open Batteries
let tri =
  [|
    [| 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 () =
  let size = Array.length tri in
print_int size; print_newline();
  (* set each entry to the best possible result *)
  for n = 1 to size - 1 do
    tri.(n).(0) <- tri.(n).(0) + tri.(n-1).(0);
    for i = 1 to n-1 do
      tri.(n).(i) <- tri.(n).(i) + (max tri.(n-1).(i-1) tri.(n-1).(i));
    done;
    tri.(n).(n) <- tri.(n).(n) + tri.(n-1).(n-1)
  done;
  Array.fold_left max (-1) tri.(size-1) |> print_int;
  print_newline()

 set each entry to the best possible result 
open Batteries
let tri =
  [|
    [| 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 () =
  let size = Array.length tri in
print_int size; print_newline();
  for n = 1 to size - 1 do
    tri.(n).(0) <- tri.(n).(0) + tri.(n-1).(0);
    for i = 1 to n-1 do
      tri.(n).(i) <- tri.(n).(i) + (max tri.(n-1).(i-1) tri.(n-1).(i));
    done;
    tri.(n).(n) <- tri.(n).(n) + tri.(n-1).(n-1)
  done;
  Array.fold_left max (-1) tri.(size-1) |> print_int;
  print_newline()
