// list of 3 integers
let list1 = [1; 2; 3]

// list of 1 triple of integers
let list2 = [1,2,3]
printfn "%b" (list2 = [(1,2,3)]) // -> true

// questa non è una lista(!)
let list3 = (1,2,3)

let rec len l =
  if l = [] then
    0
  else
    1 + (len (List.tail l))

printfn "%A" (len [1; 2; 3; 4])

let rec revList l c =
  if l = [] then
   []
  else if List.length l - c = 0 then
    [List.head l]
  else
    l.[List.length l - c] :: (revList l (c+1))

printfn "%A" (revList [1; 2; 3; 4] 1)
printfn "%A" (revList [1] 1)
printfn "%A" (revList [] 1)

let rec sumList (l : int list) =
  if l = [] then
    0
  else
    List.head l + (sumList (List.tail l))

printfn "%A" (sumList [1; 2; 3; 4])


let rec maxList (l : int list) currentMax =
  if l = [] then
    currentMax
  else
    if (List.head l > currentMax) then
      maxList (List.tail l) (List.head l)
    else
      maxList (List.tail l) currentMax


printfn "%A" (maxList [1; 2; 3; 4] 0)

let rec nth l n =
  match (l, n) with
  | ([], _) -> failwith "Empty list"
  | (x::_, 0) -> x
  | (_::tail, n) when n > 0 -> nth tail (n-1)
  | _ -> failwith "n is negative"

printfn "%A" (nth [1; 2; 3; 4] 0)
printfn "%A" (nth [1; 2; 3; 4] 3)

let rec gcd m n =
  match (m,n) with
  | (x,y) when x<=0 || y<=0 -> failwith "Non-positive number inserted"
  | (x,y) when x>y -> gcd (x-y) y
  | (x,y) when x<y -> gcd x (y-x)
  | _ -> m

printfn "%A" (gcd 2048 1234)

let rec zip l l' =
  match (l,l') with
  | ([],[]) -> []
  | (x::xs,y::ys) -> (x,y)::(zip xs ys)
  | _ -> failwith "Lists have different lengths"

let rec zipAndCut l l' =
  match (l,l') with
  | ([],_)|(_,[]) -> []
  | (x::xs,y::ys) -> (x,y)::(zip xs ys)

let rec unzip (l: ('a*'b) list ) =
  match l with
  | [] -> ([],[])
  | (a,b)::l' ->
    let (h,k)=(unzip l')
    (a::h,b::k)

printfn "%A" (unzip [(0,0);(1,1);(2,1);(3,2);(4,3);(5,5);(6,8);(7,13)])
printfn "%A" (unzip [])