as I see every third level element in the hash being printed, not just the third level elements associated with the current second level.

That's not possible from the code you printed. It would suggest that %categories doesn't contain what you think it does.

Note that there can be different levels of hierarchy

Sounds like you need a recursive solution. 

sub print_tree {
   my ($tree, $depth) = @_;
   $depth ||= 0;
   my $indent = '...' x $depth;
   for (sort keys %$tree) {
      print($indent, /^\s*\z/ ? "<blank>" : $_, "\n");
      print_tree($tree->{$_}, $depth+1);
   }      
}

print_tree(\%categories);

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In reply to Re: Printing a tree-view of a hash of hashes by ikegami
in thread Printing a tree-view of a hash of hashes by pdxperl

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