
WRITELN(d:3, e:20);
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CS_PAS
39.
1999/2000
COURSE MANUAL
The Delphi system delivered with the PC which you got as a Christmas present is great, except
for one thing. The sin function which should be built-in, isn't! However you remember that sin
can be expressed as a series:
sin  =  -
3
5
7



+
+ ...
3! 5! 7!
over the range 0    2
Remember that n! = n  (n-1)  (n-2) ... 2  1. Write a procedure:
PROCEDURE get_sin(theta:REAL);
which will remedy the situation by working out the value of sin(theta) and assigning it to a
variable my_sin. One slight problem is that the series has an infinite number of terms, and your
computer (although the latest model) is finite! This means that you can only calculate sin to a
given precision. I suggest that 0.000001 is good enough, so you should stop adding terms to the
total when you come across a term which is less than this amount. (It can be shown that the terms
are always decreasing in value).
This problem is more complicated than it looks, and is an example of a calculation in which you
do have to take account of the finite size of numbers that can be represented. You can't just
calculate the numerator and denominator of a term separately and divide the one by the other,
each gets too large. Look at what you have to do to the nth term to get the (n+1)th term. Note
that as far as I can see, the series only gives the correct result if 0 <= theta <= 2*pi. You might
like to check this out by plotting for values of theta around 40!
40.
(i)
(ii)
(iii)
What is the difference between a local and a global variable?
Explain how global variables enable procedures to communicate with each other.
In the program given below, which variables are local and which global.
What would be written to the screen by the program?
PROGRAM test;
VAR c, d:INTEGER;
PROCEDURE first(c:INTEGER);
VAR d:INTEGER;
BEGIN
d := 5;
WRITE(c); WRITE('
'); WRITELN(d);
c := d+2;
d := c-3
END;
PROCEDURE second(a:INTEGER);
BEGIN
WRITE(c); WRITE('
'); WRITELN(a);
d := d+9
END;
BEGIN
c := 13;
d := 7;
WRITE(c); WRITE('
first(d+2);
WRITE(c); WRITE('
second(c);
WRITE(c); WRITE('
END.
'); WRITELN(d);
'); WRITELN(d);
'); WRITELN(d)
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41.
1999/2000
Look at the following program. I have missed out a number of semi-colons. I've also put in some
which should not be there. Finally there are some which, although not illegal are unnecessary.
Modify the program so that it is legal, and identify the unnecessary semi-colons.
PROGRAM plot_it
USES csPlot, IO;
CONST
x_step = 1.0;
x_max = 360.0;
y_max = 20.0;
VAR x, y_s, y_c : REAL
BEGIN
DrawAxes(x_max, y_max);
x:=0.0
REPEAT
y_s:=10*(1.0+SIN(radians(x/57.2958)));
y_c:=10*(1.0+COS(radians(x/57.2958)))
IF (0.0 <= x) AND (x <= x_max) AND
(0.0 <= y) AND (y <= y_max);
THEN
BEGIN;
PlotPoint(x,y_s);
PlotPoint(x,y_c)
END;
ELSE
DisplayStringToUser('Out of range');
x := x + x_step;
UNTIL x > x_max;
REPEAT UNTIL ExitClicked
END.
42.
COURSE MANUAL
What does the following program print out?
PROGRAM mystery;
VAR
ar: ARRAY[1..8] OF INTEGER;
k, m, tmp: INTEGER;
BEGIN
FOR k:= 1 TO 8 DO
ar[k] := 3*k;
ar[8] := 0;
m := 8 div 2;
ar[m] := ar[m] + 1;
m := m div 2;
tmp := ar[m];
ar[m] := ar[m+1];
ar[m+1] := tmp;
FOR k := 5 TO 7 DO
ar[8] := ar[8] + k;
FOR k := 8 DOWNTO 1 DO
WRITE(ar[k]:4);
WRITELN
END.
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COURSE MANUAL
43.
A list of names is contained in a text file (names.txt), one name (string) per line. Write a
program to read them into an array of strings, sort them alphabetically and then output them to
the screen in alphabetical order. Look at the Sorting problem in the next section, and use the
algorithm given there to do the alphabetical sort.
44.
Write a Pascal program to read a sequence of integers from a text file (named integers.txt)
and to print them out in two different ways. Each integer should be printed out in a field of width
eight. Use an array to hold the integers.
(i)
Write the main program which reads up to 100 integers (each of which is on a separate
line) terminated by end of file. Indicate where the two output procedures of (ii) and (iii)
below have to be declared and called in the main program.
(ii)
Write a procedure row_order which outputs the integers input in (i). Commence the
output with the heading ROW ORDER, underlined by a sequence of minus signs, and
then output the integers in rows across the page, ten per row. Output the first ten
integers in the first row, the next ten integers in the second row, and so on. The final
row may be partially filled.
(iii ) Write a procedure column_order which outputs the integers input in (i). Commence the
output with the heading COLUMN ORDER, underlined by a sequence of minus signs,
and then output the integers in columns down the page, ten per column. Arrange the
output so that on completion the first ten integers will appear in the first column, the
next ten integers in the second column, and so on. In this case you may assume that
there are exactly 100 integers input.
45.
A string variable str is to be printed out left justified in a field of width 20 characters
Assuming that str will always contain strings of 20 characters or less, show how this can be
achieved.
46.
Look again at the practical Credit Analysis. Write a program that will print out for each
customer his name, the total value of unpaid orders and the total value of all his orders. The input
file has the same format except that we can detect the end of file (there is no explicit 'end'
marker'). Assume that there will be no more than 100 customers. You will need to set up three
arrays:
name: ARRAY[1..100] OF STRING;
{ for the names}
paid: ARRAY[1..100] OF CHAR;
{to show if the order has been paid}
value:
ARRAY[1..100] OF REAL; {the values of the orders}
The output should look like:
NAME
UNPAID
TOTAL
smith
jones
atkinson
185.28
42.75
0.00
414.99
42.75
464.46
47. Write a function which, given a temperature in degrees Centigrade will return the same temperature
in degrees Fahrenheit. Assume both temperatures are real numbers.
48. Write a function which returns the length of the hypotenuse (c) of a right angled triangle given the
lengths of the two other sides (a and b):
c2 = a 2 + b 2
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COURSE MANUAL
49. KAREL is seized with a sudden desire to know whether the world he lives in is square. Write a
function which will return TRUE if it is, and FALSE otherwise:
FUNCTION square : BOOLEAN;
You can assume that there are no internal walls. It doesn't matter where he ends up.
50. Look at the program scope11.dpr. What would be the output if n were declared as a variable
parameter in:
PROCEDURE proc_eleven(VAR n:INTEGER)
51. Find an alternative solution to Practical Problem 8(b) - the Treasure Hunt, using a two-dimensional
array of integers to record the number of beepers on each Point; then examine that array to
determine which Point contains the maximum number of beepers.
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Practical Exercises
1. KAREL Goes Shopping
On the way home from the supermarket, KAREL's shopping bag gets ripped slightly at the bottom,
leaking a few expensive items. These groceries are represented by beepers. The initial situation, when
KAREL discovered the leak, is represented in Figure 2-7(a). Program KAREL to pick up all the
dropped items, line them up along the eastern wall of his house, as shown in Figure 2-7(b) and then
return to his starting position. The world to use is shopping.
2. Harvesting
These problems have all to do with picking up and putting down beepers which are contained within a
rectangular area. KAREL always starts off outside this area, facing towards the bottom left hand Point,
one block from it. His exact task, and the starting state of the 'field' will vary from problem to problem.
Test each program on the sample world given, but note that it should work in any world which
conforms with the given specification.
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(a) KAREL's initial situation is shown in Figure 3.2 (harvest). His task is to end up with all the
beepers in his bag - see Figure 3.2(b).
(b) Some of the beepers are missing - as in Figure 4.1 (harvestm). Again, his task is to end up with
all the beepers in his bag.
(c) The world is the same as for part (b), but his task is to pick up the beepers that are there, and to put
down beeper on the Points where there aren't any. You can assume that he starts with a large number of
beepers in his bag.
(d) There may be zero, one or two beepers on each Point - see Figure 4.3(a) (harveste). KAREL's
task is to leave the field with exactly one beeper on each Point (so that it looks like Figure 3.2).
(e) On any Point there can be any number (zero, one or more ) of beepers; see Figure 4.10
(harvestu). KAREL's task - as in parts (a) and (b) - is to remove all of the beepers.
(f) This task is identical to that of part (e) except that there are internal walls. These may be horizontal
or vertical and are guaranteed only to be one block long. In principle they can be between any two
adjacent Points, but in fact it is the case that no two internal walls touch each other in any way. Modify
your program so that KAREL can still harvest the field. Hint: Given that the walls are only one block
long and don't touch, you know that you can always go round them - so write a procedure to do just
that. Test your program in harvestw, shown in Figure 4.11.
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3. Diamond Shaped Field
Figure 3-4 illustrates an odd-shaped field of beepers.
Write a program that harvests all these beepers. The
world to use is diamond.
Hint: this task is not too different from the harvesting
example. If you see the correspondence between these
two harvesting tasks, you should be able to develop a
program for this task that is similar to the original
harvesting program.
4. Say 'HELLO'
KAREL wants to send his greetings to the other
inhabitants of his universe, so he needs to plant a field of beepers that broadcasts his message to alien
astronomers. Program KAREL to plant the message of beepers shown in Figure 3-5. OK ... you have to
construct the rest of the HELLO. KAREL's start position is (2,3) facing north; he has 51 beepers in his
bag and there are no beepers set out (hello). His final position is up to you.
5. Wall-Hugging and Mazes
(a) Write an procedure named follow_wall_right, assuming that whenever KAREL executes
this instruction there is a wall directly to his right. Figure 4-5 shows all four of the different position
changes that he must be able to make (i.e. from the position in (a) to the position in (b). The effect of
repeatedly executing this procedure will be to make KAREL 'hug' (i.e. stay in contact with) the righthand wall of any world he is put in - assuming that there is initially a wall to his right.
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(b) Using this procedure write a program to enable KAREL to find a beeper in a maze that contains no
islands. This task can be accomplished for this kind of maze by commanding KAREL to move through
it with his right side always next to a wall as discussed above. The figure below shows one example of
such a maze; it is found in maze1. A different example is in maze2.
(c) As an interesting side issue, consider the worlds shown in Figures 5.10 and 5.11 - found in
hurdles1 and hurdles2 respectively. The objective is to get to the beeper by 'jumping' the 'hurdles'
- which get progressively more complex. You can see the solutions to these as progressive refinements
to the 'hurdling' problem discussed in PATTIS in section 4.4 and the problem on page 59. By this I
mean that one would write procedures to 'jump up' and 'jump down' with a procedure to 'go along the
top' for Figure 5.11.
However if you change your point of view, you can look at these as being solved by the 'right wall
hugging' algorithm you have just developed. Try your program in these worlds. Does it work? If not,
why not.
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(d) Not all mazes are easily amenable to 'wall hugging'. The figure below shows one which isn't. The
class of mazes of which this is a member can be described as follows:
KAREL is in a world in which there are horizontal internal walls. Walls can be of any length up
to 29 blocks and may or may not join an external wall. KAREL is placed somewhere in the
world. His direction is not specified, nor do we know if he is next to a wall. His task is to get to
the Point (30,20) and to turn himself off when he gets there.
Test your program on maze3 (which is not the world shown in the figure).
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6. Follow the Path
KAREL is put at one "end" of a path of beepers - an example world is shown below in Figure 5.12 contained in path1. The other end is marked by a pile of two beepers. There are no forks in the path i.e. any beeper is adjacent to two and only two beepers (apart from the ends of the path). KAREL's task
is to get to the other end.
There are no internal walls. You can chose whether or not to leave the beepers behind. A different test
world is path2.
7. Escape
KAREL is in a room composed of internal walls. The door is one block wide. See, for example, Figure
5.4 above. KAREL's task is to escape. We don't know where he starts (inside the room), nor which way
he is facing, nor the size of the room, nor the location of the door. We know that there are no other
internal walls. KAREL is carrying a large number of beepers which he can put down if he wants - this
may or may not be useful. room1 contains the world shown above. Other suitable worlds are room2,
room3 and room4.
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8. Treasure Hunts
(a) KAREL is sent on a treasure hunt. He starts on a Point with a number of beepers. He counts them by
picking them up and putting them in his beeper bag. The number of beepers picked up, when
considered as a two digit integer between 01 and 39, determines where he is to go next. If the first digit
is 0 he goes north; if it is 1 he goes east, if 2, south, and if 3, west. The second digit tells him how many
blocks to move. Thus if he is on a Point with 25 beepers, he should go south 5 blocks.
If he ends up on a Point which has beepers on it, he repeats this process. If the Point has no beepers
then he has reached the treasure and should turn himself off (and start digging!). If he encounters any
walls, he should turn through 180° and carry on until he has moved the required number of blocks.
Consider the example world. In case you can't read it,
the numbers of beepers are:
Point
Number
(3,2)
(7,2)
(7,5)
(4,5)
14
25
33
2
KAREL starts on Point (3,2) - although for the sake of
clarity I haven't shown him. He finds 14 beepers - this
means 'go east (1) 4 blocks'. He ends up on (7,2).
Here there are 25 beepers. This means 'go south 5
blocks'. He tries to do this but after one block meets a
wall. He turns around and goes north 4 blocks (the 5
he has to go, less the one already gone). He ends up
on Point (7,5); the beepers there get him to (4,5) where he finds 2 beepers. The first digit is (implicitly)
0 so he goes north 2 blocks. to Point (4,7). There are no beepers on that Point, so he has found the
treasure.
Note that in order to solve this problem you need to recognise that if n is a variable containing the
number of beepers on a corner, then n div 10 will give the 'tens' part of that number (the first digit);
for example 14 div 10 is equal to 1. n mod 10 will give the 'units' part (or second digit); so 14 mod
10 is equal to 4.
Write a program to solve this task and test it in treasur1 and treasur2.
(b) KAREL goes on a different kind of Treasure Hunt. On some Points (but not all) there are piles of
one or more beepers. In part (a) the beepers were signposts to the treasure; this time the beepers are the
treasure. KAREL's task is to find the Point with the largest number of beepers on it, and to return to that
Point and turn himself off (presumably with a satisfied smile on his face). We are not told where
KAREL starts, nor which way he is facing. There are no internal walls. In order to count the beepers he
will need to pick up them up, but when he leaves the Point, the pile should be as he found it.
By way of example, in the world shown KAREL should turn himself off on Point (7,5).
Note that this time, KAREL has no information as to where the beepers are, and will have to search his
entire world in a systematic manner. He will need to examine each Point, if there is a pile there to count
it, to remember which is the largest pile and where it is, and finally to return to the largest.
Try out your program in treasur3 and in treasur4.
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9. Criss-Cross
KAREL is put somewhere on a cross. The cross is
composed of one vertical line of beepers and one
horizontal line. A sample world is given above. His task
is to get to the centre of the cross i.e. the point where
there are beepers on all four sides of him. He must leave
the cross the way he found it - with all beepers in their
original positions. There are no internal walls, and you
can assume that KAREL will always be far enough
away from any external wall that you needn't bother
about it.
(a) Assume that he is placed at the end of one of the
arms (you don't know which) facing towards the centre;
try world cross1.
(b) Assume that he may be placed anywhere on the
cross, facing in any direction; try world cross2.
10. Fair Shares
(a) KAREL is presented with a row of piles of beepers. For example in the world shown below, there
are four beepers on the first Point of the row, two on the second, five on the third , and one on the
fourth. There are internal vertical walls at each end of the row, but no other internal walls. KAREL is
on the first Point (i.e. the most westerly) of the row, facing east; he isn't shown for the sake of clarity.
His task is to distribute the beepers evenly over the four Points in the row; thus in the example given, he
would end up with three beepers on each Point in the row. You can assume that there are exactly
enough beepers on the Points to achieve this. KAREL starts with no beepers in his bag. fair1
provides a test world.
b) This is the same task as the one above but with the following complication - the internal walls have
been removed. However you can assume that there are no gaps in the row i.e. that when KAREL
discovers a Point without any beepers, he has come to the end of the row. fair2 provides a test world.
11. Rectangles
All of the tasks in this exercise are concerned with rectangles of beepers - this also includes squares. In
all cases, KAREL starts facing east at the bottom left-hand corner of the rectangle - as shown in Figure
8.1. We don't know the dimensions of the rectangle. You can make the following assumptions:
• KAREL starts with a large number of beepers in his bag; if he needs more beepers than he
picks up, he will have them.
• his initial position and the size of the rectangles are such that he never risks bumping into an
external wall; there are no internal walls.
• the length of a side of a rectangle is defined as the number of blocks that it covers - not the
number of beepers along it; thus the rectangle in Figure 8.1 is four blocks by three blocks.
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(a)
KAREL's task is to pick up all the beepers in the rectangle, ending up where he started, facing
the same way.
(b)
The task is to move the rectangle and to set it out again exactly as it was before. The new
location will be specified relative to the original location; the relative movement will be
specified by the user and KAREL must ask for this information. Thus the following dialogue
would lead to KAREL laying out a 4x3 rectangle to the north-east of Point (7,6).
How far to move in X? 4
How far to move in Y? 3
KAREL will need to measure and remember the dimensions of the rectangle in appropriate
variables.
(c)
This is almost the same as the previous task, except that in the replaced rectangle, the width
should become the height, and vice versa.
(d)
As before he has to set out a new rectangle. The size and shape of this rectangle should be
determined as follows:
•
If it is possible to plot a square which has the same area as the original rectangle, then he
should do so. Hint: use a conditional loop to work out the areas of squares of side length 1,
2, 3, ... and stop when the area is the same as or greater than the area you are looking for.
•
Otherwise, if it is possible to plot a square with the same perimeter as the original
rectangle, then he should do so;
•
Otherwise he should plot a rectangle with the same perimeter as the original one, but with
a different shape.
Test your solution on rect1, rect2 and rect3.
Complications
You can make the problem more complex as follows:
(i)
Occasionally a unkind programmer plays a trick on KAREL, and puts him in the kind of world
shown in Figure 8.1(a) where the beepers form four lines at right angles but the lines don't join
up to make a rectangle. However, you can assume that even if the lines don't make a rectangle,
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they will be at right angles in an anti-clockwise sense as shown in Figure 8.1(a). If KAREL isn't
on a closed rectangle, he should turn himself off. Hint: compare the lengths of opposite sides.
Try world rect4.
(ii)
KAREL starts somewhere along one of the sides of the rectangle - but he doesn't know which
one or how far along. The displacement of the rectangle is relative to its south-west corner, so
you will have to determine where that is.
12. Sorting
KAREL has to sort piles of beepers. He finds himself in a world like that shown in Figure 8.2. His task
is to move the piles of beepers around to achieve the situation shown in Figure 8.3 where the piles are
in ascending order of height. His starting position is at the base of the rightmost pile facing west, and
you can assume that the piles are always at the bottom left hand corner of his world as shown. However
he doesn't know how many piles there are, nor how many beepers there are in each. It doesn't matter
where he ends up.
One possible algorithm to use is a bubble sort. If we refer to a pile by its X co-ordinate and if there are
n piles, then the algorithm is:
for i := 2 to n do
for j := n downto i do
if the pile on j is less than the pile on (j-1)
then swap the two piles
For example, if n=4, we can show the numbers in each pile at the end of each iteration (and the
corresponding values of i and j):
Position
i
j
1
2
3
4
2
2
2
3
3
4
4
3
2
4
3
4
7
7
7
2
2
2
2
3
3
2
7
7
3
3
5
2
3
3
3
7
5
2
5
5
5
5
5
7
Start
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See how the lower number 'bubbles' down towards the correct end. How would you sort in descending
order?
If you choose SORTING in the Computing Science folder, you can see this program in operation.
Write your own code, and demonstrate its operation on sort1 (as shown overleaf) and sort2.
This isn't the only way to sort, but bubble sort is a very popular method. There are more efficient way of
doing the sort but this implementation shows clearly what is going on. If you already know about
ARRAYS, you might like to modify this solution to store the sizes of the piles in an array, and sort its
contents.
13. KAREL Draws a Line
A straight line can be defined by the equation
y = ax + b.
Write a program which will prompt the user to enter the two coefficients (a and b), and then get
KAREL to plot the line by putting beepers down on the appropriate Points for all values of x between 1
and 30 inclusive. If any value of y is outside his world, then he should recognise this, and not try to plot
the point. We don't know where KAREL starts, nor which way he is facing. He has enough beepers to
complete any line we ask him to plot. There are no internal walls.
As an example this is the plot of the line:
y = 2x - 5.
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14. Find the Top
KAREL goes mountain climbing. He starts at Point (1,1) facing east and is faced with a range of
mountains. At the far end of the range is a beeper. His task is to climb over the mountains to get the
beeper. As he crosses them, he should find the highest point. Once he has collected the beeper, he
should climb back to that highest point, plant the beeper there and turn himself off.
15. Plotting
In all of these exercises you should use the procedures:
procedure DrawAxes(x_max, y_max: REAL)
puts X and Y axes on the screen; x_max and y_max specify the maximum x and y values that are to
be plotted.
procedure PlotPoint(x,y: REAL)
plots a single point with the given co-ordinate system.
function ExitClicked: BOOLEAN
returns FALSE until the user clicks Exit on the menu - at which point it returns TRUE.
Note that the parameters to these procedures should be actual values in the real world (meters).
DrawAxes works out the necessary transformations from the real world co-ordinates to screen coordinates, and they are remembered within the unit for use when PlotPoint is called.
Use ExitClicked in a loop at the end of your program to give you a chance to see the results:
REPEAT
{do nothing}
UNTIL ExitClicked
To access these procedures and functions you need:
USES csPlot;
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Remember the facilities for interacting with the user (which were described earlier):
procedure DisplayStringToUser(MessageString:String)
function GetStringFromUser(Question:String): String
function GetIntegerFromUser(Question:String): Integer
function GetRealFromUser(Question:String): Real
(a) Sine Waves
Draw the function: y =10 (sin + 1) where  goes from 0 to 360 degrees (2radians
(b) Circles
Write a program that prompts the user for the centre and radius of a circle, and then plots a sequence of
points to form that circle on the screen in a co-ordinate system in which both x and y go from 0 to 100.
If any point falls outside the range 0 to 100 (in either x or y), then don't plot it.
If  is an angle measured clockwise from the horizontal, the radius of the circle is R, and its centre is
the point (x0, y0), then all points with co-ordinates (x0 + R cos y0- R sinlie on the circle. Make up
the circle from (say) 1000 points at equi-spaced increments of between 0 and 2

You might also like to try to think of another way of solving the problem using equal increments of x.
(c) Modulated Sine Wave
Write a program that plots the function:
y = 10 (sin + 1) (1 - 1/ e
/1000
) (where  is expressed in degrees
over the range 0    1000.
16. Golf
You will need to include
USES csPlot, IO;
(a) The objective is to develop a very simple golf-playing program which plots the flight of a golf ball
on the screen.
Firstly, here's some necessary physics. We'll work in a standard co-ordinate system with the origin (0,0)
in the bottom left hand corner. The golf ball is launched from the origin. Assuming that there is no air
resistance, the equations of motion are:
x = vx t
y = vy t -
1/ g
2
t2
vx is the initial X component of the velocity given to the ball
vy is the initial Y component of the velocity given to the ball
g is the acceleration due to gravity (9.81 m/s2).
These initial values of vx and vy are given by:
vx = v cos

vy = v sin
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Where v is the magnitude of the initial velocity, and  is the angle that the initial trajectory makes with
respect to the horizontal
Let us take it that the maximum length of a stroke is 250 m. and that a golf ball never rises above 50 m.
- use these as values for x_max and y_max. You are going to read in the values of angle () and velocity
(v) from the user, and plot the resulting trajectory by repeated calls to PlotPoint .
To simulate the motion of the ball you will need to work out, and plot the position of the ball at equal
closely spaced time intervals, t. We'll use a constant for this; 0.01 seconds is a good choice.
CONST time_step = 0.01
If the ball is moving with a velocity of vx in the horizontal direction and with a vertical velocity of vy ,
then the ball's new position at the end of the time step can be calculated from its old position by using
the formulae:
x = xold + t vx
y = yold + t vy
Gravity will affect the ball's movement, so you will need to declare a constant g = 9.81 and decrease
the vertical velocity of the ball by t g each timestep. Thus:
vy = vyold - t g
Now, we don't know how far the ball will go, so we simulate until it hits the ground, i.e. y=0 . However,
remember that checking that a real number is exactly equal to 0.0 is undesirable, so we check for y
going negative. We shouldn't plot this negative value, nor indeed any point which is outside the range,
so before plotting any point we need to check that:
0  x  xmax and 0  y  ymax
The algorithm looks like this:
plot the axes
ask the user to type in the velocity
ask the user to type in the angle
calculate the initial values of the x and y velocities
set the values of x and y to 0
draw the ball at (x,y)
repeat
copy x to xold (likewise for y)
work out the new x and y at the end of the time step
if x is in range and y is in range
then draw the ball at (x,y)
update the y velocity
until y < 0
wait until Exit is clicked
How do we get the input from the user? Assuming that v and theta have been declared as real variables,
you would have something like:
v:=GetRealFromUser('Enter the velocity in m/sec’);
People think more naturally in degrees rather than radians (well at least I do), so it makes sense to ask
for the angle in degrees. However sin and cos need the angle in radians - the program will have to
perform the conversion: 1 radian = 57.2958.
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Once you've written your program, test it with a range of velocities and angles. Try velocities between
10 and 70 m/s, and angles between 15 and 60.
If you think that your program is in an infinite loop, try choosing Exit from the menu bar. Depending on
the exact circumstances it may get you out. Otherwise you will have to restart the computer.
(b) You could try to modify your program to allow for the effect of air resistance. One way to do this
would be to reduce the velocity by a very small percentage every time step.
(c) The aim now is to take the previous program and turn it into a little game. Implementing this
program in full will take some time. You might try to implement only part of the specification. If you
choose GOLF from the Computing Science Menu, you can see the complete program in operation.
Suppose that we are playing a round of golf with four clubs in our bag. These are a driver, a four iron, a
wedge, and a putter. The choice of club determines: (i) the angle at which the ball is struck; (ii) the
range of velocities available, according to the following table (any serious golfers are requested not to
be put off at this point by any gross error or simplification!):
Club
Code
Angle in
degrees
Minimum
velocity (m/s)
Maximum
velocity
(m/s)
1
2
3
4
15
40
60
0
44
22
11
-
70
32
24
-
Driver
Four Iron
Wedge
Putter
When the program starts the length of the hole is set; assuming that length is a real variable:
length := 100 + 350 * Random
The real function Random returns a real number randomly chosen between 0 and 1.
Set x_max to be 1.2*length. Any ball landing beyond x_max is out of bounds. If you land in bounds but
beyond x_max, the next shot should be played back towards the hole.
The user is then asked what club is to be used and replies with one of the codes 1 to 4 as above. A
putter may only be selected if the ball is on the green (i.e. within 10 meters of the hole), and in this
situation, this is the only club that may be selected. Any putt made within 2 meters of the hole is
regarded as being sunk. It takes two putts to hole out from anywhere else on the green. Any further
away and you can't use your putter. A driver may only be selected for the first shot.
The user is then asked what velocity is to be given to the ball (unless the club selected is the putter); the
result needs to be checked against the ranges given in the table, and the question asked again until a
satisfactory reply is received.
The first trajectory of the ball is plotted, starting from (0,0) and a record is kept of where it lands. The
equation of motion for y is the same as before. For x it is:
x(t) = x_start + v cos t
The dialogue is repeated, and the second stroke is plotted from the place where the first one landed. A
running total is kept of the number of strokes taken. If a putter is chosen then one stroke is added if the
hole is less than 2 metres away, and two strokes if less than 10 metres. The aim (as with real golf) is to
get the ball in the hole with as few strokes as possible.
The algorithm look like this:
work out length of hole
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plot axes
set stroke count to zero
set x_start to zero
repeat
increment stroke count
ask user for club and check that it is OK
if putter
then
ball in hole
if outside one putt range
then increase stroke count by another one
else
ask user for velocity and check that it is OK
get the angle for the chosen club
if x_start > length then reverse the direction of the shot
plot the trajectory from x_start and get x_final
if x_final > xmax
then out of bounds
else x_start becomes x_final
until ball in hole or ball out of bounds
if ball in hole
then tell the user the number of shots
else tell the user that the ball is out of bounds
wait until Exit is clicked
To tell the user how many strokes (s)he has taken or that s(he) is out of bounds:
DisplayStringToUser('Number of strokes is ' + IntToStr(stroke_count);
DisplayStringToUser('Sorry - out of bounds');
IntToStr is a built-in function that converts an integer to its representation as a string; remember to
include SysUtils in your USES. The ‘+’ in the first DisplayStringToUser joins the two
strings together.
You can use the following procedure from csPlot:
PlaceFlag(x:REAL)
This does what it says - plots a flag at the x position given by the parameter x.
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17. Digital and Analogue Clocks
This exercise is concerned with producing graphical clock displays, either digital or analogue. The aim
is to display the current time (in hours, minutes and seconds) and to the display every second. It will
help if you run the programs CLOCKS in the Computing Science folder.
You will need to include csClocks and Graphics in your USES.
Digital Clock
This is based on the standard seven-segment display used in digital watches and clocks to display a
digit. Our clock has six digits. Digits one and two display the hour, digits three and four display the
minutes and digits five and six show the seconds. So, for example, the time of 02:35 and 18 seconds
would be displayed as
Digit number:
1
2
3
4
5
6
The individual segments are numbered as follows:
1
2
6
7
5
3
4
On the screen, individual he segments can be lit using the procedure:
Light(position, segment:INTEGER)
The input parameter position determines which digit on the screen is to be affected and should be in
the range 1 to 6. The input parameter segment determines which segment is to be lit up; it must be in
the range 1 to 7. There is no way to delete individual segments. Instead, individual digits can be
deleted from the screen by using the procedure
DeleteDigit(position:INTEGER)
where position is a number from 1 to 6.
The current time is to be obtained using the functions
Hour: INTEGER
Minute:INTEGER
Second:INTEGER
which return the current hour (in 24-hour clock time), minute and second, respectively.
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NB: Before the procedures described above may be used, you must call the procedure
InitialiseDigital at the beginning of your program. This also draws the dots which appear
between the hours and minutes, and between the minutes and seconds.
You need to be able to know when it is time to update your display (i.e. when the end of the current
second is up). One way to do this is to compare the value of seconds with the last value read; as soon as
they are different then update. So assuming you have the last value of the seconds in a variable called
sec then you could have the loop:
REPEAT
{do nothing}
UNTIL sec <> Second
The whole program should be in a loop which continues until ExitClicked is TRUE
One question that you will have to consider in your design, is how often to update the minutes and
hours in your display.
Analogue Clock
The idea here is to create a standard clock-face showing the current hour (in 12-hour clock time),
minute and second (updated every second).
The procedure InitialiseAnalogue should be used at the beginning of your program rather than
InitialiseDigital. This will draw a clock-face without hands (i.e. a circle with surrounding
numbers from 1 to 12) in the middle of the screen as well as initialising certain features you will use.
The basic approach is the same as for the digital clock, but instead of updating digits on the screen, you
need to update the hands of the clock.
In order to do this, you will need to use the procedure:
DrawHand(length, angle:REAL)
The constant ClockRadius, also defined in the csClock, is to be used for the length of the second
and minute hands, whilst the hour hand should be a bit shorter - perhaps about two-thirds of that length.
The angle to be used with DrawHand should be in radians (remember that 360° is equal to 2*pi
radians) measured clockwise (!) from the vertical. To get the angles required to point the hands at the
correct numbers on the clock, use the following formulae:
hours_angle :=2*pi*hrs/12;
minutes_angle:=2*pi*min/60;
seconds_angle:=2*pi*sec/60;
Each hand should be a separate colour; this is achieved by using the predefined procedure
SetColor(color:integer) (note the American spelling) where color is one of the following
predefined constants:
clBlack
clRed
clYellow
clBlue
clSilver
clAqua
clLime
clFuchsia
clWhite
SetColor should be called each time a different hand is drawn. Deletion of a hand (or hands) at a
given angle is achieved by calling:
SetColour(black)
DrawHand(length, angle)
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18. Credit Analysis
Your task is to write a simple credit analysis program for a small company. They keep a file of orders
that have been placed; for each order they record:
•
•
•
•
the name of the customer (as a string);
whether the order has been paid (as a single character - y or n);
the number of items in the order, assuming that the order is all for the same item (as an
integer);
the unit cost of each item (as a real number in pounds).
Each piece of information is recorded on a separate line. For example, an order from smith for 5 items
at £5.67 each which has been paid would look like:
smith
y
5
5.67
The file consists of a number of orders. The end of the file is marked by the single string end in place of
the name. For example:
smith
y
12
5.60
jones
n
3
7.80
atkinson
y
23
1.07
smith
y
34
2.78
smith
n
32
5.79
atkinson
y
5
87.97
jones
n
43
0.45
smith
y
13
5.23
end
Your program should do the following:
i)
Prompt the user for the name of the customer whose credit status we want to analyse, and
read in this name.
ii)
For each order placed by this customer, write out on a single line:
• the word paid if the order has been paid and unpaid otherwise;
• the number of items in the order;
• the unit cost;
• the value of the order.
iii)
Write out
• the total value of the unpaid orders for this customer;
• what this represents as a percentage of the value of all of his/her orders (both paid and
unpaid);
• what it represents as a percentage of the value of all unpaid orders from all customers.
Here's an example of the interaction for the given data:
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Whose account do you want to look at? smith
Orders for smith
Status
Quantity
Unit Cost
Order Value
paid
paid
unpaid
paid
12
34
32
13
5.60
2.78
5.79
5.23
67.20
94.52
185.28
67.99
The total value of unpaid orders from smith is 185.28
This represents 45% of the total orders he has placed.
This represents 81% of the total of unpaid orders.
Hit <RETURN> to exit
You should generate the headings and layout as shown above. The percentages should be rounded to
the nearest integer.
The last line is needed so that you have time to look at the output. The code is:
WRITELN('Hit <RETURN> to exit');
REPEAT UNTIL KeyPressed
You will need to include
USES WinCrt;
Besides making it possible to write to and read from a text window, WinCrt provides one function and
one procedure which are useful:
function KeyPressed: Boolean
procedure DoneWinCrt
returns true when <RETURN> is pressed
closes down the text window
You will also need to chose Projects|Options and click the Linker tab. Then check the box beside
Generate console application
Initially it is a good idea to write your program so that it takes the input data from the keyboard. This
will lead to a somewhat confused presentation on the screen, but will give you more control over what
is going on. Then modify your program so that it takes input from a data file. There are two files
available, their full path names are:
contains the data given above
is longer.
L:\delphi\data\orders_1.txt
L:\delphi\data\orders_2.txt
To open a file for reading you need to include, at the start of your program:
VAR
data : TEXT;
...
AssignFile(data, 'L:\delphi\data\orders_1.txt');
Reset(data);
Except at the beginning where you read in the name of the customer we are interested in, all subsequent
calls to READLN should refer to this file:
READLN(data, ...)
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If you have time, think carefully about the different kinds of error which could arise and implement
ways of trapping and dealing with them.
19. Heights
A file L:\delphi\data\heights.txt contains the names of individuals and their heights in
meters.
There is one data item per line - a name, a height, a name, a height, etc. An example file would be:
James
1.79
Freda
1.56
Hugh
1.89
Alison
1.65
Elaine
1.67
Martin
1.90
Lucy
1.45
The program should print out the average height, and the name of everyone who is more than 20 cm
away from the average. For the above data this would be:
The average is 1.70
Freda
Hugh
Lucy
20. Birthdays
The exercise is concerned with a group of people, their ages and their birthdays. The basic data is
contained in a file which contains:
•
•
•
the name of the person (as a string)
the day and month of their birthday (as a string)
the year of their birth (as an integer)
Each piece of information is recorded on a separate line. For example the entry for Dave would look
like:
Dave
13 July
1953
The file consists of this data on a number of individuals; for example:
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Dave
13 July
1953
Sarah
24 June
1967
Tom
2 December
1959
COURSE MANUAL
Mike
10 March
1966
Anne
24 June
1945
Fred
16 August
1957
(a) Your program should do the following:
1.
Read the names, birthdays, and years of birth from the file into separate arrays.
2.
Prompt the user for the name of an individual and read in his/her name.
3.
If the name isn't in the file then print out an appropriate message, otherwise do the following:
Print out the full date of birth (including year) of the individual.
If there is anyone in the file who shares the same birthday as the individual (day and month but
not necessarily the year) then say so.
Print out how many people in the file are younger than that individual; younger means that
they were born in a later year - don't try to look at birthdays to see if they were born later in the
same year - just say that such a person is not younger.
4.
Repeat steps 2 and 3 until the user enters end to the prompt in step 2.
Thus given the file above, one might have the following interaction (user input in italics):
Enter a name: Dave
Dave was born on 13 July 1953
4 people are younger than Dave
Enter a name: Jack
Jack is not in the file
Enter a name: Anne
Anne was born on 24 June 1945
Anne has the same birthday as Sarah
0 people are younger than Anne
Enter a name: end
Here is some outline pseudo-code to help you get started:
read the data from the file into three arrays
{one for the names, one for the birthday and one for the year}
REPEAT
get the chosen name
IF the name isn't 'end' THEN
go through the array of names looking for the chosen name
IF you find it THEN
write out the birthday
go through the array of names
build up the total of those that are younger
IF you find someone with the same birthday THEN
write an appropriate message
IF you haven't found the chosen name THEN
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write out an appropriate message
UNTIL the name is 'end'
Test data is available at the start in a file L:\delphi\data\birthday.txt
(b) If two people share the same birthday, work out and report the 'probability of this happening. The
probability that two people in a group of n have the same birthday is:
365
364
363
365 - n + 1
p(n) = 1 - 365 365 365 
365
So you would report:
The probability of this happening in a group of 6 people is
0.04
21. Rates of Exchange
The file L:\delphi\data\rates.txt contains information which allows the conversion of
different currencies to pounds sterling. The file consists of a sequence of pairs of lines. The first line
contains the name of the currency as a string of characters, the second contains the amount of that
currency that is equivalent to one pound sterling (i.e. the rate) as a real number. Thus the first two lines
might be:
dollar
1.48
which means that there are 1.48 dollars to the pound. Assume that the file will contain data on no more
than 20 currencies (but the number might be less than 20).
Write a program which reads in the conversion data and conducts an interactive dialogue to ask the user
for the name of a currency and an amount, and prints out the corresponding amount in sterling. The
program should continue to prompt for a currency and amount until the user types the string end.
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22. Possible Routes
An airline operates flights between pairs of cities as shown in the diagram below. The arrows indicate
the directions of the flights - just because there is a flight from Paris to London, does not mean that
there is a flight from London to Paris.
London
Amsterdam
Paris
Rome
Berlin
Madrid
Cairo
Lagos
The information on origin/destination pairs is held in a text file (L:\delphi\data\routes.txt)
with the name of each city on a separate line. Of each pair, the first is the origin and the second is the
destination. The data represented in the above diagram would be coded in the file as follows:
Paris
London
Paris
Lagos
Lagos
Paris
Lagos
Madrid
Lagos
Cairo
Madrid
London
Madrid
Rome
Cairo
Lagos
Cairo
Berlin
London
Madrid
London
Amsterdam
Amsterdam
Rome
Amsterdam
Berlin
Rome
Amsterdam
Rome
Cairo
Berlin
Cairo
Your task is to write a program which will:
•
•
•
obtain from the user the name of an initial origin;
obtain the name of a final destination;
if there is a direct connection between the initial origin and the final destination then inform
the user;
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•
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COURSE MANUAL
otherwise tell the user of all possible ways of getting from the origin to the destination with
only one intermediate stop; note that there may be no such routes;
if the user types in the names of cities which are not recognised, or if there are no routes, the
program is not required to take any action;
the program finishes when the user types none as the reply to the first question.
Thus a possible dialogue might be:
What is the initial origin? Amsterdam
What is the final destination? Berlin
Direct flight
What is the initial origin? Lagos
What is the final destination? Rome
Connection via Madrid
What is the initial origin? Paris
What is the final destination? Madrid
Connection via London
Connection via Lagos
What is the initial origin? Amsterdam
What is the final destination? London
What is the initial origin? none
Think how you would extend your program to find routes with any number of intermediate stops - this
is not easy!
23. Barkings Bank
Barkings Bank has been concerned that it doesn't exercise sufficient control over its staff who trade in
shares. It wants to set up a computer system which will monitor their performance on a daily basis. Let
us follow the activities of a given trader (let's call him Nick) during a typical day.
He starts the day holding different numbers of different shares. The value of these shares is determined
by the number he holds and the price per share at the end of the previous day. He also has a certain
amount of cash which he can use to buy and sell shares. During the day he trades, buying and selling
quantities of shares at the price prevailing at the time; if he buys he uses his cash to pay for them - if he
sells, what he gets is added to his cash reserve. At the end of the day he enters the prices quoted on the
exchange for each of his shares. Note that this 'end of trading' price will not necessarily be that at which
he traded the shares during the day, nor indeed their valuation at the end of the previous day. If the
value of his shares at the end of the day plus the cash he holds at that time is greater than the sum of the
value and cash at the beginning of the day, then Nick has made a profit. If not, he'd better take the next
plane out!
The program you are to write works as follows:
At the beginning of the trading day, when the program is started, it reads in from a text file the position
at the end of the previous days trading. An example of such a file is shown below:
Value
7500.00
Cash
2500.00
BT
1000
Thorn
2000
Boots
500
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The fist line always consists of the string Value followed on the next line by a real number which is
the value of his share holdings as calculated at the end of the previous day's trading. The third line is
always the string Cash followed on the next line by his cash holding (a real) also at the end of the
previous day.
Next are a series of pairs of lines: the first is the name of the share (a string) and the second is the
number of those shares held at the close of trading (an integer). Note that he never trades in more than
50 different shares.
The program now prompts Nick for a series of transactions which are entered at the keyboard. Firstly he
is prompted to enter the type of the transaction, which can have of one of three values. If he enters end
this means that trading has finished for the day, and there are no more transactions.
If he enters buy or sell then the program should prompt for three more entries: the name of the share
(a string), the number of shares bought or sold (an integer), the price at which they were bought or sold.
For example the transactions on a (very!) light day might be:
Enter transactions:
Type of transaction: buy
Share: BT
Quantity: 200
Price: 2.25
Type of transaction: sell
Share: Thorn
Quantity: 500
Price: 2.00
Type of transaction: end
When trading is over, the program should prompt Nick for the 'end of trading' prices for each of his
shares. It then works out the total value of his holdings, and tells him if he has made a profit or loss and
of how much. An example of such an interaction is:
Enter share prices at the end of trading:
BT : 1.25
Thorn : 2.1
Boots : 2.2
You made a loss of 1200.00
Finally the program writes out a new file showing his position at the end of that day - this will be used
as the input file the following day, and has exactly the format described above. The file written
following the previous example would be:
Value
5750.00
Cash
3050.00
BT
1200
Thorn
1500
Boots
500
Your program should read the data for the previous day's trading from a file called:
L:\delphi\data\sthold.txt
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which refers to a file containing test data (not that used in the example above).
Your program should write out the position at the end of trading to a file on your floppy disc. You
should call the file endhold.txt, so you will need to use statements like:
AssignFile(end_holdings, 'endhold.txt');
Rewrite(end_holdings);
Carry out a test run of your program on the data given in sthold.txt. You should enter several
transactions before entering the prices at the end of trading. Suitable values for these are:
Barclays
BT
Dixons
GEC
Granada
Guinness
ICI
Manweb
MFI
Stagecoach
6.03
3.62
2.09
2.93
4.94
4.21
2.51
5.91
1.25
2.36
You should print out the contents of endhold.txt (as well as your program listing) and hand both in
with your floppy disc.
You could extend your program to:
•
•
•
•
allow the user to tell the program that he is dealing in a new share. This will have a transaction
type of new (and implies buying);
delete any share if the user's holding falls to zero in it;
incorporate suitable error checking (e.g. not trading shares that he doesn't have);
write out the time of the next flight to Kuala Lumpur if his losses exceed £800 million!
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24. Squash
The task is to write a program which plays a simple game of Squash. Everyone should be capable of
tackling part (a).
It will help if you run the program SQUASH in the Computing Science folder; this implements a
solution to part (a). You will be prompted to enter a speed. Try a value of 15 - higher values make the
ball move more slowly. A left mouse click releases a ball. You can control the position of the bat by
moving the mouse. When you have missed the ball, you can get another with another left mouse click.
To exit the game, chose Stop.
If you have any problem at all with the Maths/Physics, please consult your tutor.
(a) The object of this program is to play a simple game of squash, in which the player controls a bat on
the right hand side of the screen using the mouse. The game ends when the player misses the ball.
x_left
x_right
y_top
Vy
bat
ball
Vx
y_bottom
To make the Squash procedures and functions available you will need:
USES csSquash
The game starts with no ball in play. When the left mouse button is clicked, the ball should appear. You
should use the function:
function LeftMouseClick:BOOLEAN
which will return TRUE if the left mouse button has been clicked and FALSE otherwise. So to wait and
do nothing until the left mouse button is clicked you can say:
REPEAT {do nothing}
UNTIL LeftMouseClick
In my version of the program you can move the bat (see later) before clicking, but this isn’t obligatory.
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In order to control the bat with the mouse, you should use the following function and procedures:
function GetMouse:REAL
GetMouse will return the vertical position of the mouse (in the range y_bottom to y_top). To show the
bat, you will need:
procedure DrawBat(y:REAL)
procedure DeleteBat(y:REAL)
where y represents the middle of the bat. The mouse has been set up so that the bat will not go beyond
the boundaries defined by y_top and y_bottom, and it will always stay at the right-hand side of the
court.
Once the left mouse button is clicked, you will need to make the ball appear - this can be anywhere you
want in the court. In my version it appears at the right-hand side of the court, aligned vertically with the
centre of the bat. When it appears the simulation should start. The initial x and y components of the
ball's velocity will be provided in the supplied variables initial_x_velocity and
initial_y_velocity. These initial velocities are calculated for you - you just need to copy the
values into your own variables.
To simulate the motion of the ball you will need to work out, and plot the position of the ball at equal
time intervals, t. You should use the given constant delta_t for this interval. If the ball is moving
with a velocity of vx in the horizontal direction and with a vertical velocity of vy , then the ball's new
position can be calculated from its old position by using the formulae:
x = xold + t vx
y = yold + t vy
See the Golf practical for more details. Gravity will affect the ball's movement, so you will need to
declare a constant g = 9.81 and decrease the vertical velocity of the ball by t g each timestep.
Thus:
vy = vyold - t g
Note that in the absence of air resistance, vx will not change (other than on collision with the left wall or
the bat - see later).
The ball may be drawn and removed from the screen using the procedures:
procedure DrawSquashBall(no:INTEGER;x,y:REAL)
procedure DeleteSquashBall(x,y:REAL)
The first parameter in DrawSquashBall requires a ball number from 1 to 3 - you can have 3 balls in
play, but in this version just use ball number 1. The x and y refer to the co-ordinates at which you want
to draw or delete the ball. The ball will appear (or disappear) with its centre on (x, y).
During the course of its motion, three things can happen to the ball:
(i)
(ii)
(iii)
it can hit one of the three walls and bounce off;
it can hit the bat at the right hand side of the court and bounce off;
it can miss the bat at the right hand side of the court.
The ball has hit the top wall when
yball + r  ytop
where yball is the y co-ordinate of the ball and r is its radius. You will need to work out the tests for
hitting the other walls. The ball is soft and ‘gives’ a bit - this means that you are allowed to plot the ball
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when its centre is slightly closer to the wall than the radius of the ball. If the ball is at the right hand side
of the court, you will need to determine whether it has hit or missed the bat. The following diagram may
help you decide how to do this.
bat_y + 1/2*bat_height
bat_y
ball_y
bat_y - 1/2*bat_height
There is a predefined constant called ball_radius for you to use, which holds the value of the
radius of the ball.
What happens to the ball when it hits a wall depends on which wall it hits. Consider the left hand wall.
When the ball hits this wall, the y-component of its velocity (vy) will not change. However, before the
collision the ball's horizontal velocity (vx) will have been negative (going from right to left) and this
will now be reversed i.e.
vx := -vx
This is also true if the ball bounces off the bat. Similarly, if the ball hits the top or the bottom walls, its
horizontal velocity will remain unchanged, but its vertical velocity will be reversed:
vy := -vy
The game should end when the ball misses the bat at the right hand side of the court.
How fast the ball moves will depend on the way your program is written, and on the speed of the
computer it runs on. A procedure:
SquashDelay(Del:INTEGER)
is provided should you need to slow things down. On my version a value in the range 8 to 14 produces
reasonable results. You might like to use:
GetIntegerFromUser(Question:STRING): INTEGER
at the start of the program (as I have done) to prompt the user with a string Question and use the
value typed in reply for Del. Remember to include IO in USES.
Here is a full list of the constants, variables, functions and procedures provided in csSquash. The
‘constants’ and ‘variables’ are in fact calls to functions (to stop you changing them) but this doesn’t
make any difference as far as your program is concerned.
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Constants and Variables
ball_radius:INTEGER
bat_height:INTEGER
x_left:REAL
x_right:REAL
y_top:REAL
y_bottom:REAL
delta_t:REAL
initial_x_velocity:INTEGER
initial_x_velocity:INTEGER
The radius of the ball
The height of the bat
The x co-ordinate of the left wall
The x co-ordinate of the edge of the bat
The y co-ordinate of the top wall
They co-ordinate of the bottom wall
The increment in time to be used
The initial value of the ball's horizontal velocity
The initial value of the ball's vertical velocity
Procedures
Draws the bat with its vertical centre at y, at the right
hand side of the court
DeleteBat(y:REAL)
Deletes the bat with centre at y
DrawSquashBall(no:INTEGER; x,y:REAL)
Draws ball number no with its centre at the specified
position - in part (a) there is only one ball - number 1
DeleteSquashBall(x,y:REAL)
Deletes the ball at the specified location
SquashDelay(Del:Integer)
Introduces a delay to slow the game down.
DrawBat(y:REAL)
Functions
GetMouse:REAL
LeftMouseClick:BOOLEAN
ExitClicked: BOOLEAN
Returns the vertical position of the mouse, i.e. where the
centre of the bat should be.
Determines whether left mouse button has been clicked
As before
The two commands in the squash court window have the following properties:
Pause will halt the game temporarily until restarted
Exit will exit the program
Here is some pseudo-code to get you started. My version of the program repeatedly releases a ball
every time the left mouse button is clicked. A simple version would just finish when the ball has been
missed once.
FIRST LEVEL REFINEMENT
squash:
initialise
REPEAT
draw the ball at its current position
work out next position of ball
handle any collision with left wall
handle any collisions with roof and floor
IF the position of the bat has changed
THEN delete the bat and redraw it
IF the ball hits the bat
THEN handle the collision
ELSE the ball has missed
delay if necessary
delete the ball at its previous position
UNTIL the ball has missed the bat
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(b) You can make the game more complex by playing with more than one ball. DrawSquashBall
allows you to specify which one of three differently coloured balls to draw on the screen. Try to
develop your program so that more than one ball can be in play at a time, and so that collisions between
the balls occur.
(c) You may develop your program so that it becomes a breakout-style game. There are two
procedures supplied which enable you to do this:
DrawBrick(col:TColor; x, y:REAL)
RemoveBrick(x, y:INTEGER)
DrawBrick draws a brick with the same dimensions as the bat onto the screen with its centre on (x, y)
in colour col where col is one of the following predefined constants:
clBlack
clRed
clYellow
clBlue
clSilver
clAqua
clLime
clFuchsia
clWhite
You will need to include Graphics in your USES to make these colours available.
RemoveBrick deletes the brick at location (x, y) on the screen. In order to enable collision detection
with the bricks, two constants,:
brick_width:INTEGER
brick_height:INTEGER
are provided. When the ball hits a brick, the brick should disappear and the appropriate adjustments
made to the velocity of the ball.
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25. Billiards
The task is to write a program which plays a simple game of billiards. Everyone should be capable of
tackling part (a). It will help if you run the program BILLIARDS in the Computing Science folder; this
implements a solution to the first stage. If you have any problem at all with the Maths, please
consult your tutor.
The meaning of some of the terms used below will be clear if you refer to the following Figure.
x_right
x_left
top
y_top
direction
of travel
y

right
left
x
bottom
y_bottom
(a) A ball is placed on a billiard table which has the normal six pockets. The player is prompted to enter
an angle which determines the initial trajectory of the ball. This angle is specified in degrees
clockwise from the y-axis as shown. The ball is always struck with the same velocity, v; the velocities in
the x and y directions will be:
vx = v sin(
vy = v cos(
where  is in radians (1 radian = 57.2958 degrees).
You should simulate the motion of the billiard ball until it either comes to rest or ends up in a pocket. If
it comes to rest without going into a pocket then prompt the user for another angle, and continue to
simulate the motion from the place where the ball came to rest. Carry on prompting and simulating until
the ball is in a pocket.
To simulate the motion, you will need to work out, and plot the position of the ball at equal time
intervals, t. You should use the given constant delta_t (see below) for this interval. Thus:
xnew = xold + t vx
ynew = yold + t vy
This means that as long as it does not hit a cushion (see below) the ball will continue in a straight line ( 
will remain unchanged).
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Due to friction, the ball slows down until it eventually comes to a stop. To simulate this you should
subtract v from the velocity each time step. You should use the given constant delta_v (see below)
for this decrease. Thus, for each time step::
vnew = vold - v
In the course of its motion, three things can happen to the ball:
(i)
(ii)
(iii)
it can come to a stop (see above);
it can hit a wall and bounce off;
it can go into a pocket.
When the ball hits a wall, what happens depends on which wall it hits. Consider when the ball hits the
'top' wall. In terms of the angle 
new =  - ld
This is also true when the ball hits the 'bottom' wall. Likewise, if the ball hits the 'left' or 'right' walls we
have:
new = 360 - ld
(This comes from a consideration of the physics of elastic collisions. In all cases the sign of the
component of the velocity perpendicular to the wall is reversed. In the case of the 'top' wall the ydirection is perpendicular, so in this case it is the y-component of the velocity which is reversed.)
If the walls were perfectly rigid, the ball would hit the top wall when:
yball + r= ytop
where yball is the y co-ordinate of the ball and r is its radius.
However, as with a real billiards table, the walls have cushions which 'give' a little when the ball comes
into contact with them. For the top wall we have a 'hit' when:
yball + r  ytop
You will need to work out the tests for hitting the other three walls.
A number of constants, variables, procedures and functions are provided in the csBill unit:
Constants
radius (INTEGER)
The radius of the ball
initial_velocity (REAL) The initial velocity given to the ball
delta_t (REAL)
The increment in time to be used in the simulation
delta_v (REAL)
The decrease in velocity which takes place every time step
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Variables
These are assigned values within the unit, and should be treated as 'read-only' -i.e. like constants.
x_left: INTEGER
x_right: INTEGER
y_top: INTEGER
y_bottom: INTEGER
x_spot: INTEGER
y_spot: INTEGER
The x co-ordinate of the left wall
The x co-ordinate of the right wall
The y co-ordinate of the top wall
The y co-ordinate of the bottom wall
The x co-ordinate of the place where the ball is placed at the start
of the game.
The corresponding y co-ordinate.
Procedures
PutBall(ball: INTEGER; x, y: REAL)
Draws ball number ball at the specified position. In part (a), there is
only one ball - number 1.
DeleteBall(x, y: REAL) Delete the drawing of the ball at the specified location.
BillDelay(del:INTEGER) Introduces a delay so that the ball doesn’t move too fast; you will
have to experiment with the exact value of the number that you pass
to it - this will depend on your program, and on the machine it is
running on.
Functions
InPocket (x, y: REAL): BOOLEAN
Returns TRUE whenever the position denoted by the parameters lies
within any of the six pockets - it doesn't differentiate between the
different pockets..
ExitClicked: BOOLEAN
As before
The Billiard window has two menu items: Pause/Resume (which allow you to do just that) and Exit
(which can be used at any time if your program is not doing what you want, and also at the end of the
game)
If at any time you call PutBall, DeleteBall or InPocket with co-ordinates which place the
centre of the ball off the table, you will get an error message and the program will terminate.
(b) You should now use your simulation to play a game between two players. The file
L:\delphi\data\billiard.txt contains the name of the first player followed by the name of
the second player. Then comes a number of angles (expressed as an integer number of degrees) at
which the ball is hit for a stroke; in each pair the first corresponds to a stroke from the first player; this
is always followed by a stroke from the second.
For example:
Hendry
Higgins
100
35
265
187
45
78
This represents a six stroke match in which Hendry's first stroke is hit at 100 degrees.
The rules of the match are simple. The ball is placed on the spot. The first player hits it as specified. If
it comes to a halt without going in a pocket, the second player plays it from where it stops. If it goes in a
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pocket, then the player who plays the stroke gets a point and the ball is placed on the spot for the other
player. The winner is the player who gets the most balls in pockets (i.e. the most points).
Your program should read in the data from the file, and output the results to the screen in the following
format (assuming that the second, fourth and fifth strokes go in a pocket):
Hendry
Higgins
Hendry
Higgins
Hendry
Higgins
100
35
265
187
45
78
Pocket
Pocket
Pocket
Higgins wins by 2 points to 1
If the match is a draw, the last line should be:
A draw: 3 points each
Note that the last shot does not necessarily end up in a pocket. You can assume that both players play
the same number of strokes in strict alternation.
It is a good idea to redraw the table each time a ball goes into a pocket.
(c) Develop your program to deal with more than one ball and collisions between balls. PutBall
allows you to specify the colour of the ball - three colours are available:
1 = white; 2 = red; 3 = black.
26. Frequency Histogram
A given file contains a number of integers, one per line. The integers (apart from the first) are generated
randomly over the range given by the first integer. For example, if the file were to contain the following
integers:
20
10
11
13
8
12
10
8
9
7
15
then the range of the random numbers would be in the range 1..20; the random numbers would be 10,
11, 13 ... You can assume that the range will not exceed 100.
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Your task is to plot a frequency histogram of the random numbers. The histogram for the numbers
given above would look like:
In general the file will be a lot larger than the example given. Sample files are in:
L:\delphi\data\rand?.txt
Graphical output should be obtained with the augmented csPlot; you will need the following
procedures:
DrawAxes(x_max, y_max : REAL)
PlotLine(x1, y1, x2, y2 :REAL)
DrawAxes puts X and Y axes on the screen; x_max and y_max specify the maximum x and y values
that are to be plotted although you can actually use x values a bit larger than x_max (a fact which I've
exploited in the example).
PlotLine plots a line from (x1, y1) to (x2, y2).
The data files will contain distributions of four types: uniform, unimodal, bimodal or none of these.
Your program should apply tests to the distributions to identify which type is present, and inform the
user with:
DisplayStringToUser
The tests are:
uniform:
unimodal:
bimodal:
all frequencies deviate by less than 10% from the mean frequency.
there is a single maximum frequency;
the distribution has two maxima separated by a minimum which is less than 50% of
either maximum.
Start by recognising the uniform distribution. If you have time, try the other two.
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27. Translation
A text file L:\delphi\data\convert.txt contains information which allows the conversion of
measurements between UK and metric units. The information is coded as triples; each triple consists of
three lines. The first line contains a string specifying a UK unit, the second contains a real number and
the third line contains a string specifying the corresponding metric unit. The real number says how
many metric units are contained in the given UK unit. Each line contains only one word or number. For
example, the contents of the file might be:
inch
2.54
cm
yard
0.91
m
mile
1.61
km
acre
0.4
hectare
gallon
4.55
litre
pound
0.45
kg
ton
1.02
tonne
This states, for example, that 1 inch = 2.54 cm.
Your task is to write a program that:
•
•
•
•
•
asks the user to enter a quantity as a real number;
asks the user to enter a unit of measurement (UK or metric);
converts the quantity to the alternate system and writes out the result (to two places of
decimals);
if the unit is not recognised, then inform the user that no conversion is possible;
the program stops when the user types 0 as the quantity.
Thus a possible dialogue might be:
Enter a quantity: 3.2
Enter a unit: inch
3.2 inch = 8.13 cm
Enter a quantity: 24.5
Enter a unit: litre
24.5 litre = 5.38 gallon
Enter a quantity: 19.6
Enter a unit: foot
The unit foot is not recognised
Enter a quantity: 0
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Additional Tasks:
A text file L:\delphi\data\words.txt contains pairs of words, the first is an English word and
the second is its French equivalent. Each line contains only one word. For example, the contents of the
file might be:
boy
garcon
girl
fille
father
pere
mother
mere
son
fils
Your task is to write a program that:
•
•
•
•
•
asks the user to enter a word;
if the word is an English word, then print out its French equivalent;
if the word is a French word, then print out its English equivalent;
if the word is not in the file, then inform the user that no translation is available;
the program stops when the user types the word end (which is not one of the words in the
file);
Thus a possible dialogue might be:
Enter a word: mere
The English translation of mere is mother
Enter a word: son
The French translation of son is fils
Enter a word: sun
There is no translation for: sun
Enter a word: end
Suppose that the dictionary file were extended to be multi-lingual; this means that rather than containing
pairs of words it contained sets of words; each set contains words of the same meaning in several
different languages. Thus an English/French/German dictionary file might be:
boy
garcon
Junger
girl
fille
Madchen
father
pere
Vater
mother
mere
Mutter
son
fils
Sohn
dog
chien
Hund
Extend your solution so that the user specifies a word in any of the three languages, and then the
language into which that word is to be translated. The program should find the appropriate translation
and then write it out. A possible dialogue might be:
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Enter a word: mere
Translate mere into: German
The German for mere is Mutter
Enter a word: Hund
Translate Hund into: English
The English translation of Hund is dog
Enter a word: pere
Translate pere into: French
pere is a French word
Enter a word: cat
There is no translation for: cat
Enter a word: end
Consider the problems of extending the program to cope with a larger number of languages.
28. Shapes
An engineering firm cuts a number of standard shapes from sheet metal. The standard shapes, their
dimensions, and the corresponding areas are:
SHAPE
square
circle
triangle
DIMENSION(S)
side: s1
radius: s1
three sides s1, s2, s3
rectangle
45 degree rhombus
two sides s1, s2:
side: s1
AREA
SQR(s1)
pi*SQR(s1)
SQRT(s*(s-s1)*(s-s2)*(s-s3))
where: s =(s1+s2+s3)/2
s1*s2
SQR(s1)/SQRT(2.0)
Write a program which reads in the names of shapes followed by their dimensions from a text file and
writes out the name of each shape and its area. The end of the data is indicated by the 'end of file'. Once
all of the data has been handled, the program should print out the total area and the average area. An
example of the input data is in L:delphi\data\shapes.txt:
SHAPE
circle
triangle
square
circle
rhombus
rectangle
square
AREA
91.6
30.9
8.4
784.3
10.8
98.0
60.8
The output should be:
Total area
=
Average area =
1084.7
155.0
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29. Intensive Care Unit (ICU)
Patient data from an ICU is available in a text file as a sequence of integers, one per line; samples are
taken at equi-spaced time intervals.
(a) Write a program to plot the data.. A sample data files is L:\delphi\data\icu1.txt (and
icu2.txt and icu3.txt)
(b) Add low pass filtering:
f(t) = c*f(t-1) + (1-c)*r(t)
where f(t) is the filtered data at time t and r(t) is the raw data. Plot the filtered data as well as the raw
data.
(c) Use an average window filter:
f(w,t) = average of w raw data points centred on t
(d) A third filter is the median filter. This also involves moving a window over the data, but rather than
taking the average of the values in the window to represent the filtered value at its mid-point, we look
for the value which is the median of those values (i.e. there are as many values greater than the median
as there are values less). This involves sorting the values in the window into order, and then taking the
one in the middle. For example, suppose the values in the window (w = 7) are:
124 204 46 183 195 156 166
Sorting them gives:
46 124 156 166 183 195 204
and the median value is 166.
30. Retracing Your Steps
Look again at Problem 5(b) in which KAREL explores a maze to find a beeper. Modify the solution so
that KAREL can carry the beeper back to where he started by the shortest route. This means that he will
have to record the Points he visits on the way out, and remove from his record those Points that he visits
twice (i.e. when he has been down a 'blind alley').
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