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Re: Multiple Combinatorics

by BrowserUk (Pope)
on Apr 15, 2012 at 11:14 UTC ( #965146=note: print w/ replies, xml ) Need Help??


in reply to Multiple Combinatorics

Update: My sets can overlap too. For exmaple I may have 4 sets like '0..7','1-6', '6-12',and '3..9'.

You don't say how many from each of those four sets, so I did 2 from each, but it should be obvious where to change the numbers supplied to permuteSets for different requirements.

The following runs in 1.7MB and takes a few seconds for wc -l to count the results:

#! perl -slw use strict; sub nFor(&@) { my $code = shift; die "First argument must be a code ref" unless ref( $code ) eq 'CO +DE'; my @limits = @_; my @indices = ( 0 ) x @limits; for( my $i = $#limits; $i >= 0; ) { $i = $#limits; $code->( @indices ), ++$indices[ $i ] while $indices[ $i ] < $limits[ $i ]; $i = $#limits; $indices[ $i ] = 0, ++$indices[ --$i ] while $i >= 0 and $indices[ $i ] == $limits[ $i ]; } } sub permuteSets (&@) { my $code = shift; my @subsets; while( @_ ) { my( $n, $set ) = ( shift, shift ); push @subsets, []; nFor { push @{ $subsets[-1] }, [ @{ $set }[ @_ ] ] } (scalar @ +{ $set } ) x $n; } nFor{ $code->( map{ @{ $subsets[ $_ ][ $_[ $_ ] ] } } 0 .. $#subsets + ); } map scalar @$_, @subsets; } permuteSets{ print join '-', @_; } 2, [0..7], 2, [1..6], 2, [6..12], 2, [3..9]; __END__ C:\test>965138 | wc -l 5531908 C:\test>965138 0-0-1-1-6-6-3-3 0-0-1-1-6-6-3-4 0-0-1-1-6-6-3-5 0-0-1-1-6-6-3-6 0-0-1-1-6-6-3-7 0-0-1-1-6-6-3-8 0-0-1-1-6-6-3-9 0-0-1-1-6-6-4-3 0-0-1-1-6-6-4-4 0-0-1-1-6-6-4-5 0-0-1-1-6-6-4-6 0-0-1-1-6-6-4-7 0-0-1-1-6-6-4-8 0-0-1-1-6-6-4-9 0-0-1-1-6-6-5-3 ... 7-7-6-6-12-12-9-6 7-7-6-6-12-12-9-7 7-7-6-6-12-12-9-8 7-7-6-6-12-12-9-9
I also need to eliminate duplicate items. In the case of overlapping sets, every resulting row should satisfy the initial condition.

I don't suppose you'd care to describe the application?

AFAIK, there in no combinatorics algorithm that would address those requirements, so it is going to be a post-production step and is left as a exercise.


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