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p11.erl
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-module(p11).
-export([answer/0]).
%% What is the greatest product of four adjacent numbers in any direction
%% (up, down, left, right, or diagonally) in the 20×20 grid?
-define(GRID, [
[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]
]).
answer() ->
H = horiz(?GRID),
V = vert(?GRID),
D = dia(?GRID),
lists:max([H,V,D]).
horiz(Grid) ->
lists:max(
lists:map(fun(Row) -> horiz(Row, 0) end, Grid)
).
horiz([A,B,C,D|Row], Prod) ->
P = A*B*C*D,
NewProd = case P > Prod of
true -> P;
_Else -> Prod
end,
horiz([B,C,D|Row], NewProd);
horiz(_, Prod) -> Prod.
vert(Grid) ->
Rotated = rotate_grid(Grid),
horiz(Rotated).
rotate_grid(Grid) ->
rotate_grid(Grid, 1, []).
rotate_grid(Grid, N, Rotated) when N > length(Grid) -> lists:reverse(Rotated);
rotate_grid(Grid, N, Rotated) ->
Row = lists:map(fun(Row) -> lists:nth(N, Row) end, Grid),
rotate_grid(Grid, N+1, [ Row | Rotated ]).
dia(Grid) ->
dia(Grid, 0).
dia([ R1, R2, R3, R4 | Rest], Prod ) ->
L2R = l2r(R1, R2, R3, R4, Prod),
R2L = l2r(R4, R3, R2, R1, L2R),
dia( [ R2, R3, R4 | Rest], R2L );
dia(_Grid, Prod) -> Prod.
l2r([A1 | A ], [_B1, B2 | B], [_C1, C2, C3 | C], [_D1, D2, D3, D4 | D], Prod) ->
P = A1*B2*C3*D4,
NewProd = case P > Prod of
true -> P;
_Else -> Prod
end,
l2r(A, [B2 | B], [C2, C3 | C], [D2, D3, D4 | D], NewProd);
l2r(_A, _B, _C, _D, Prod) -> Prod.