-- Maximum path sum I
--
-- 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 = print (maxPath triangle)

-- recursion is beautiful (sometimes)
maxPath :: [[Int]] -> Int
maxPath [[x]] = x
maxPath (top:rest) = head top + max (maxPath $ map init rest) (maxPath $ map tail rest)

triangle =
    [ [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]
    ]