Euler Project: Problem 18

By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.

3
7 4
2 4 6
8 5 9 3

That is, 3 + 7 + 4 + 9 = 23.

Find the maximum total from top to bottom of the triangle below:

75
95 64
17 47 82
18 35 87 10
20 04 82 47 65
19 01 23 75 03 34
88 02 77 73 07 63 67
99 65 04 28 06 16 70 92
41 41 26 56 83 40 80 70 33
41 48 72 33 47 32 37 16 94 29
53 71 44 65 25 43 91 52 97 51 14
70 11 33 28 77 73 17 78 39 68 17 57
91 71 52 38 17 14 91 43 58 50 27 29 48
63 66 04 68 89 53 67 30 73 16 69 87 40 31
04 62 98 27 23 09 70 98 73 93 38 53 60 04 23

NOTE: As there are only 16384 routes, it is possible to solve this problem by trying every route. However, Problem 67, is the same challenge with a triangle containing one-hundred rows; it cannot be solved by brute force, and requires a clever method! ;o)

main :: IO()
main = print $ foldr1 maxEleList rowData 

maxEleList :: [Int] -> [Int] -> [Int]
maxEleList xs ys = maxOfTwo upperList lowerList
                    where   upperList = zipWith (curry turpleSum) xs ys
                                 lowerList = zipWith (curry turpleSum) xs (tail ys)

maxOfTwo :: [Int] -> [Int] -> [Int]
maxOfTwo [] [] = []
maxOfTwo (x:xs) (y:ys) = max x y : maxOfTwo xs ys 

turpleSum :: (Int, Int) -> Int
turpleSum (x, y) = x + y 

rowData :: [[Int]]
rowData = map (map (\x -> read x :: Int) . words) [r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15] 

r1 = "75"
r2 = "95 64"
r3 = "17 47 82"
r4 = "18 35 87 10"
r5 = "20 04 82 47 65"
r6 = "19 01 23 75 03 34"
r7 = "88 02 77 73 07 63 67"
r8 = "99 65 04 28 06 16 70 92"
r9 = "41 41 26 56 83 40 80 70 33"
r10 = "41 48 72 33 47 32 37 16 94 29"
r11 = "53 71 44 65 25 43 91 52 97 51 14"
r12 = "70 11 33 28 77 73 17 78 39 68 17 57"
r13 = "91 71 52 38 17 14 91 43 58 50 27 29 48"
r14 = "63 66 04 68 89 53 67 30 73 16 69 87 40 31"
r15 = "04 62 98 27 23 09 70 98 73 93 38 53 60 04 23" 

*Main> main
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