Here are the source files for some short programs I've written
which may be useful or interesting to others. Please don't use them for
your homework solutions. For one thing, you might flunk. I'm not a
professional programmer, and don't even play one on T.V. These represent
the best work I can do, but hopefully not the best work you
can do.

The towers of
hanoi. A classic
elementary programming exercise in recursion.

Boxtext: A little
utility for printing text in a box. The text can be given on the command line
or read from stdin. You can use this to spiff up your interactive shell
scripts.
 Implementation of the
Euclidean Algorithm. The Euclidean Algorithm is an elementary algorithm
for finding the greatest common divisor of two numbers.

A
template for
processing commandline arguments. This is basically an elaboration of
the stuff in section 5.10 of K&R. Supports option arguments, combining
singleletter options, and using  to denote the end of options.

Miles, a
utilty for runners. Prints all combinations of lanes and laps on a track
that equal an even number of miles to within a desired tolerance.

Benford, a program
for investigating Benford's Law.
Benford's law, a curious empirical observation, says that the
relative frequency for the most significant digit equaling k is commonly
distributed as log((k+1)/k). The story is that
the pages near the beginning of the book in old tables
of common logarithms were often more heavily worn than pages near the
end. Since people usually went to such tables to look up the logarithms
of data they observed, this would seem to imply a nonuniform
distribution for the most significant digit of the mantissa.
There is by now a sizable literature on Benford's law. See, for
example, T.P. Hill, "The SignificantDigit Phenomenon", Amer. Math.
Monthly, April 1995, 322327, and the references given there.

A utility to
copy over an existing
file. In both Unix and DOS the redirection > first truncates the target
file to zero length. The redirection >> appends new data at the end of
the target file. This program allows new data to be written on top of an
existing file starting from the beginning.
 Calculate the expected amount of time to
cover (i.e., obtain
for the first time) a specified sequence of binary digits in a stream of
random digits. (Contains another potentially useful routine, PrintAsDecimal,
which prints an arbitrarily long string of 0s and 1s as a base 10 decimal.)
Algorithm: (pointed out to me by P.Griffin ) If s is the given string of
length n Then E T(s) = E T(t) + 2^n, where t is the longest string
such that s starts and ends with t. Perhaps surprisingly, the algorithm
shows that the expected time is always an integer.
The algorithm applies much more generally, e.g., to find the expected
time to first encounter a given sequence of states in a finitestate
ergodic Markov chain. (In that case, 2^n must be replaced by a
quantity depending on the transition matrix and stationary
probabilities.)
Also see:
 Example 4.20, pp 160161 in S.M. Ross, Introduction to
Probability Models 5th Ed., Academic Press, San Diego, 1993
 G. Blom, On the mean number of random digits until a given sequence
occurs, J. Appl. Prob. 19(1982), 136143.
 P.T. Nielsen, On the expected duration of a search for a fixed pattern
in random data, IEEE Trans. Information Theory 19(1973), 702704.
For a proof and other discussion, consult my paper
The Expected time to find a string in a random binary
sequence.
Here is a cgibased
demo which accepts
only strings of 32 digits or fewer.
 Program to print out examples of the
long division
algorithm. With the advent of calculators the long division algorithm is
quickly becoming a lost art. So that future generations may understand how
we suffered in 4th grade, I offer this program. It is capable of solving
very large examples.
Try a cgibased
demo .
 C code for solving
Kepler's equation. This code illustrates 5 different methods for
solving kepler's equation, a transcendental equation whose solution is one
of the key steps in determining the position of a planet or satellite on its
orbit. The source code is extensively documented including references to
sources for further information.
 An implementation of the
bisection method
for finding roots of equations. Not an efficient method, but instructive
for calculus students studying the intermediate value theorem.
 The definitive
leapyear program.
 Calculate the date of
Easter and related things.

A recursive descent parser for translating roman numerals into integers. For the history of roman
numerals see pp 242246 of Number Words and Number Symbols: A Cultural History
of Numbers, Karl Menninger (transl. Paul Broneer), MIT press, 1977.
 Tutney
Tutney is a spelling language which my parents used to communicate with
each other when I was a toddler and they didn't want me to be able to follow
what they were saying. I am unsure of the origins of tutney. My parents claim
it originated in the part of upstate New York where they grew up (Boonville
area,) but I have met people from other parts of the world who know tutney.
The rules are simple: vowels are pronounced as is, but consonants (except
for a few exceptions) are pronounced by doubling the consonant with the letter
u interposed. The exceptions are q (prounounced quack), y (pronounced yack),
j (pronounced judge), w (pronounced wack), and h (pronounced hash).
Surprising proficiency can be attained with a little practise.
For example, here
is a translation of the previous paragraph into tutney.
And here is a
lex source file for a program to translate English ( or any language using the
same alphabet!) into tutney. Here is
C language source file for a program to do the same thing. Finally,
here is an executable for Windows XP built from
the C source. This is a console application. To use it, you would say the
following at a command prompt: tutney < source > destination. Or say
tutney /h for further usage information.

A program for studying happy
numbers. A happy number n is one with the following property: let f(n)
be the sum of squares of the decimal digits of n. The sequence f(n), f(f(n)),
... must eventually fall into a cycle. If the cycle is 1,1,1,..., then the
number n is happy. Otherwise it is unhappy. Our program allows different
bases and also introduces the concept of an ecstatic number: an ecstatic
number is happy in every base up to a certain limit (which measures its
ecstasy.) (Also see the Mathematica site for more on this somewhat obscure topic.)

A program for simulating
J. Parrondo's paradoxical game. This involves two games of chance which
by themselves are unfavorable, but which when alternated at random become
favorable. See J. Parrondo's website
for more information.

A program for printing a nicely formatted pascal's triangle. It is written for simplicity rather
than efficiency.

C source for an implementation of the strstr library routine
using the KnuthMorrisPratt algorithm. Includes a wrapper main program
that allows searching for the first occurrence of a string in a file, printing
the failure failure, counting the number of occurrences of a string in
a file, and other applications. For further information on the algorithm,
consult the paper
Knuth, D.E., J.H. Morris, and V.R. Pratt, "Fast pattern matching
in strings", SIAM J. Computing, 6:2, 323350.

C source for a study of recursive functions. As
it stands, this is the world's slowest implementation of the power function.
It could easily be extended to give even slower implementations of other, more complex,
arithmetic functions.

A program that writes the settheoretic definition of
ordinal numbers. The sequence of ordinals is
defined in terms of the null set, 0, by 0, {0}, {0,{0}}, ...

A program to search a dictionary for anagrams.
The idea for this comes from Programming Pearls, Jon Bentley, 2nd Ed.,
Addison Wesley, Reading, 2000. Bentley's book is an excellent source of
ideas for programming projects.

A program to print numbers in led style. I.e., like
this:
_ _ _
_  _  _ _
_    _ 

A program illustrating several methods for generating all
permutations of 1...n. This subject has a large
and interesting literature, and this program only begins to scratch the
surface. See, e.g., the survey article: R. Sedgewick, Permutation Generation
Methods, ACM Computing Surveys 9(1977), 137164.

A program to generate pages of random arithmetic
problems. Research has shown that mental exercise can help stave
off dementia. Use this program to generate a list of random arithmetic
exercises with an additional page of answers.

A program to illustrate a constructive proof of the
SchroderBernstein Theorem. The proof in question is due to M. Hellman.
See, e.g, E. Mendelson, Introduction to Mathematical Logic, 3rd Edition,
Wadsworth and Brooks/Cole, Monterey, 1987, pp 198199.
 A program to tabulate the hypergeometric function.
Allows you to vary the parameters and variable at will, and can used either
from the command line or in an interactive mode. Output can also be written
in XML which links a stylesheet named function_table.css, if it exists. By
rolling your own stylesheet you can control the appearance of the tables
produced. I intend to use this code as the base for a suite of
programs to calculate various special functions if my ambition does not
desert me. At any rate, tables of the hypergeometric function are hard to
find, so this may fill a need. (This program is very naive. It is only
a starting point.)
 Lisper: a program to generate random balanced parenthisis expressions,
i.e., things like (()()((()()))). The name is based upon the unoffical reading
of the Lisp programming language acronym: Lots of Insipid Silly Parentheses.
 Ackermann: a program to calculate Ackermann's
function (as far as that is possible.) The source code hopefully contains
instructive comments related to this function and its properties and
significance.
 An introspective C program. It prints its
own source code listing to stdout. This output could then be compiled and
run; that output could be compiled and run .... In essence, it is a very
simple, source code level, computer virus. (Addendum: Such programs have
been termed "quines" after the logician W. Quine. Apparently the writing of
one's own quine is a kind of rite of passage for programmers. See
The Quine Page for
much more information.)
 A program to demonstrate information packing
functions. An information packing function is a function C(x,y) of whole
numbers with whole number values which is 11. The idea is that such a
function packs the information in 2 natural numbers into a single natural
number. Suitable extraction functions H ("head") and T ("tail") then
retrieve the information via H(C(x,y)) = x and T(C(x,y)) = y. With some
care, all 3 functions can be constructed so as to be primitive recursive.
The importance of such functions in recursion theory is that they allow
functions of several variables to be treated as functions of a single
variable. This program illustrates a particularly simple and efficient
function C. The idea comes from the beautiful book of Marvin Minsky,
Computation: finite and infinite machines, Prentice Hall, Englewood
Cliffs, N.J., 1967.
 Compute the Catalan numbers. The source code
documents some key points about the theory of these numbers and their uses
in combinatorics.
 Euler's totient function. The implementation
is highly recursive.
 My own solution to the firing squad
synchronization problem. This old problem, attributed to J. Myhill,
asks the following: suppose we have n determinisitic finite automata arranged
in a line. All the machines have identical state transition diagrams except
for the two on either end, which are allowed to be different. The transitions
of each machine are allowed to depend on the states of its nearest
neighbors, but not on those of any other machine. The
machine on the left end is designated "the general." Alone among the machines
it has some volition, so that at some time it enters a special state we may
call "fire when ready." The problem is to design all the machines so that
they will at some point enter a state called "fire" simultaneously.
The trick is to make the design independent of n, so that if we inserted
an arbitrary additional number of machines in the line, the solution
would still work (though it would probably take longer for the machines
to synchonize.)
My solution is neither efficient nor elegant, but it does seem to work.
The code could use lots of polishing, but I can't stand to look at it
anymore.

More to come ... ?