Project Euler #65

65.ml

#load "nums.cma";;

open Big_int;;
open List

let p a n =
  let rec p_inner acc m =
    let pn k =
      let an = big_int_of_int (nth a (k - 2))
      in
      let pn_1 = nth acc (k - 1)
      in
      let pn_2 = nth acc (k - 2)
      in
        add_big_int (mult_big_int an pn_1) pn_2
    in
    if m = (n + 2) then
      pn m
    else
      p_inner (acc @ [pn m]) (m + 1)
  in
    p_inner [zero_big_int; unit_big_int] 2;;

let rec gen_e_fraction n = 
  if n = 0 then
    [2]
  else
    (gen_e_fraction (n - 1)) @ [1; 2*n; 1]

let ea = gen_e_fraction 100;;

let sum_digits n =
  let rec i_sum_digits acc m =
    if eq_big_int m zero_big_int then
      acc
    else
      let (q, r) = quomod_big_int m (big_int_of_int 10)
      in
        i_sum_digits (add_big_int acc r) q
  in
    i_sum_digits zero_big_int n;;

let p_100 = p ea 99;;
Printf.printf "%s -> %s\n" (string_of_big_int p_100)
  (string_of_big_int (sum_digits p_100));;