module List = ListLabels

type ('k, 'v) t =
  | Node of 'k * 'v * ('k, 'v) t * ('k, 'v) t
  | Leaf

let empty = Leaf

let rec set t ~k ~v =
  match t with
  | Leaf -> Node (k, v, Leaf, Leaf)
  | Node (k', v', l, r) when k < k' -> Node (k', v', set l ~k ~v, r)
  | Node (k', v', l, r) when k > k' -> Node (k', v', l, set r ~k ~v)
  | Node (k, _, l, r) -> Node (k, v, l, r)

let rec get t ~k =
  match t with
  | Leaf -> None
  | Node (k', _, l, _) when k < k' -> get l ~k
  | Node (k', _, _, r) when k > k' -> get r ~k
  | Node (_, v, _, _) -> Some v

let rec member t ~k =
  match t with
  | Leaf -> false
  | Node (k', _, l, _) when k < k' -> member l ~k
  | Node (k', _, _, r) when k > k' -> member r ~k
  | Node _ -> true

let to_edges t =
  let rec to_edges_from k1 t =
    match t with
    | Leaf -> []
    | Node (k2, _, l, r) ->
        (k1, k2) :: ((to_edges_from k2 l) @ (to_edges_from k2 r))
  in
  match t with
  | Leaf -> []
  | Node (k, _, l, r) -> (to_edges_from k l) @ (to_edges_from k r)

let to_dot t ~k_to_string =
  let (edges, _) =
    List.fold_left (to_edges t)
      ~init:("", "\n")
      ~f:(fun (edges, sep) (k1, k2) ->
        let k1, k2 = k_to_string k1, k_to_string k2 in
        (Printf.sprintf "%s%s    %S -> %S;\n" edges sep k1 k2, "")
    )
  in
  "digraph G {" ^ edges ^ "}"