A better solution to the maze finding problem

01-mazes.p6

# bitstring; positions 0..11 correspond to vertical walls; 12..23 to horizontal;
# 24 to the outer wall
# RAKUDO: can't do `0 x 24 ~ 1` here: RT #123602
my @old = "0000000000000000000000001";

#   00  01  02
# 12  13  14  15
#   03  04  05
# 16  17  18  19
#   06  07  08
# 20  21  22  23
#   09  10  11

# neighboring relation; for example, wall 0 neighbors 3, 12, 13, and
# the outer wall
my @n =
    [3, 12, 13, 24], [4, 13, 14, 24], [5, 14, 15, 24],
    [0, 6, 12, 13, 16, 17], [1, 7, 13, 14, 17, 18], [2, 8, 14, 15, 18, 19],
    [3, 9, 16, 17, 20, 21], [4, 10, 17, 18, 21, 22], [5, 11, 18, 19, 22, 23],
    [6, 20, 21, 24], [7, 21, 22, 24], [8, 22, 23, 24],
    [0, 3, 13, 24], [0, 1, 3, 4, 12, 14], [1, 2, 4, 5, 13, 15], [2, 5, 14, 24],
    [3, 6, 17, 24], [3, 4, 6, 7, 16, 18], [4, 5, 7, 8, 17, 19], [5, 8, 18, 24],
    [6, 9, 21, 24], [6, 7, 9, 10, 20, 22], [7, 8, 10, 11, 21, 23], [8, 11, 22, 24];

sub p($s, $n) { $s.substr($n, 1) }
sub n($s, $n) { [+] (p($s, $_) for @n[$n].list) }
sub ch($s, $n) { $s.substr(0, $n) ~ "1" ~ $s.substr($n + 1) }

my %symmetries =
    id   => 0..24,
    rot1 => <15 19 23 14 18 22 13 17 21 12 16 20 2 5 8 11 1 4 7 10 0 3 6 9 24>,
    rot2 => <11 10 9 8 7 6 5 4 3 2 1 0 23 22 21 20 19 18 17 16 15 14 13 12 24>,
    rot3 => <20 16 12 21 17 13 22 18 14 23 19 15 9 6 3 0 10 7 4 1 11 8 5 2 24>,
    flip => <9 10 11 6 7 8 3 4 5 0 1 2 20 21 22 23 16 17 18 19 12 13 14 15 24>,
    frt1 => <12 16 20 13 17 21 14 18 22 15 19 23 0 3 6 9 1 4 7 10 2 5 8 11 24>,
    frt2 => <2 1 0 5 4 3 8 7 6 11 10 9 15 14 13 12 19 18 17 16 23 22 21 20 24>,
    frt3 => <23 19 15 22 18 14 21 17 13 20 16 12 11 8 5 2 10 7 4 1 9 6 3 0 24>,
;

for 1..9 {
    my %new;
    for @old -> $s {
        for ^24 -> $n { # this doesn't include the outer wall
            next if p($s, $n);

            if n($s, $n) == 1 {
                my @w = ch($s, $n).comb;
                my $min = [min] (@w[%symmetries{$_}.list].join for %symmetries.keys);
                %new{$min}++;
            }
        }
    }

    @old = %new.keys;
    note +@old;
}

say .substr(0, 24) for @old.sort;

02-draw-em.p6

constant COLUMNS = 5;

my @mazes;
sub print_mazes {
    return unless @mazes;

    for ^9 -> $n {
        sub line($maze) { $maze.lines[$n] }
        say (line($_) for @mazes).join("  ");
    }
    say "";
    @mazes = ();
}

for lines() -> $line {
    my $maze = q:to/EOF/;
        +--+--+--+--+
        |  :  :  :  |
        +..+..+..+..+
        |  :  :  :  |
        +..+..+..+..+
        |  :  :  :  |
        +..+..+..+..+
        |  :  :  :  |
        +--+--+--+--+
        EOF

    my $pos = 0;
    $maze .= subst(':', { $line.substr($pos++, 1) ?? '|' !! ' ' }, :g);
    $maze .= subst('..', { $line.substr($pos++, 1) ?? '--' !! '  ' }, :g);

    @mazes.push: $maze;
    if @mazes >= COLUMNS {
        print_mazes;
    }
}

if @mazes {
    print_mazes;
}

03-all-the-mazes

+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+
|           |  |           |  |           |  |           |  |           |
+  +--+--+--+  +  +--+--+--+  +  +--+--+--+  +  +--+--+--+  +  +--+--+--+
|           |  |           |  |           |  |           |  |           |
+  +--+--+--+  +  +--+--+--+  +  +--+--+--+  +  +--+--+--+  +--+  +--+--+
|           |  |           |  |           |  |           |  |           |
+  +--+--+--+  +--+  +--+--+  +--+--+  +--+  +--+--+--+  +  +  +--+--+--+
|           |  |           |  |           |  |           |  |           |
+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+

+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+
|           |  |           |  |           |  |           |  |           |
+  +--+--+--+  +  +--+--+--+  +  +--+--+--+  +  +--+--+--+  +  +--+--+--+
|           |  |           |  |           |  |           |  |           |
+--+  +--+--+  +--+  +--+--+  +--+  +--+--+  +--+--+  +--+  +--+--+  +--+
|           |  |           |  |           |  |           |  |           |
+--+  +--+--+  +--+--+  +--+  +--+--+--+  +  +  +--+--+--+  +--+  +--+--+
|           |  |           |  |           |  |           |  |           |
+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+

+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+
|           |  |           |  |           |  |           |  |           |
+  +--+--+--+  +  +--+--+--+  +  +--+--+--+  +  +--+--+--+  +--+  +--+--+
|           |  |           |  |           |  |           |  |           |
+--+--+  +--+  +--+--+--+  +  +--+--+--+  +  +--+--+--+  +  +  +--+--+--+
|           |  |           |  |           |  |           |  |           |
+--+--+  +--+  +  +--+--+--+  +--+  +--+--+  +--+--+  +--+  +--+  +--+--+
|           |  |           |  |           |  |           |  |           |
+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+

+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+
|           |  |           |  |           |  |           |  |           |
+--+  +--+--+  +--+  +--+--+  +--+  +--+--+  +--+  +--+--+  +--+  +--+--+
|           |  |           |  |           |  |           |  |           |
+  +--+--+--+  +--+  +--+--+  +--+  +--+--+  +--+--+  +--+  +--+--+--+  +
|           |  |           |  |           |  |           |  |           |
+--+--+  +--+  +--+  +--+--+  +--+--+  +--+  +--+  +--+--+  +--+  +--+--+
|           |  |           |  |           |  |           |  |           |
+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+

+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+
|           |  |           |  |           |  |           |  |           |
+  +--+--+--+  +  +--+--+--+  +  +--+--+--+  +  +--+--+--+  +  +--+--+--+
|           |  |           |  |           |  |           |  |           |
+  +--+--+--+  +  +--+--+--+  +  +--+--+--+  +--+  +--+--+  +--+  +--+--+
|           |  |           |  |           |  |           |  |           |
+  +--+--+  +  +--+  +--+  +  +--+--+  +  +  +  +--+--+  +  +--+  +--+  +
|        |  |  |        |  |  |        |  |  |        |  |  |        |  |
+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+

+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+
|           |  |           |  |           |  |           |  |           |
+  +--+--+--+  +  +--+--+--+  +  +--+--+--+  +  +--+--+--+  +  +--+--+--+
|           |  |           |  |           |  |           |  |           |
+--+  +--+--+  +--+--+  +--+  +--+--+  +--+  +--+--+  +--+  +--+--+--+  +
|           |  |           |  |           |  |           |  |           |
+--+--+  +  +  +  +--+--+  +  +--+  +--+  +  +--+--+  +  +  +  +--+--+  +
|        |  |  |        |  |  |        |  |  |        |  |  |        |  |
+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+

+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+
|           |  |           |  |           |  |           |  |           |
+  +--+--+--+  +  +--+--+--+  +--+  +--+--+  +--+  +--+--+  +--+  +--+--+
|           |  |           |  |           |  |           |  |           |
+--+--+--+  +  +--+--+--+  +  +  +--+--+--+  +  +--+--+--+  +  +--+--+--+
|           |  |           |  |           |  |           |  |           |
+--+  +--+  +  +--+--+  +  +  +  +--+--+  +  +--+  +--+  +  +--+--+  +  +
|        |  |  |        |  |  |        |  |  |        |  |  |        |  |
+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+

+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+
|           |  |           |  |           |  |           |  |           |
+--+  +--+--+  +--+  +--+--+  +--+  +--+--+  +--+  +--+--+  +--+  +--+--+
|           |  |           |  |           |  |           |  |           |
+--+  +--+--+  +--+  +--+--+  +--+  +--+--+  +--+--+  +--+  +--+--+  +--+
|           |  |           |  |           |  |           |  |           |
+  +--+--+  +  +--+  +--+  +  +--+--+  +  +  +  +--+--+  +  +--+  +--+  +
|        |  |  |        |  |  |        |  |  |        |  |  |        |  |
+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+

+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+
|           |  |           |  |           |  |           |  |           |
+--+  +--+--+  +--+  +--+--+  +--+  +--+--+  +--+  +--+--+  +--+--+  +--+
|           |  |           |  |           |  |           |  |           |
+--+--+  +--+  +--+--+--+  +  +--+--+--+  +  +--+--+--+  +  +  +--+--+--+
|           |  |           |  |           |  |           |  |           |
+--+--+  +  +  +  +--+--+  +  +--+  +--+  +  +--+--+  +  +  +  +--+--+  +
|        |  |  |        |  |  |        |  |  |        |  |  |        |  |
+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+

+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+
|           |  |           |  |           |  |           |  |           |
+--+--+  +--+  +--+--+  +--+  +--+--+  +--+  +--+--+  +--+  +--+--+  +--+
|           |  |           |  |           |  |           |  |           |
+  +--+--+--+  +  +--+--+--+  +--+  +--+--+  +--+  +--+--+  +--+  +--+--+
|           |  |           |  |           |  |           |  |           |
+--+  +--+  +  +--+--+  +  +  +  +--+--+  +  +--+  +--+  +  +--+--+  +  +
|        |  |  |        |  |  |        |  |  |        |  |  |        |  |
+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+

+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+
|           |  |           |  |           |  |           |  |           |
+--+--+  +--+  +--+--+  +--+  +--+--+  +--+  +--+--+  +--+  +--+--+  +--+
|           |  |           |  |           |  |           |  |           |
+--+--+  +--+  +--+--+  +--+  +--+--+  +--+  +--+--+--+  +  +--+--+--+  +
|           |  |           |  |           |  |           |  |           |
+  +--+--+  +  +--+  +--+  +  +--+--+  +  +  +  +--+--+  +  +--+  +--+  +
|        |  |  |        |  |  |        |  |  |        |  |  |        |  |
+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+

+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+
|           |  |           |  |           |  |           |  |           |
+--+--+  +--+  +--+--+--+  +  +--+--+--+  +  +--+--+--+  +  +--+--+--+  +
|           |  |           |  |           |  |           |  |           |
+--+--+--+  +  +  +--+--+--+  +  +--+--+--+  +  +--+--+--+  +--+  +--+--+
|           |  |           |  |           |  |           |  |           |
+--+--+  +  +  +  +--+--+  +  +--+  +--+  +  +--+--+  +  +  +  +--+--+  +
|        |  |  |        |  |  |        |  |  |        |  |  |        |  |
+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+

+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+
|           |  |           |  |           |  |           |  |           |
+--+--+--+  +  +--+--+--+  +  +--+--+--+  +  +--+--+--+  +  +--+--+--+  +
|           |  |           |  |           |  |           |  |           |
+--+  +--+--+  +--+  +--+--+  +--+--+  +--+  +--+--+  +--+  +--+--+  +--+
|           |  |           |  |           |  |           |  |           |
+--+  +--+  +  +--+--+  +  +  +  +--+--+  +  +--+  +--+  +  +--+--+  +  +
|        |  |  |        |  |  |        |  |  |        |  |  |        |  |
+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+

+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+
|           |  |           |  |           |  |           |  |           |
+--+--+--+  +  +--+--+--+  +  +--+--+--+  +  +  +--+--+--+  +  +--+--+--+
|           |  |           |  |           |  |           |  |           |
+--+--+--+  +  +--+--+--+  +  +--+--+--+  +  +  +--+--+--+  +  +--+--+--+
|           |  |           |  |           |  |           |  |           |
+  +--+--+  +  +--+  +--+  +  +--+--+  +  +  +  +--+  +--+  +--+  +  +--+
|        |  |  |        |  |  |        |  |  |     |     |  |     |     |
+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+

+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+
|           |  |           |  |           |  |           |  |           |
+  +--+--+--+  +  +--+--+--+  +  +--+--+--+  +  +--+--+--+  +  +--+--+--+
|           |  |           |  |           |  |           |  |           |
+  +--+--+--+  +--+  +--+--+  +--+  +--+--+  +--+  +--+--+  +--+--+  +--+
|           |  |           |  |           |  |           |  |           |
+--+  +--+  +  +  +--+  +--+  +--+  +  +--+  +--+  +--+  +  +  +--+  +--+
|     |     |  |     |     |  |     |     |  |     |     |  |     |     |
+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+

+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+
|           |  |           |  |           |  |           |  |           |
+  +--+--+--+  +  +--+--+--+  +  +--+--+--+  +  +--+--+--+  +  +--+--+--+
|           |  |           |  |           |  |           |  |           |
+--+--+  +--+  +--+--+  +--+  +--+--+--+  +  +--+--+--+  +  +--+--+--+  +
|           |  |           |  |           |  |           |  |           |
+--+  +  +--+  +--+  +--+  +  +  +--+  +--+  +--+  +  +--+  +--+  +--+  +
|     |     |  |     |     |  |     |     |  |     |     |  |     |     |
+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+

+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+
|           |  |           |  |           |  |           |  |           |
+--+  +--+--+  +--+  +--+--+  +--+  +--+--+  +--+  +--+--+  +--+  +--+--+
|           |  |           |  |           |  |           |  |           |
+  +--+--+--+  +  +--+--+--+  +  +--+--+--+  +--+  +--+--+  +--+  +--+--+
|           |  |           |  |           |  |           |  |           |
+  +--+  +--+  +--+  +  +--+  +--+  +--+  +  +  +--+  +--+  +--+  +  +--+
|     |     |  |     |     |  |     |     |  |     |     |  |     |     |
+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+

+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+
|           |  |           |  |           |  |           |  |           |
+--+  +--+--+  +--+  +--+--+  +--+  +--+--+  +--+  +--+--+  +--+  +--+--+
|           |  |           |  |           |  |           |  |           |
+--+  +--+--+  +--+--+  +--+  +--+--+  +--+  +--+--+  +--+  +--+--+--+  +
|           |  |           |  |           |  |           |  |           |
+--+  +--+  +  +  +--+  +--+  +--+  +  +--+  +--+  +--+  +  +  +--+  +--+
|     |     |  |     |     |  |     |     |  |     |     |  |     |     |
+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+

+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+
|           |  |           |  |           |  |           |  |           |
+--+  +--+--+  +--+  +--+--+  +  +--+--+--+  +  +--+--+--+  +  +--+--+--+
|           |  |           |  |           |  |           |  |           |
+--+--+--+  +  +--+--+--+  +  +  +--+--+--+  +  +--+--+--+  +--+  +--+--+
|           |  |           |  |           |  |           |  |           |
+--+  +  +--+  +--+  +--+  +  +  +--+  +  +  +--+  +  +  +  +  +--+  +  +
|     |     |  |     |     |  |     |  |  |  |     |  |  |  |     |  |  |
+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+

+--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+  +--+--+--+--+
|           |  |           |  |           |  |           |  |           |
+  +--+--+--+  +  +--+--+--+  +  +--+--+--+  +  +--+--+--+  +  +--+--+--+
|           |  |           |  |           |  |           |  |           |
+--+  +--+--+  +--+--+  +--+  +--+--+  +--+  +--+--+--+  +  +--+--+--+  +
|           |  |           |  |           |  |           |  |           |
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