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-- Largest product in a grid
--
-- Problem 11
-- In the 20×20 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
--
-- 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?
main = do
-- print (largest_product grid)
print grid
largest_product :: [[Int]] -> Int
largest_product g = maximum [largest_row, largest_col, largest_diag]
where largest_row = 3
largest_col = 3
largest_diag = 3
max4 :: [Int] -> Int
max4 [x] = x
max4 (x:xs) = max (sum (take 4 (x:xs))) (max4 xs)
grid :: [[Int]]
grid = map (map read) (map words (lines grid_str))
grid_str = "08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08\n\
\49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00\n\
\81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65\n\
\52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91\n\
\22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80\n\
\24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50\n\
\32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70\n\
\67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21\n\
\24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72\n\
\21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95\n\
\78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92\n\
\16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57\n\
\86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58\n\
\19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40\n\
\04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66\n\
\88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69\n\
\04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36\n\
\20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16\n\
\20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54\n\
\01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48"
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