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Project Euler

2012-09-15 - euler, haskell

What is the greatest product of four adjacent numbers in any direction (up, down, left, right, or diagonally) in the 2020 grid?

http://projecteuler.net/problem=11 It took me forever to find out that transpose existed and that I could use zipWith to get a diagonal - but after that its gets easy.

euler11 =
 maximum(
	(maxGridProduct q10Grid)  			       --max of row products
	:(maxGridProduct $ transpose q10Grid)   		       --max of column products
	:(maxGridProduct $ diagonalGrid q10Grid)		        --max of first diagonal
	:(maxGridProduct $ diagonalGrid $map reverse q10Grid)	--max of second diagonal
	:(maxGridProduct $ diagonalGrid $ transpose q10Grid)	--max of first transposed
	:(maxGridProduct $ diagonalGrid $map reverse $ transpose q10Grid)--max of second
	: []
   )

maxGridProduct :: [[Int]] -> Int
maxGridProduct grid = maximum $ map maxRowProduct grid

maxRowProduct :: [Int] -> Int
maxRowProduct line = maximum
		. map (product . take 4)
		$ tails
		$ line

diagonalGrid grid = map (diagonalRow grid) [0..(length grid)]

diagonalRow :: [[Int]] -> Int -> [Int]
diagonalRow grid offset = zipWith (!!) grid [offset .. max]
	where
	len = length $ grid!!0
	max = len - 1

q10Grid ::[[Int]]
q10Grid = map (map read) $ stringNum
  where stringNum = map words $ lines " \
\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"