Assignment2Template.ml

(*
Honor code comes here:

First Name: WEI-HENG
Last Name: LIN
BU ID: U79873457

I pledge that this program represents my own
program code and that I have coded on my own. I received
help from no one in designing and debugging my program.
I have read the course syllabus of CS 320 and have read the sections on Collaboration
and Academic Misconduct. I also understand that I may be asked to meet the instructor
or the TF for a follow up interview on Zoom. I may be asked to explain my solution in person and
may also ask you to solve a related problem.
*)

let rec print_list (ls: int list): unit =
  let rec aux ls = match ls with
    | [] -> print_string ""
    | e::[] -> print_int e
    | e::l -> 
      let _ = print_int e 
      in let _ = print_string "; " 
      in aux l

  in let _ = print_string "[" 
  in let _ = aux ls
  in         print_string "]" 

let rec print_some_list (ls: int list option): unit = 
  match ls with
  | None -> ()
  | Some l -> print_list l


let rec list_of_tuple_as_string list =
  let rec aux list = 
    match list with 
    | None -> "None"
    | Some [] -> ""
    | Some ((a,b)::[])-> "(" ^ (string_of_int a) ^ "," ^ (string_of_int b) ^ ")"
    | Some ((a,b)::t)-> "(" ^ (string_of_int a) ^ "," ^ (string_of_int b) ^ ")" ^ ";" ^ aux (Some t)
  in "[" ^ aux list ^ "]"

let between (n:int) (e:int): int list = 
  let rec aux n e l = 
    if n > e then l
    else aux n (e-1) (e::l) 
  in aux n e []





let rec safe_zip_int (ls1: int list) (ls2: int list) : ((int * int) list) option = 
  let rec aux ls1 ls2 acc = 
    match (ls1,ls2) with
    | [],[] -> acc
    | (h1::t1),[] -> aux t1 [] None
    | [],(h2::t2) -> aux [] t2 None
    | (h1::t1),(h2::t2) -> 
      match acc with
      | None -> None
      | Some tuples -> aux t1 t2 (Some(tuples@[(h1,h2)]))
  in aux ls1 ls2 (Some [])


let rec pell (i: int) : int = 
  let rec aux i acc1 acc2 = 
    match i with
    | 0 -> acc1
    | _ -> aux (i-1) acc2 (2*acc2+acc1)
  in aux i 0 1


let tetra (n : int) : int = 
  let rec aux n acc1 acc2 acc3 acc4 = 
    match n with
    | 0 -> acc1
    | _ -> aux (n-1) acc2 acc3 acc4 (acc1+acc2+acc3+acc4)
  in aux n 0 1 1 2



let rec toDec (i : int) : int list option = 
  let rec aux i acc = 
    if i < 0 then None
    else match i with
      | 0 -> acc
      | x -> 
        match acc with
        | None -> None
        | Some ls -> aux (i/10) (Some(ls@[(i mod 10)]))
  in aux i (Some [])


let rec sum (a : int list) (b : int list) : int list =  
  let rec aux a b flag acc = 
    if flag = false 
    then match a,b with
      | [],[] -> acc
      | a,[] -> aux [] [] false (acc@a)
      | [],b -> aux [] [] false (acc@b)
      | [x],[y] -> if x+y <=9 then aux [] [] false (acc@[x+y]) else aux [1] [] false (acc@[(x+y) mod 10])     (*if x+y >=10, where x and y are the 2 only digits left then let a = [1]*)
      | (h1::t1),(h2::t2) -> 
        if h1+h2 <= 9 then aux t1 t2 false (acc@[h1+h2])
        else aux t1 t2 true (acc@[(h1+h2) mod 10])
    else match a,b with
      | [],[] -> acc
      | a,[] -> aux a [1] false (acc)
      | [],b -> aux [1] b false (acc)
      | [x],[y] -> if x+y+1 <=9 then aux [] [] false (acc@[x+y+1]) else aux [1] [] false (acc@[(x+y+1) mod 10])
      |(h1::t1),(h2::t2) -> 
        if (h1+h2+1) <= 9 then aux t1 t2 false (acc@[h1+h2+1])
        else aux t1 t2 true (acc@[(h1+h2+1) mod 10])
  in aux a b false []



let rec pell2 (i: int) : int list = 
  let rec aux i acc1 acc2 = 
    match i with
    | 0->acc1
    | _ -> aux (i-1) acc2 (sum (sum acc2 acc2) acc1)
  in aux i [] [1]


(* let _ = 
   print_list (pell2 50) *)