Hi! I modified you loop as follows. I addess a @hist array, which works as a stack. The output seems to be exactly what you want.

my @hist;
sub print_hash {

    my($href) = @_;

    foreach my $key (keys %$href) {
        if (ref($$href{$key}) eq 'HASH') {
            my $href2 = $$href{$key};
            push @hist, $key;
            print_hash($href2);
            pop @hist;
        } else {
           foreach my $h(@hist) {
               print $h."/";
           }
           print "$key => $$href{$key}\n";
        }
    }
}
[download]

Output:

III => 2
I => 1
II/A => 3
II/B/1 => 4
II/B/3 => 6
II/B/2 => 5
[download]

Michele.