### Re: Find combination of numbers whose sum equals X

by choroba (Archbishop)
 on Nov 20, 2020 at 09:47 UTC Need Help??

```#!/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]

Replies are listed 'Best First'.
Re^2: Find combination of numbers whose sum equals X
by harangzsolt33 (Friar) on Nov 20, 2020 at 15:27 UTC
Wow, thank you very much for all your answers! These replies have been very enlightening! :-)

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