in reply to How to restrict partitions

#!/usr/bin/perl -w
use strict;
use Algorithm::Loops qw( NestedLoops );
$| = 1;

my @sum= shift || 20;
my $terms = shift || 4;

print "Ways to get a sum of $sum[0] from $terms unique addends:\n";

my $tries= 0;
my $iter= NestedLoops(
    [ ( sub {
            my $n = @_ ? 1+$_[-1] : 1;
            my $t = $terms - @_;
            my $m = $sum[$#_]/$t-($t-1)/2;
            return [ $n .. int $m ];
    } ) x $terms ],
    {
        OnlyWhen => sub {
            $tries++;
                0 == ( $sum[@_]= $sum[$#_] - $_[-1] )
            &&  $terms == @_;
        },
    },
);
my @cnt;
my $seq= 0;
while(  @cnt= $iter->()  ) {
    printf "%d) %s\n", ++$seq, join ' + ', @cnt
}
print "($tries tries)\n";

[download]

- tye        

Replies are listed 'Best First'.
Re^2: How to restrict partitions (NestedLoops)
by crunch_this! (Acolyte) on Jan 27, 2014 at 00:20 UTC

    Instead of printing out the partitions, how could I plug them into (I guess) an array & then use them in a polynomial? What I've been using up to now (thx to hdb months ago) is

    while (my ($x, $y, $z) = @{ $iter->next // [] }) {
        
    push @wants,
    map { { join(', ', $x, $y, $z) => $_ } }
    grep { is_approximately_an_integer( @$_ ) } [
        poly_roots(
            poly_derivative(
                            
            # expanded form of x*(x - $x)*(x - $y)*(x - $z)
            1, -$x - $y - $z, $x*$y + $x*$z + $y*$z, -$x*$y*$z, 0
            )
        )       
    ];
}

    [download]

    The stuff in the while is from the Algorithm::Combinatorics module & the subroutine goes through the zeros of the polynomial's derivative to pick out the ones that have zeros that are all close enough to an integer. I guess it would be to get the elements of @cnt in the prog above but I'm not sure how to do that. Is it as simple as replacing the $x, $y, $z with $cnt[0], $cnt1, $cnt2 in the code above? Or maybe defining my $x = $cnt[0]?

    (a couple minutes later)

    my @cnt;
my $seq= 0;
my $x = $cnt[0];
my $y = $cnt[1];
my $z = $cnt[2];

while(  @cnt = $iter->()  ) {
    #printf "%d) %s\n", ++$seq, join ' + ', @cnt
    map { { join(', ', $x, $y, $z) => $_ } }
    grep { is_approximately_an_integer( @$_ ) } [
        poly_roots(
            poly_derivative(
                            
            # expanded form of x*(x - $x)*(x - $y)*(x - $z)
            1, -$x - $y - $z, $x*$y + $x*$z + $y*$z, -$x*$y*$z, 0
            )
        )       
    ];
}

    [download]

    Actually, now that I've tried that, I get errors in the line with the map & also the following one with the grep saying $x, $y, $z are uninitialized which I don't understand because I set them to be elements of @cnt.

[reply]
[d/l]
[select]
      while(  my( $x, $y, $z ) = $iter->()  ) {

      [download]

      - tye        

[reply]
[d/l]
        I got it working. Thx again! You & hdb are lifesavers :)
[reply]

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