haskell problem 13 -> 18, 20

1 files changed, 60 insertions, 0 deletions

diff --git a/haskell/018-maximum_path_sum.hs b/haskell/018-maximum_path_sum.hs
new file mode 100644
index 0000000..fa15fe9
--- /dev/null
+++ b/haskell/018-maximum_path_sum.hs
@@ -0,0 +1,60 @@
+-- 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]
+    ]