{-
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)
Solution:
No need to keep all paths.
For each NUMBER in the n'th row, there is one optimal way to get there.
Thus, we go row-by-row, and for each element in each row calculate the
best-way to get there (which is simply choosing between two possible ones.)
-}
-- answer: 1074
module E18 where
txtToPyramid :: String -> [[Int]]
txtToPyramid txt = toPyramid nums 0
where
nums = map read $ words txt :: [Int]
toPyramid :: [Int] -> Int -> [[Int]]
toPyramid [] i = []
toPyramid ns i = [take (i+1) ns ] ++ toPyramid (drop (i+1) ns) (i+1)
nextRow :: [Int] -- previous row, with Values of max path so far
-> [Int] -- current row values
-> [Int] -- current row Max path values
nextRow p r = zipWith max r1 r2
where
l = length p
r1 = ( zipWith (+) p (take l r) ) ++ (drop l r)
r2 = [head r] ++ (zipWith (+) p (tail r) )
findRow :: Int -> [[Int]] -> [Int]
findRow 0 pyramid = pyramid!!0
findRow l pyramid = nextRow (findRow (l-1) pyramid) (pyramid!!l)
main = do
txt <- readFile "euler18.txt"
let p = txtToPyramid txt
print $ maximum (findRow (length p-1) p )