You need to modify the regex a little bit, like:

...
my @strings = qw'
/usr/bin/perl
/usr/bin/ 
/perl 
/ 
perl
';

for my $string (@strings) {
   if( $string =~ m{^(.*/)(.*)$} ) {     
      print "Path = $1, Filename = $2\n"; 
   } 
   elsif( $string =~ m{^([^/]+)$} ) {     
      print "No path, Filename = $1\n"; 
   }
}
...
[download]

(One variant of many, close to your original program.)

Regards

mwa