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Re: Find combination of numbers whose sum equals X

by choroba (Archbishop)
on Nov 20, 2020 at 09:47 UTC ( #11123877=note: print w/replies, xml ) Need Help??


in reply to Find combination of numbers whose sum equals X

#!/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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