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067_maximum_path_sum_II.hs
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067_maximum_path_sum_II.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 in triangle.txt
-- (right click and 'Save Link/Target As...'), a 15K text file containing a triangle with
-- one-hundred rows.
-- NOTE: This is a much more difficult version of Problem 18. It is not possible to try every
-- route to solve this problem, as there are 299 altogether! If you could check one trillion (1012)
-- routes every second it would take over twenty billion years to check them all.
-- There is an efficient algorithm to solve it. ;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 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