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prime factorization using base 1

by tye (Cardinal)
on Jan 17, 2001 at 10:43 UTC ( #52469=snippet: print w/ replies, xml ) Need Help??

Description: I recently realized the power of base-1 numbers. They don't have the arbitrary range limitations of Perl's regular number representations while converting between the two is nearly trivial. Plus finding prime base-1 numbers is particularly compact code in Perl. And when the primality test fails you are also handed some factors! So base-1 numbers are perfect for finding prime factorizations! They aren't very space efficient, unfortunately (hey, no one's perfect).

So factor1() returns the prime factorizations of base-1 numbers (as base-1 numbers). factor10() just converts a base-10 number into a base-1 number so factor1() can factor it and then converts the returned list of base-1 factors into base 10 again.

One line of test code is included that factors any base-10 numbers given on the command line.

Now updated to be faster!

#!/usr/bin/perl -w
use strict;

sub factor1 {
    return @_  if  $_[0] !~ /^(..+?)\1+$/;
    return map { factor1($_) }
        ( "$1", $_[0] =~ s/$1/1/g, $_[0] )[0,-1];

sub factor10 {
    return map {length} factor1( 1x$_[0] );

print join $/, map { join " ", factor10($_) } @ARGV;
Comment on prime factorization using base 1
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Re: prime factorization using base 1
by clemburg (Curate) on Jan 17, 2001 at 14:46 UTC

    Our regex engine is truly The Little Engine That Could! Nice idea, tye. Going back to the fundamentals often pays ;-) ...

    Here is something similar I worked out for a statistics module that needed tie-adjusted ranks (a "tie" occurs in a list of numbers if two numbers have exactly the same value - something that most statistics algorithms don't really like because it violates their assumptions about continuous distributions).

    sub ties { my @val = sort @_; return () unless @val; my @delta = (1) x @val - 1; for (my $i = 1; $i < @val; $i++) { $delta[$i - 1] = $val[$i] - $val[$i - 1] ? 1 : 0; } my @ties = map {length} split /1+/, join '', @delta; shift @ties unless $ties[0]; return map {++$_} @ties; }

    Christian Lemburg
    Brainbench MVP for Perl

Re: prime factorization using base 1
by ambrus (Abbot) on Dec 16, 2010 at 10:18 UTC

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