Eleven.hs

import Control.Exception.Base (assert)
import Data.Array (listArray, (!), indices)


board = listArray ((0, 0), (19, 19)) [
  8, 2, 22, 97, 38, 15, 0, 40, 0, 75, 4, 5, 7, 78, 52, 12, 50, 77, 91, 8,
  49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 4, 56, 62, 0,
  81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 3, 49, 13, 36, 65,
  52, 70, 95, 23, 4, 60, 11, 42, 69, 24, 68, 56, 1, 32, 56, 71, 37, 2, 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, 3, 45, 2, 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, 2, 62, 12, 20, 95, 63, 94, 39, 63, 8, 40, 91, 66, 49, 94, 21,
  24, 55, 58, 5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72,
  21, 36, 23, 9, 75, 0, 76, 44, 20, 45, 35, 14, 0, 61, 33, 97, 34, 31, 33, 95,
  78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 3, 80, 4, 62, 16, 14, 9, 53, 56, 92,
  16, 39, 5, 42, 96, 35, 31, 47, 55, 58, 88, 24, 0, 17, 54, 24, 36, 29, 85, 57,
  86, 56, 0, 48, 35, 71, 89, 7, 5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58,
  19, 80, 81, 68, 5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 4, 89, 55, 40,
  4, 52, 8, 83, 97, 35, 99, 16, 7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66,
  88, 36, 68, 87, 57, 62, 20, 72, 3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69,
  4, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 8, 46, 29, 32, 40, 62, 76, 36,
  20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 4, 36, 16,
  20, 73, 35, 29, 78, 31, 90, 1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 5, 54,
  1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 1, 89, 19, 67, 48]

boardSize = 20

type Point = (Int, Int)
type Line = [Point]

allIndices :: [Point]
{-All valid (y, x) indices which appear on the board.-}
allIndices = indices board

acrossIndices :: [Line]
{-Indices for all four-cell rows in the board-}
acrossIndices = buildIndices getIndices isValid
  where
    getIndices (y, x) = [(y, x), (y, x + 1), (y, x + 2), (y, x + 3)]
    isValid (y, x) = (x + 3) < boardSize

downIndices :: [Line]
{-Indices for all four-cell columns in the board-}
downIndices = map (map flipTuple) acrossIndices
-- The down indices are just the across indices with
-- their (y, x) pairs flipped
  where
    flipTuple (y, x) = (x, y)

rightDiagIndices :: [Line]
{-Indices for all four-cell diagonal lines on a right-ward slant.-}
rightDiagIndices = buildIndices getIndices isValid
  where
    getIndices (y, x) = [(y, x), (y + 1, x + 1), (y + 2, x + 2), (y + 3, x + 3)]
    isValid (y, x) = (y + 3) < boardSize && (x + 3) < boardSize

leftDiagIndices :: [Line]
{-Indices for all four-cell diagonal lines on a left-ward slant.-}
leftDiagIndices = buildIndices getIndices isValid
  where
    getIndices (y, x) = [(y, x), (y + 1, x - 1), (y + 2, x - 2), (y + 3, x - 3)]
    isValid (y, x) = (y + 3) < boardSize && (x - 3) > 0

buildIndices :: (Point -> Line) -> (Point -> Bool) -> [Line]
{-Helper function for building indice lists given a function to determine
if an index is a valid starting point and a function to build the indices
from that starting point.-}
buildIndices getIndices isValid = map getIndices $ filter isValid allIndices

getProduct :: Line -> Int
{-Given a list of indices, return the product found by multiplying
the values at each index together.-}
getProduct indices = product $ map getCell indices
  where
    getCell = (board !)

answer = maximum $ concatMap (map getProduct) lines
  where
    lines = [acrossIndices, downIndices, rightDiagIndices, leftDiagIndices]

main = do
  assert (getProduct [(0,0), (0, 1), (0, 2), (0, 3)] == 8 * 2 * 22 * 97) (return ())
  print answer