Calculate Value Of Function Using Recursion In Ocaml Assignment Solution.

open Printf

(*************************************************

0) Fill in your name and PID on the lines below.

*)

let name = "YOUR NAME";;

let id = "YOUR PID OR ID";;

let _ = printf "\n-----NAME: %s ID: %s -----\n" name id;;

let todo (type t) (x : t) : 'a =

  let module M = struct exception Todo of t end in

  raise @@ M.Todo x

;;

open Num

(*

Suppose

  f(0) = 1,

  f(1) = 2,

  6*f(n)*f(n+1) - 5*f(n)*f(n+2) + f(n+1)*f(n+2) = 0

Calculate f(n) for any integer n >= 0.

*)

let rec f(n:int): string = (* Note that the result type is string. Whatever big

integer you use, convert it back to string in the end. *)

  let f_n (fn_2:num) (fn_1:num): num =

    div_num (mult_num (mult_num (num_of_int 6) fn_2) fn_1)

            (sub_num (mult_num (num_of_int 5) fn_2) fn_1)

  in

  let rec f_p (m:int) (fn_2:num) (fn_1:num): num =

    if m = n then

      fn_1

    else

      f_p (m + 1) fn_1 (f_n fn_2 fn_1)

  in

  if n = 0 then

    string_of_int 1

  else if n = 1 then

    string_of_int 2

  else

    let f0 = num_of_string (f 0) in

    let f1 = num_of_string (f 1) in

    string_of_num (f_p 1 f0 f1)

;;

printf "%d - %s\n" 7 (f 7); (* This is your own way of quick manual testing. *)

open OUnit

module Tests = struct

  let testingPrint act exp =

    print_string "Expected ";

    print_string exp;

    print_endline "\n got ";

    print_string act;

    print_endline "\n-----";;

  let testing n expectedOutput =

    let act = f n in

      printf "Testing func %d:\n" n;

      testingPrint act expectedOutput;

      print_endline "";

      assert_equal expectedOutput act;;

  let suite =

    "func" >:::

        [

          "n = 14" >:: (fun _ -> testing 14 "16384";);

          "n = 17" >:: (fun _ -> testing 17 "131072";);

          "n = 21" >:: (fun _ -> testing 21 "2097152";);

          "n = 35" >:: (fun _ -> testing 35 "34359738368";);

          "n = 43" >:: (fun _ -> testing 43 "8796093022208";);

          "n = 55" >:: (fun _ -> testing 55 "36028797018963968";);

          "n = 67" >:: (fun _ -> testing 67 "147573952589676412928";);

          "n = 71" >:: (fun _ -> testing 71 "2361183241434822606848";);

          "n = 81" >:: (fun _ -> testing 81 "2417851639229258349412352";);

        ]

;;

end

let _ =

  run_test_tt_main Tests.suite

;;