euler11

gistfile1.hs

grid :: [[Int]]
grid = [[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]]

windowed :: Int -> [a] -> [[a]]
windowed size ls = 
	(case ls of 
		[] -> []
		x:xs -> 
			if length ls >= size then 
				(take size ls) : windowed size xs
			else windowed size xs)

findValue :: Int -> Int -> [[Int]] -> Int
findValue x y grid = (grid !! x) !! y 

hasItemSingle :: [a] -> Int -> Bool
hasItemSingle array position = position >= 0 && (length array - 1) >= position

hasItem :: [[a]] -> Int -> Int -> Bool
hasItem array x y = hasItemSingle array x && hasItemSingle (array !! x) y

diagonalAt :: Int -> Int -> [[Int]] -> [Int]
diagonalAt x y grid = [findValue (x+z) (y+z) grid | z <- [0..(length grid)], hasItem grid (x + z) (y + z)]

diagonalUpwaysAt :: Int -> Int -> [[Int]] -> [Int]
diagonalUpwaysAt x y grid = [findValue (x+z) (y+(z * (-1))) grid | z <- [0,-1..(length grid * (-1))], hasItem grid (x + z) (y + (z *(-1)))]						

diagonalPositions :: [[Int]] -> [(Int, Int)]
diagonalPositions grid = [ (x,y) | x <- [0..(length grid)], y <- [0..length $ grid !! 0 ]]

diagonals :: [[Int]] -> [[Int]]
diagonals grid = filter (\x -> length x > 4) . map (\(x,y) -> diagonalAt x y grid) $ (diagonalPositions grid)

diagonalsUp :: [[Int]] -> [[Int]]
diagonalsUp grid = filter (\x -> length x > 4) . map (\(x,y) -> diagonalUpwaysAt x y grid) $ (diagonalPositions grid)

leftToRight = concatMap (windowed 4) grid
topToBottom = concatMap (windowed 4) [[row !! (n-1) | row <- grid] | n <- [1..length grid]]
diagonalValues = concatMap (windowed 4) (diagonals grid)
diagonalUpValues = concatMap (windowed 4) (diagonalsUp grid)

problem_11 = maximum $ map product $ topToBottom ++ leftToRight ++ diagonalValues ++ diagonalUpValues