# Project Euler #018

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

``````type BinaryTree =
| Node of int * BinaryTree * BinaryTree
| Empty

let rec calculate tree =
match tree with
| Node (n, left, right) -> n + List.max [(calculate left); (calculate right)]
| Empty -> 0

let s_data =
[
"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";
]

let rec data_tree (data : string list) row i =
let data_row row_number = data.[row_number].Split(' ') |> Seq.map (fun s -> System.Int32.Parse(s)) |> Seq.toList
let length = data.Length
match row with
| 15 -> Empty
| _ -> Node ((data_row row).[i], data_tree data (row + 1) i, data_tree data (row + 1) (i + 1))

data_tree s_data 0 0 |> calculate;;
``````