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use strict;
use warnings;
...
  print join',',sort num @{$groups{$gid}{list}};
  print "]\n";
}

840 [103,118,130,143,158,188]
840 [88,261,154,123,116,98]
...
862 [198,150,126,132,135,121]
863 [105,121,132,145,162,198]
863 [183,109,172,148,122,129]

  ($minsum,$maxsum) = ($max,$min);
  foreach my $gid (keys %groups){
...
      $largest_gid = $gid;
    }
  }