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018_maximum_path_sum_I.hs
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018_maximum_path_sum_I.hs
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-- 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)
oneStep :: Int -> Int -> Int -> Int
oneStep top left right = max (top + left) (top + right)
oneRow :: [Int] -> [Int] -> [Int]
oneRow top below = oneRowAux top below []
oneRowAux :: [Int] -> [Int] -> [Int] -> [Int]
oneRowAux top below resL
| top == [] = resL
| otherwise = oneRowAux (tail top) (tail below)
(resL ++ [oneStep (head top) (head below) (head $ tail below)])
-- calculates the maximum path sum in a given triangle represented by a list of lists.
maxPathSum :: [[Int]] -> [Int]
maxPathSum grid = foldr oneRow (last grid) (take (length grid -1) grid)
main :: IO()
main = print $ maxPathSum [[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]]
-- [[3],[7 4],[2 4 6],[8 5 9 3]]
-- maxPathSum -> 23
-- [[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]]