Largest product in a grid

AUTHOR

Moritz Lenz

In the 20×20 grid below, four numbers along a diagonal line have been marked in bold.

    08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
    49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
    81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
    52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
    22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
    24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
    32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
    67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
    24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
    21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
    78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
    16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
    86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
    19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
    04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
    88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
    04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
    20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
    20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
    01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48

The product of these numbers is 26 × 63 × 78 × 14 = 1788696.

What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 20×20 grid?

use v6;



my @m =
    [<08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08>],
    [<49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00>],
    [<81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65>],
    [<52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91>],
    [<22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80>],
    [<24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50>],
    [<32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70>],
    [<67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21>],
    [<24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72>],
    [<21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95>],
    [<78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92>],
    [<16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57>],
    [<86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58>],
    [<19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40>],
    [<04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66>],
    [<88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69>],
    [<04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36>],
    [<20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16>],
    [<20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54>],
    [<01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48>];

sub prod ($x is copy, $y is copy, $dx, $dy) {
    my $prod =  @m[$y][$x];
    for 1..3 {
        $x += $dx;
        $y += $dy;
        $prod *= @m[$y][$x];
    }
    return $prod;
}

my $max = 0;

# diagonals
for 0 .. 16 -> $x {
    for 0 .. 16 -> $y {
        $max = $max max prod($x, $y,     1, 1)
                    max prod($x, $y + 3, 1, -1);
    }
}

# horizontal
for 0..16 -> $x {
    for 0..19 -> $y {
        $max = $max max prod($x, $y, 1, 0);
    }
}

# vertical
for 0..19 -> $x {
    for 0..10 -> $y {
        $max = $max max prod($x, $y, 0, 1);
    }
}

say $max;

# vim: expandtab shiftwidth=4 ft=perl6

AUTHOR

See Also