Solution for Quiz of the Week #23 : parenths

hello qotw discussers,

so I created all the possible combinations,
then had some fun with "eval" to see what was valid.

is "( ) ) ( ( )" ok? find out by $@ after:
eval "\$a = ( 1 ) * 1 ) * 1 * ( 1 * ( 1 );";

thanks for the puzzle,
tom

>> start of code >>

# parens.pl
#

use strict;
use warnings;

unless( $ARGV[0] )
{
    $ARGV[0] = 5;
}

my $size = $ARGV[0] * 2;
my $start_line = '(' x ($size/2) . ')' x ($size/2);

my %patterns;

#####
# mix things up and store.
# 
# mix them up by exchanging two letters
# there must be a better way.

for my $left_pos ( 1..$size - 2 )
{
    for my $right_pos ( 1..$size - 2 )
    {
        my $swapped = $start_line;
        $swapped = swap_two_letters( $swapped, $left_pos, $right_pos );

        $patterns{ $swapped } = 1;

        for my $left_pos_b ( 1..$size - 2 )
        {
            $swapped = swap_two_letters( $swapped, $left_pos_b, $right_pos
);
            $patterns{ $swapped } = 1;

            for my $right_pos_b ( 1..$size - 2 )
            {
                $swapped = swap_two_letters( $swapped, $left_pos_b,
$right_pos_b );
                $patterns{ $swapped } = 1;
            }
        }
    }
}

# print "\n\n****************\n\n";

my $total_count = 0;
my $pass_count = 0;

my %solution = find_valid_code( \%patterns );


##### show the results
###

my $need_count = 1;
my $size_in = $size / 2;
for( 1 .. $size/2 )
{
    $need_count *= $_;
}
$need_count -= 1;

$need_count = "????";

# print "\n\n******* all possible ******** \n\n";

for my $out ( sort( %patterns ) )
{
    last if( $out eq '1' );

#    print "$out\n";
}

print "\n\n******* solution ******** \n\n";

for my $out ( sort( %solution ) )
{
    last if( $out eq '1' );

    print "$out\n";
}

print "total possible patterns: $total_count\n";
print "total that ran as code : $pass_count\n";
print "total sought  ( for $size_in ): $need_count\n";




exit( 0 );

##########################################################

sub swap_two_letters
{
    my $string = shift;
    my $pos_A = shift;
    my $pos_B = shift;

    my $letter_left = substr( $string, $pos_A, 1 );
    my $letter_right = substr( $string, $pos_B, 1 );

    substr( $string, $pos_A, 1 ) = $letter_right;
    substr( $string, $pos_B, 1 ) = $letter_left;

    return $string;
}

# find_valid_code
#
# some are not valid.
# try to run them as code to filter out bad ones.
# use eval to see what works.
#
# prepare code by inserting 1 and * characters
#
# ((())) becomes $a = ( 1 * ( 1 * ( 1 ) * 1 ) * 1 ); and passes
# ()()() becomes $a = ( 1 ) * 1 * ( 1 ) * 1 * ( 1 ); and passes 
# ())(() becomes $a = ( 1 ) * 1 ) * 1 * ( 1 * ( 1 ); and fails

sub find_valid_code
{
    my $pattern_hash_ref = shift;
    my %solution;

    for my $out ( sort( %$pattern_hash_ref ) )
    {
        last if( $out eq '1' );

        $total_count ++;

        my $code = '$a = (';

        for my $pos( 1..length( $out )-1 )
        {
            my $last = substr( $out, $pos-1, 1 );
            my $next = substr( $out, $pos, 1 );
            my $add  = "1";

            if( $last eq ')' )  #  ) 1  ->  ) * 1
            {
                $add = '*' . $add;
            }

            if( $next eq '(' )  #  1 (  ->  1 * (
            {
                $add .= '*';
            }
                                #  ( )  ->  ( 1 )
            $add = '1' if( $last eq '(' and $next eq ')' );

            $code .= $add . substr( $out, $pos, 1 );
        }

        $code .= ';';

        my $a;
        eval( "$code" );
        if( $@ )
        {
#            print "gave an error: $code\n";
        }
        else
        {
#            print "code ran ok  : $code\n";
            $solution{ $out } = 1;
            $pass_count++;
        }
    }

    return %solution
}



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