blazar has asked for the wisdom of the Perl Monks concerning the following question:

I've recently joined Project Euler. Problem 11 naturally suggested me a functional programming like solution which is probably not the fastest, but who cares? It takes a fraction of second anyway. And it was fast and fun to write.

My code is as follows:

#!/usr/bin/perl -l

use strict;
use warnings;
use List::Util qw/max reduce/;

my @dir=map { my $i=$_; [map $i*$_, 0..3] } 1, 22, 21, 20;
my @data=map { split, 0 } <DATA>;
print max map {
    my $base=$_;
    map {
        my @offs=@$_;
        no warnings qw/uninitialized once/;
        reduce { $a * $b } map $data[$base+$_], @offs;
    } @dir;
} 0..$#data;

__END__
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

[download]

Now it seems probable that this may look much better in Perl6, and I know how some aspects of it may look like, but I can't fill in all the blanks so to say. Probably something like the following:

my @dir=map -> $i { [map $i*$_, 0..3] } 1, 22, 21, 20;
my @data=map { split, 0 } =<DATA>;
say reduce -> $a, $b { $a>$b ?? $a !! $b } map -> $base {
    map -> $offs {
        [*] map $data[$base+$_], @$offs;
    } @dir;
} 0..@data.something;

[download]

(Note that I'm not particularly interested in the DATA section -I don't even know if the syntax has been fixed yet-, as much as in these three statements.)

Update: since a private /msg warned me that the problem is not visible (it should, but maybe not from the link I gave) if you're not subscribed, for completeness here it is:

In the 20x20 grid below, four numbers along a diagonal line have been marked in red.

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

[download]

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

What is the greatest product of four numbers in any direction (up, down, left, right, or diagonally) in the 20x20 grid?

Note: I didn't reproduce the red mark here. I hope it's easy to understand the problem nonetheless.

Update: oops, I had pasted the wrong problem. Corrected now...

Replies are listed 'Best First'.
Re: How to write this in Perl 6?
by TimToady (Parson) on Dec 02, 2006 at 17:47 UTC
    Here's a version that works under pugs: 
    #!/usr/bin/pugs

my @DATA = q:to/END/.split(/\n/);
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
END

my @dir = map -> $i { [map {$i*$_}, 0..3] }, 1, 22, 21, 20;
my @data = map { .comb, 0 }, @DATA;
say max map -> $base {
    map -> $offs {
        [*] map { @data[ $base + $_ ] }, @$offs;
    }, @dir;
}, 0..@data.end;

    [download]
    I would generally prefer to write max as [max], but that's not implemented yet. Also it prints the result in E notation, albeit with sufficient precision. I think there are probably ways to use hyperops to replace some of the maps, but I need to think about it some more. There are also some unimplemented cross operators that might replace nested maps.
[reply]
[d/l]
      Here's a version that works under pugs:

      (Needless to say,) whoa! That's great. Generally I avoid replying for TY-only posts and prefer to /msg instead. But I feel like doing so publicly for this time since it's so nice to actually test the thing myself. I tried a first time and pugs seemed not to like the method call on the HERE doc string. In fact I had 6.2.12 installed; I upgraded to 6.2.13 and it still complains about something:

      *** Cannot parse regex: \n
*** Error: Error: Can't call method "__RUN__" on an undefined value.

      [download]

      But it does spit out a value.

      I would generally prefer to write max as [max], but that's not implemented yet. Also it prints the result in E notation, albeit with sufficient precision.

      Indeed, especially since the original problem expected an exact answer in terms of an integer. (The value spitted out doesn't seem to match the Perl 5 version one, but that's definitely a side note in this context. I don't know whether that could be related to the messages above.)

      I think there are probably ways to use hyperops to replace some of the maps, but I need to think about it some more. There are also some unimplemented cross operators that might replace nested maps.

      That's great as well. The maps look very natural to me, but I'd be delighted to see what hyperops could do instead of them. And I'm particularly excited about the potential cross operators which I also find quite natural, in fact it's one of the first things I asked in p6l: I can do without them, but I miss them more than, say, the somewhat "dual" zip operator. Of course the advantage becomes more evident with more nesting levels than just two...

[reply]
[d/l]
[select]
        Okay, if we install a workaround version of XX that only does two arrays (compliments of Gothmog++): 
        multi infix:<XX> (@a, @b) is equiv(&infix:<¥>) {
    @a.map: -> $a {
        @b.map: -> $b {
            ($a, $b)
        }
    }
}

        [download]
        then the following seems to work in the devel version of pugs: 
        my @dir = map -> $i { [map {$i*$_}, 0..3] }, 1, 22, 21, 20;
my @data = map { .comb, 0 }, @DATA;
say max gather {
    for ^@data XX @dir {
        take int [*] @data[ $^base »+« $^offs ];
    }
}

        [download]
        The first two lines are unchanged. I used gather/take to let me use a for loop and get the inputs in front. The int suppresses the floating notation. The two parameters are passed using placeholder variables, which work as long as they're not nested inside internal braces. (They rely on "base" coming before "offs" in alphabetical order.) And I just used a slice to pull out the four values instead of another map. (Note also that the hyperoperator is still behaving under the old specs of dwimming both sides, but that actually won't work under the latest specs, which requires the quote to be reversed to get dwimmery on that side.) Oh, I also used the unary ^ to get a range from 0 up to the size of the array, which also helped because the XX doesn't quite parse with the correct precedence yet for some reason, so saying 0..^@data would have required extra parens in the current pugs.
[reply]
[d/l]
[select]

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