find all unique-path 4x4 mazes

01-mazes.p6

# bitstring; positions 0..11 correspond to vertical walls; 12..23 to horizontal
my $s = "0" x 15 ~ "1" x 9;

#   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];

repeat until $s eq "1" x 9 ~ "0" x 15 {
    # this is a quick way to find the next bitstring with the same amount of 1s
    # trick learned long ago from http://blog.plover.com/CS/parentheses.html
    $s ~~ s[ .* <( 01 (.*) ] = "10" ~ $0.comb.sort.join;
    # the final 1 represents the outer wall
    my @w = +«$s.comb, 1;

    # each iteration of this loop melts away walls at the "fringes", attached
    # to at most one thing. the loop stops when it can't melt anything more.
    repeat while my $changed {
        $changed = False;
        for ^24 -> $n {
            next unless @w[$n];
            if [+](@w[ @n[$n].list ]) < 2 {
                @w[$n] = 0;
                $changed++;
            }
        }
    }

    # the maze has all single paths if we succeeded in melting away everything
    # except the outer wall
    next unless [+](@w) == 1;
    say $s;
}

# real	154m50.969s
# user	153m40.178s
# sys	0m22.463s

02-symmetry.p6

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

my %symmetries =
    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>,
    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>,
    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>,
    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>,
    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>,
    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>,
    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>,
;

MAZE:
for lines() -> $line {
    my @w = $line.comb;
    next MAZE if $line gt @w[%symmetries{$_}.list].join
        for %symmetries.keys;
    say $line;
}

# real	3m38.140s
# user	3m35.802s
# sys	0m0.652s

03-draw-em.p6

constant COLUMNS = 8;

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;
    }
}

print_mazes;

# real	0m13.790s
# user	0m13.510s
# sys	0m0.113s

04-mazes

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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