Project Euler No. 11

# Problem

> In the 20×20 grid below, four numbers along a diagonal line have been marked in red.
> 
> 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
>
> The product of these numbers is $26 × 63 × 78 × 14 = 1788696$.
> 
> What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 20×20 grid?


# Code in Haskell

```haskell:Euler_011.hs
module Main where
import Data.List

rawdata = 
	["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"]

digits = map (readlist.words) rawdata
  where readlist  = map (read::String->Integer)

rotate [] = []
rotate (x:xs) = x : rotate (map (0:) xs)

sproduct n [] = []
sproduct n a@(x:xs) = (nproduct n (take n a)) : sproduct n xs
  where nproduct n a	
    | length a == n = product a 
    |otherwise = 0

horizontal = map (sproduct 4) digits
vertical = map (sproduct 4) (transpose digits)
leftdiagonal = map (sproduct 4) (transpose $ rotate  digits)
rightdiagonal = map (sproduct 4) (transpose $ rotate $ reverse digits)

main = print answer
  where 
    answer = maximum $ concat $ map concat [horizontal, vertical, leftdiagonal, rightdiagonal]
```

# Answer

7******4