here's a interesting real-world algoritm to have fun with.

attached below is the Perl documentation that i wrote for a function

called "reduce", which is really the heart of a larger software.

The implementation is really simple, but the key is to understand what

the function should be. I'll post Perl and Python codes tomorrow for

those interested. If you are a perl programer, try to code it in

Python. (it's easy.)

This is brought to you by the Perl-Python a-day community. To

subscribe, see

http://xahlee.org/perl-python/python.html
Xah

http://www.velocityreviews.com/forums/(E-Mail Removed)
http://xahlee.org/PageTwo_dir/more.html
-------------------------------

=pod

e.g. reduce( $pairings, $a_pair) retured the first argument with some

pairs deleted.

Detail:

we have n things, represented by numbers 1 to n. Some of these are

identical. We want to partition the range of numbers 1 to n so that

identical ones are grouped together.

To begin comparison, we generate a list of pairings that's all

possible parings of numbers 1 to n. (of course order does not matter,

and the pairing does not contain repeations) This is the first

argument to reduce.

We'll go thru this pairings list one by one and do comparisons, remove

the pair once it has been compared. However, more pairs can be removed

if a we find a pair identical.

For example, suppose we know that 2 and 4 are identical, and if the

pairing list contains (2,3) and (4,3), one of them can be deleted

because now 2 and 4 are the same thing.

(We do this because we expect the comparison operation will be

expensive.)

reduce( $pairings, $a_pair) returns a reduced $pairings knowing that

$a_pair are identical.

The first argument $pairings must be in the form of a hash. e.g.

{'1,5' => [1,5],'3,5' => [3,5],'2,4' => [2,4],'4,5' => [4,5],'1,3' =>

[1,3],'2,5' => [2,5],'1,2' => [1,2],'3,4' => [3,4],'2,3' =>

[2,3],'1,4' => [1,4]}

(Note that keys are strings of the pairs separated by a comma.)

$a_pair is a reference to a list of the form [$a,$b].

(different pairs may be deleted if the hash's pairs are given in

different order. i.e. 3,4 instead of 4,3)

The return value is a reference to a hash.

The program is deterministic but exactly which pairs are deleted is

unspecified. If the input is all possible pairs of 2 things out of n,

maximum reduction is guaranteed.

=cut