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Re: How to generate restricted partitions of an integer

by tye (Sage)
on Nov 12, 2004 at 09:11 UTC ( #407313=note: print w/replies, xml ) Need Help??


in reply to How to generate restricted partitions of an integer

This one takes the desired total and/or the list of denominations on the command line and shows all possible combinations:

#!/usr/bin/perl -w use strict; use Algorithm::Loops qw( NestedLoops MapCarMin ); my @sum= shift || 100; my @size= ( 100, 50, 20, 10, 5 ); @size= @ARGV if @ARGV; my $tries= 0; my $iter= NestedLoops( [ ( sub { my $n= $sum[@_]/$size[@_]; ! $n ? [] : @_ < $#size ? [ 0 .. $n ] : [ $n .. int $n ]; } ) x @size ], { OnlyWhen => sub { $tries++; not $sum[@_]= $sum[$#_] - $_[-1]*$size[$#_]; }, }, ); my @cnt; my $seq= 0; while( @cnt= $iter->() ) { printf "%d) %s\n", ++$seq, join ' + ', MapCarMin { !$_[0] ? () : join '*', @_ } \@cnt, \@size; } print "($tries tries)\n";

And here's a sample run:

> perl change.pl 103 100 33 10 3 | more 1) 1*10 + 31*3 2) 4*10 + 21*3 3) 7*10 + 11*3 4) 10*10 + 1*3 5) 1*33 + 1*10 + 20*3 6) 1*33 + 4*10 + 10*3 7) 1*33 + 7*10 8) 2*33 + 1*10 + 9*3 9) 1*100 + 1*3 (56 tries) >

- tye        

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