Table Of ContentThe Alien, Numbereater and other Programs
for Personal Computers
Some other computing books from the Macmillan Education Press
Beginning BASIC P. E. Gosling
Continuing BASIC P. E. Gosling
Microprocessors and Microcomputers Eric Huggins
A Practical Introduction to Pascal I. R. Wilson and A. M. Addyman
The Alien, Numbereater
and other Programs for
Personal Computers
John Race
Senior Lecturer,
Department of Computer Science
Brunei University
©JohnRace 1981
All rights reserved. No part of this publication may be reproduced or
transmitted, in any form or by any means, without permission
Firstpublishedl981 by
THE MACMILLAN PRESS LTD
London and Basingstoke
Associated companies in Delhi Dublin
Hong Kong Johannesburg Lagos Melbourne
New York Singapore and Tokyo
ISBN 978-0-333-28079-9 ISBN 978-1-349-05175-5 (eBook)
DOI 10.1007/978-1-349-05175-5
The paperback edition of this book is sold subject to the condition that it
shall not, by way of trade or otherwise, be lent, resold, hired out, or
otherwise circulated without the publisher's prior consent in any form of
binding or cover other than that in which it is published and without a similar
condition including this condition being imposed on the subsequent
purchaser
Contents
Introduction 2
Palindromes 4
Brackets 8
Orbit 13
Pascal's Triangle 25
Superlife 26
Double Density Histograms 39
Spiral Program 45
Remover 50
Prime? 61
Playfair 62
The Alien 67
General Input Program 71
Clear 75
Numbereater 77
Appendix: Amendments to Programs for later PETs
with revised ROMs 80
83
Index
Introduction
From the age of sixteen we can own machines which are physically much
more powerful than we are. A Victorian engine driver would have been
quite shocked and alarmed at the way young people can now afford to buy,
and are allowed to drive, weird conveyances that are more convenient and
efficient than his. His engine was far too complex and expensive for
amateurs. To some extent, the older generation of computer users look
upon the mass market in home computers with the same shocked alarm as
the Victorian engine driver would have viewed the moped - even to the
extent of denying that the new machine was a real vehicle at all.
But now you can buy, and you should buy as soon as you can, a machine
- the home computer - which can outperform some of your mental muscles,
as the moped outperforms your leg muscles. Of course you are its super
ior in many other ways. Unlike it, you can reason by analogy, think
laterally, use your imagination. But it can calculate quickly and prec
isely, follow specified procedures without deviating by accident or imp
ulse, and write and draw tirelessly. A teacher of the old school would
certainly call such abilities mental ones, and award high marks to
pupils who showed them. What is happening is that, just as we had to
learn to accept, and then enjoy, the fact that machines could be strong
er than us, so we must now learn how to accept and enjoy the intellect
ual powers of computers, which in general happily complement our own.
Again, the motorbike overcomes air resistance and friction more spect
acularly than we can, but needs us to balance it and direct it. Simil
arly a computer will beat us in following defined logical and mathematic
al procedures, but needs us to set the problem and define the proced
ures. Then, together, we can set off and travel far afield for enjoy
ment and profit.
This book is for people - students, teachers, or just enthusiasts, at
home or in school or college. It is intended as a source of ideas for
projects, a series of examples of techniques and applications, and a
comfort to those who, like the author, write programs too often that do
not work properly, and who then brood over our shortcomings and try to
discover more reliable methods for converting our brilliant ideas into
sound computer systems.
Those who run courses in schools or colleges may find the book useful as
a source of worked examples and as recommended background reading, part
icularly if the course revolves round the use of BASIC. The programs in
the book are mostly in BASIC, and in particular, Commodore PET BASIC.
However, although the computer used is the small PET 2001 8K, the pro
grams should be transportable with more or less amendment to other BASIC
computers such as APPLE, TANDY, SORCEROR, or the British NASCOM, ACORN,
or SINCLAIR computers. There are also examples of Assembler and machine
code programs for the MCS 6502 microprocessor, used on PET, APPLE 2, and
many other systems. If you have a PET with a cassette deck you can buy
1
a cassette containing the programs in this book, by contacting me via
Uacmillan Press.
There are a number of programs in this book which require additional equ
ipment to work: a printer, an interface for a relay to drive an electric
light, a second cassette. These may be useful to those who are consider
ing extending their,system.
BASIC is a language which provokes as much antagonism among professional
computer people as the home computer itself. Indeed, it is a language
in which it is very easy to write programs that will run, but quite hard
to write programs that will run correctly. Since the professionals are
rightly concerned about high standards - computers today may kill
people in hospitals or aircraft or trains if they fail - they fear that
2
sloppy habits learned from BASIC could become engrained and pernicious.
They would prefer the enthusiast to be introduced to computers through a
more rigorous language, like PASCAL, in which control structures are
safer and programs are rejected by the rules before they try to run on
real data. Unfortunately BASIC has become almost a standard language
for micros, and variants are used even for process control and business
applications ( PLANCOL, DEC BASIC-PLUS).
But with self-discipline it is possible to write reasonably clear, fast,
safe BASIC programs and - although the author does not always take his
own medicine - some tips for overcoming the bad features of BASIC are
given in the pages that follow.
If you find any mistakes in the programs, do let me know: but I do not
accept any responsibility for anyone using a program and coming to grief
whether he is an astronaut who falls into the sun by relying on ORBIT or
a spy who uses PLAYFAIR and has his transmissions decoded by counter
intelligence.
My thanks are due to John Watson of Macmillan for encouraging the writ
ing of this book, to my son Tom for his program for finding the first
sequence of 20 non-primes, which he really did write to do his maths
prep in the 3rd form of Abingdon School: to my Brunel student Harminder
Ghattaura who wrote a 6502 program to draw double precison lines on the
PET screen using Bresenham's algorithm, and to my wife and daughters who
had to put up with the noise of a golfball clattering away in the back
ground.
It was my father's interest in codes and cyphers that prompted the pro
gram PLAYFAIR.
"Interface box" controlling electric light, Commodore PET 2001 BK,
second cassette player, Aculab printer controller, IBM printer.
3
Palindromes
Techniques: recursion, string handling, demonstration cheating.
Try running the program, and check the results with Figure 1. Adam's
famous remark to Eve, Madam I'm Adam, is a palindrome - i.e. it reads
the same backwards as forwards, if one ignores the spaces between the
words and sticks to upper case. XYZ obviously is not a palindrome.
The last trial refers to Ferdinand de Lesseps, whose palindrome is more
successful than his attempt to build the Panama canal was. (Napoleon's
'Able was I ere I saw Elba' goes in nicely, spaces and all, since each
word matches another of the same length on the other side of 'ere'}.
Now look at the program (Figure 2.}. The whole point of this program
is to show how you can construct a program to match a formal definition
of some data - in this case, a palindrome, which is defined in lines 5 -
6, recursively: that is, the definition makes use of itself. ThiS may
seem circular, and it would be, but for the fact that the definition
uses itself on a shorter, simpler case - the possible-palindrome with
its end characters removed - so that each recursion deals with a shorter
string. Secondly the definition includes a terminating condition other
than continued use of itself - the 'length 0 or 1' condition, which pro
vides an exit and prevents recursion ad infinitum.
In computer science recursion is quite useful, for example, to define a
'number': a number is a digit, or a digit concatenated (strung onto}
a number. You may also like to see recursion at work in the opposite
direction - constructing examples of recursively defined things, instead
of checking things against a recursive definition, in 'Brackets'.
Back to the program. The sequence of instructions called Palindrome
Tester is typical of this type of program. It is responsible for sett
ing up a stack of entries for holding the workings at each level of re
cursion: R$(} will contain the reply sent up by each lower-level invoc
ation of the Tester subroutine to the level above, and A$() will contain
the string sent down by one level to the level below for checking. We
clearly anticipate having palindrome-candidates of never more than 40
characters in length. Palindrome Tester also has to get the candidate
palindrome from the experimenter and place it in A$(0}, the top level.
Palindrome Tester uses the Recursive Tester ( GOSUB 1000 } and prints
the answer. Recursive Tester simply acts on the rules previously defin
ed: if the string it has in its A$(LEVEL} is empty or only one char
acter long it can return the answer YES to the routine which called upon
it - either Palindrome Tester, if it is at level 0, or a higher level
invocation of itself. Otherwise it has to check to see if it can reject
the string on the grounds that its first and last characters are not the
same ( line 1020 } •
Now at line 1030 Recursive Tester has to extract the middle part of the
string given to it, using MID$(string,I,J} which returns a substring
consisting of the J characters of 'string' starting at the Ith position.
It then gets ready to go down by adding one to LEVEL and calls itself.
On return from itself, it resets LEVEL and returns YES up\vards if and
only if its lower-level examination also said YES.
As a matter of fact one could have simplified this program a bit since
the descent into recursio~ is a straightforward one-way process - as
soon as any level says NO we could leave the program instead of relig
iously carrying NO up and up. But in many more complicated examples of
recursion, any one level cannot have the authority to decide unilateral
ly to terminate the whole process. For example, in chess, recursion can
be used to find a player's best move, a.nd each level of the BESTHOVE
4
SEARCHING
FOUND PALINDROME
LOADING
READY.
RUN
? MADAMIMADAM
MADA MI MADAM
ADAMIMADA
DAMIMAD
AMIMA
MIM
I
YES
BREAK IN 60
READY.
RUN
? XYZ
XYZ
NO
RUN
? AMANAPLANACANALPANAMA
AMANAPLANACANALPANAMA
MANAPLANACANALPANAM
ANAPLANACANALPANA
NAPLANACANALPAN
APLANACANALPA
PLANACANALP
LANACANAL
ANACANA
NACAN
ACA
c
YES
Figure 1. Results of PALINDROMES program
2 REM------------ PALINDROMES----------
3 REM
5 REM A PALINDROME IS A LETTER-STRING OF LENGTH 0 OR 1,
6 REM OR A PALINDROME WITH THE SAME LETTER ADDED TO EACH END.
8 REM
10 REM-------PALINDROME TESTER---------
15 REM
20 DIM R$(40) ,A$(40) :REM STACKS
30 INPUT A$(0): REM CANDIDATE P/DROME
40 LEVEL=O: GOSUB 1000
50 PRINT R$(0): REM REPLY YES OR NO
60 STOP
997 REM
998 REM------- RECURSIVE TESTER
999 REM
1000 R$(LEVEL)="YES":REM ASSUME IT IS
1005 PRINT TAB(LEVEL); A$(LEVEL)
1010 IF LEN(A$(LEVEL))=<l THEN 1900
1020 IF LEFT$(A$(LEVEL),l)<>RIGHT$(A$(LEVEL),l) THEN 1890
1030 A$(LEVEL+l)=MID$(A$(LEVEL),2,LEN(A$(LEVEL))-2): REM EXTRACT MIDDLE
1040 LEVEL=LEVEL+l
1050 GOSUB 1000: REM IS MIDDLE A PALINDROME?
1060 LEVEL=LEVEL-1
1070 IF R$(LEVEL+l)="YES" THEN 1900
1890 R$(LEVEL)="NO"
1900 RETURN
Figure 2. PALINDROMES program
5
