Project Euler Problem 11

haskell

http://projecteuler.net/index.php?section=problems&id=11
与えられた行列の上下左右斜めいずれかで連続する4つの数字の積のうち最大のもの

nums = [[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]]

main = print $ maximum $ (widthMulti 4 nums) ++ (widthMulti 4 (rotateRight nums)) ++ (widthMulti 4 (rotateLeft45 nums)) ++ (widthMulti 4 (rotateRight45 nums))

--水平方向の積のリスト
widthMulti :: Int -> [[Int]] -> [Int]
widthMulti _ []     = []
widthMulti max (x:xs) = (widthMulti' x) ++ (widthMulti max xs)
                           where widthMulti' xs
                                  | length xs < 4 = []
                                  | otherwise     = [foldl1 (*) (take max xs)] ++ (widthMulti' $ tail xs)

--行列を左90度回転
rotateLeft :: [[a]] -> [[a]]
rotateLeft xs = reverse $ rotateLeft' xs
           where rotateLeft' xs
          	       | all null xs = []
                       | otherwise      = [map head xs] ++ (rotateLeft' $ map tail xs)

--行列を右90度回転
rotateRight :: [[a]] -> [[a]]
rotateRight xs = foldl (zipWith (\a b -> b:a)) (replicate (length xs) []) xs

--行列を右45度回転
rotateRight45 xs = (diagonalList 0 xs) ++ (map reverse (reverse $ init (diagonalList 0 (rotateRight $ rotateRight xs))))

--行列を左45度回転
rotateLeft45 xs = (diagonalList 0 (rotateLeft xs)) ++ (map reverse (reverse $ init (diagonalList 0 (rotateRight xs))))

--行列の左上を取得
diagonalList n xs
           | n >= (length xs)    = []
           | otherwise = [diagonalList' n 0 xs] ++ (diagonalList (n+1) xs)
                          where diagonalList' x y xs
                                    | x < 0 = []
                                    | otherwise = [xs !! x !! y] ++ (diagonalList' (x-1) (y+1) xs)