-- In the 20×20 grid below, four numbers along a diagonal line have
-- been marked with asterisks.

-- 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?

module Euler.Problem011
       ( solution
       , vectors
       , submatrices
       ) where

import Numeric.LinearAlgebra.Data (Matrix, Vector, subMatrix, toRows, toColumns, takeDiag, fliprl, toList)

solution :: Int -> Matrix Double -> Integer
solution size = truncate . maximum . map (product . toList) . concatMap vectors . submatrices size

vectors :: Matrix Double -> [Vector Double]
vectors m = toRows m ++ toColumns m ++ [takeDiag m, takeDiag $ fliprl m]

submatrices :: Int -> Matrix Double -> [Matrix Double]
submatrices size matrix = do
  r <- [0..(20 - size)]
  c <- [0..(20 - size)]
  return $ subMatrix (r, c) (size, size) matrix
