#!/usr/bin/perl
use warnings;
use strict;
sub _summands {
my ($target, @numbers) = @_;
return [[]] if 0 == $target;
my @results;
for my $index (0 .. $#numbers) {
my $number = $numbers[$index];
my @remaining = @numbers[ grep $_ != $index, 0 .. $#numbers ];
next if $target - $number < 0;
my $result = _summands($target - $number, @remaining);
push @results,
map [$number, @$_],
grep ! @$_ || $number <= $_->[0],
@$result;
}
return \@results
}
sub summands {
my $results = _summands(@_);
my %unique;
for my $result (@$results) {
undef $unique{"@$result"};
}
return [ map [split ' '], keys %unique ]
}
use Test::More tests => 2;
use Test::Deep;
cmp_deeply summands(100, 1, 99, 2, 40, 50, 60, 90, 3, 5, 95, 100),
bag([100], [1, 99], [2, 3, 95], [5, 95], [2, 3, 5, 90], [2, 3, 5,
+40, 50], [40, 60]);
cmp_deeply summands(100, 5, 5, 5, 5, 10, 15, 80, 99),
bag([5, 15, 80], [5, 5, 5, 5, 80], [5, 5, 10, 80]);
Update: Sorry, I'm kind of busy, so I don't have much time to explain it. It's a classical example of Dynamic Programming - the only complication is the numbers can be repeated, which I solved using the $unique hash. It's probably possible to build the solutions in a unique way right away in the recursive function, so there won't be any postprocessing needed.
Update 2: For a speed-up, add
use Memoize;
memoize('_summands');
and, as found by
haukex in
Fastest way to "pick without replacement", replace
my $number = $numbers[$index];
my @remaining = @numbers[ grep $_ != $index, 0 .. $#numbers ];
by
my @remaining = @numbers;
my ($number) = splice @remaining, $index, 1;
map{substr$_->[0],$_->[1]||0,1}[\*||{},3],[[]],[ref qr-1,-,-1],[{}],[sub{}^*ARGV,3]
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