48 lines
2.7 KiB
Haskell
48 lines
2.7 KiB
Haskell
{-# LANGUAGE FlexibleInstances, UndecidableInstances #-}
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import Data.Array.Unboxed
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import Euler
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-- What is the greatest product of four adjacent numbers in the same direction
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-- (up, down, left, right, or diagonally) in the 20×20 grid?
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--
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grid :: UArray (Int, Int) Int
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grid = listArray ((1,1),(20,20)) $
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[ 08, 02, 22, 97, 38, 15, 00, 40, 00, 75, 04, 05, 07, 78, 52, 12, 50, 77, 91, 08
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, 49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 04, 56, 62, 00
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, 81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 03, 49, 13, 36, 65
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, 52, 70, 95, 23, 04, 60, 11, 42, 69, 24, 68, 56, 01, 32, 56, 71, 37, 02, 36, 91
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, 22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80
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, 24, 47, 32, 60, 99, 03, 45, 02, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50
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, 32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70
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, 67, 26, 20, 68, 02, 62, 12, 20, 95, 63, 94, 39, 63, 08, 40, 91, 66, 49, 94, 21
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, 24, 55, 58, 05, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72
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, 21, 36, 23, 09, 75, 00, 76, 44, 20, 45, 35, 14, 00, 61, 33, 97, 34, 31, 33, 95
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, 78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 03, 80, 04, 62, 16, 14, 09, 53, 56, 92
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, 16, 39, 05, 42, 96, 35, 31, 47, 55, 58, 88, 24, 00, 17, 54, 24, 36, 29, 85, 57
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, 86, 56, 00, 48, 35, 71, 89, 07, 05, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58
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, 19, 80, 81, 68, 05, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 04, 89, 55, 40
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, 04, 52, 08, 83, 97, 35, 99, 16, 07, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66
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, 88, 36, 68, 87, 57, 62, 20, 72, 03, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69
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, 04, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 08, 46, 29, 32, 40, 62, 76, 36
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, 20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 04, 36, 16
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, 20, 73, 35, 29, 78, 31, 90, 01, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 05, 54
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, 01, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 01, 89, 19, 67, 48
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]
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times :: (IArray a e, RangeIx i, Num e) => a i e -> a i e -> a i e
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a `times` b = zipArraysWith (*) a b
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infixl 7 `times`
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across n = ixmap ((1,1),( 20 ,20-n)) (\(a,b) -> ( a ,b+n)) grid
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down n = ixmap ((1,1),(20-n, 20 )) (\(a,b) -> (a+n, b )) grid
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diag1 n = ixmap ((1,1),(20-n,20-n)) (\(a,b) -> (a+n,b+n)) grid
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diag2 n = ixmap ((1,1+n),(20-n,20)) (\(a,b) -> (a+n,b-n)) grid
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acrossProducts = grid `times` across 1 `times` across 2 `times` across 3
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downProducts = grid `times` down 1 `times` down 2 `times` down 3
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diagProducts1 = grid `times` diag1 1 `times` diag1 2 `times` diag1 3
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diagProducts2 = grid `times` diag2 1 `times` diag2 2 `times` diag2 3
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main = print $ maximum $ concatMap elems $
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[acrossProducts, downProducts, diagProducts1, diagProducts2]
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