module Problem11 where

import           Data.List (transpose)

--
-- Problem 11: Largest product in a grid
--
-- In the 20×20 grid below, four numbers along a diagonal line have been marked
-- in red. 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?

problem11 = maximum $ map product allPerms  where

  len = 4
  allPerms = concat
    [ concatMap (perms len) horz
    , concatMap (perms len) vert
    , concatMap (perms len) diagLeft
    , concatMap (perms len) diagRight
    ]

  perms len xs@(y:ys) = let perm = take len xs in
    if length perm < len then []
    else perm : perms len ys

  horz = grid
  vert = transpose grid
  height = length horz
  width = length vert

  diag grid = grid' where
    cell x y = (grid !! y) !! x
    grid' =
      [[ cell (col + y) y | y <- [0..(height-col-1)]]
      | col <- [0..(width-1)]
      ] ++
      [[ cell x (row + x) | x <- [0..(width-row-1)]]
      | row <- [1..(height-1)]
      ]

  diagLeft = diag horz
  diagRight = diag (map reverse horz)

  grid :: [[Int]]
  grid = map (map read . words)
    [ "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"
    ]
