How is what you want to do different than a Bubble Sort where you stop on the first swap? A bubble sort moves the highest element up by one position for each pass (here a digit). What do you want to happen if the highest number is already first in the order?

Update:
Probably a better way to get the index of max value...But is this what you want?
Code should run fairly quickly albeit a bit wordy for Perl.

#!/usr/bin/perl
use strict;
use warnings;


my @array = split '', "117";
print @array, "\n";
print @array,"\n" while rot_max_left(\@array);


@array = split '', "1234";
print "\n",@array,"\n";
print @array,"\n" while rot_max_left(\@array);


sub rot_max_left
{
    my $array_ref = shift;
    
    my $maxi=0;
    return 0 unless ($maxi = get_index_of_max($array_ref));
    
    ($array_ref->[$maxi-1],$array_ref->[$maxi]) = ($array_ref->[$maxi]
+,$array_ref->[$maxi-1]);
    return $maxi;
}

sub get_index_of_max
{
  my $array_ref = shift;
  
  my $maxi = 0;
  foreach (my $i=1;$i<@$array_ref;$i++)
  {
     $maxi = $i if ($array_ref->[$i] > $array_ref->[$maxi])
  }
  return $maxi;
}

__END__
117
171
711

1234
1243
1423
4123
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