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)
In [22]:
(*
let triangle = [|
[| 8; 5; 9; 3; |]
[| 2; 4; 6; |]
[| 7; 4; |]
[| 3 |]
|]
*)
let triangle = [|
[| 04; 62; 98; 27; 23; 09; 70; 98; 73; 93; 38; 53; 60; 04; 23 |]
[| 63; 66; 04; 68; 89; 53; 67; 30; 73; 16; 69; 87; 40; 31; |]
[| 91; 71; 52; 38; 17; 14; 91; 43; 58; 50; 27; 29; 48 |]
[| 70; 11; 33; 28; 77; 73; 17; 78; 39; 68; 17; 57 |]
[| 53; 71; 44; 65; 25; 43; 91; 52; 97; 51; 14 |]
[| 41; 48; 72; 33; 47; 32; 37; 16; 94; 29 |]
[| 41; 41; 26; 56; 83; 40; 80; 70; 33 |]
[| 99; 65; 04; 28; 06; 16; 70; 92; |]
[| 88; 02; 77; 73; 07; 63; 67 |]
[| 19; 01; 23; 75; 03; 34 |]
[| 20; 04; 82; 47; 65 |]
[| 18; 35; 87; 10 |]
[| 17; 47; 82; |]
[| 95; 64 |]
[| 75; |]
|]
let rec processRow (r:int) (rprev:int[]) =
if rprev.Length = 1 then rprev.[0]
else
[|0..(triangle.[r].Length - 1)|]
|> Array.map (fun i -> triangle.[r].[i] + (max (rprev.[i]) (rprev.[1+i])))
|> processRow (1 + r)
processRow 1 triangle.[0]
Out[22]:
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