It's obviously not the best algorithm, and I rushed the implementation. 

use strict;
use warnings;

use Algorithm::Loops qw( NextPermuteNum );
use List::Util       qw( sum );

my @nums = @ARGV;

my $sum  = sum @nums;
my @best = @nums;
my $best;
@nums = sort { $a <=> $b } @nums;
do {
   my $p = $sum;
   my $q = 0;
   for my $i (0..$#nums) {
      my $x = $nums[$i];
      $p -= $x;
      $q += $x;
      my $diff = abs($p-$q);
      if (!defined($best) || $best > $diff) {
         $best = $diff;
         @best = (
            [ @nums[ 0    .. $i     ] ],
            [ @nums[ $i+1 .. $#nums ] ],
         );
      }
   }
} while ( NextPermuteNum(@nums) );

my @p = @{ $best[0] };  print(sum(@p), ": ", join('+', @p), "\n");
my @q = @{ $best[1] };  print(sum(@q), ": ", join('+', @q), "\n");

[download]
>perl script.pl 8 14 32 29
40: 8+32
43: 14+29

>perl script.pl 7 10 12 15 40
44: 7+10+12+15
40: 40

[download]

I'm not clear on the complexity of NextPermuteNum — I have a cold that is making me very tired — so maybe my analysis is wrong.

In reply to Re^6: Divide array of integers into most similar value halves by ikegami
in thread Divide array of integers into most similar value halves by Pepe

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