Hi, again. I started looking at the Euler problems [1]. I had no trouble with problems 1 through 10, but I'm stuck on problem 11. I am aware that the solutions are available ([2]), but I would rather not look just yet. In Problem 11, a 20x20 grid of numbers is given, and the problem is to find the largest product of four numbers along a straight line in the grid. The line can be horizontal, vertical, or diagonal. I figured out how to handle the horizontal and vertical products, but I'm stuck on how to approach the problem of extracting the diagonals. Here is what I have so far; it does the horizontal and vertical cases:
module Main where
import Data.List
gridText = "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"
readGrid :: (Read a) => String -> [[a]] readGrid = (map ((map read) . words)) . lines
grid :: [[Integer]] grid = readGrid gridText
makeGroups :: Int -> [a] -> [[a]] makeGroups 0 _ = [] makeGroups n xs = let ys = take n xs in if n == length ys then ys : (makeGroups n $ tail xs) else []
maxHorizontal :: (Ord a, Num a) => Int -> [[a]] -> a maxHorizontal length = maximum . map product . concat . map (makeGroups length)
maxVertical :: (Ord a, Num a) => Int -> [[a]] -> a maxVertical length = maxHorizontal length . transpose
main :: IO() main = do print $ maxHorizontal 4 grid print $ maxVertical 4 grid
To handle the diagonals, my plan is to try to extract each diagonal as a list of elements and put all the diagonals into a list; then I can use maxHorizontal. I came up with this function to try to extract the main diagonal.
getDiag :: [[a]] -> [a] getDiag = map (head . head) . iterate (tail . map tail)
The problem is, this function doesn't work unless I have an infinite grid. Could anyone provide me with some hints to lead me in the right direction? Thank you -- Ron References: [1] http://projecteuler.net/index.php?section=view [2] http://www.haskell.org/haskellwiki/Euler_problems