This was actually an interview question I had for my first job, only I had to do it in C. Here is a solution without a sort.

sub getSecondLargest
{
  my (@list) = @_;

  my ($largest, $secondlargest);

  for(my $i = 0;$i<=$#list;$i++)
  {
    if($i == 0)
    {
      if($list[0] >= $list[1])
      {
        ($largest, $secondlargest) = ($list[0], $list[1]);
      }
      else
      {
        ($largest, $secondlargest) = ($list[1], $list[0]);
      }
    }
    if($i >=3)
    {
      if($list[$i] >= $largest)
      {
        $secondlargest = $largest;
        $largest = $list[$i];
      }
      elsif($list[$i] >= $secondlargest)
      {
        $secondlargest = $list[$i];
      }  
    }
  }
  return $secondlargest;
}
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