Re: Perl Quiz of the Week #23

Guess I'm a little late, but here are two solutions which
I think are more or less canonical:

# this recursive solution uniqifies at every step.
sub parens_recursive
{
  $_[0] == 1 ? ('()') : sort keys %{ { map { ( "()$_" => 1, "($_)" =>
1, "$_()" => 1 ) } parens($_[0]-1) } }
}

# this iterative solution does a Grand Uniqification at the end.
sub parens_iterative
{
  my $n = shift;
  my @a = ('()');
  while ( --$n )
  {
    @a = map { ( "$_()", "($_)", "()$_" ) } @a;
  }
  sort keys %{{ map { $_ => 1 } @a }}
}

What I have a hard time understanding is why anyone would approach
this problem as anything other than a string-building task.
Is a math-based approach, for example, more general?

-- 
John D. Porter



		
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