type point = float * float;;
type shape =
| Point of point
| Circle of point * float (* center and radius *)
| Rect of point * point (* lower-left and upper-left *);;

let area s =
        match s with 
        | Point _ -> 0.0
        | Circle (_,r) -> 3.14156 *. (r ** 2.0)
        | Rect ((x1,y1),(x2,y2)) ->
                let w = x2 -. x1 in
                let h = y2 -. y1 in
                    w *. h;;

let area = function 
        | Point _ -> 0.0
        | Circle (_,r) -> 3.14156 *. (r ** 2.0)
        | Rect ((x1,y1),(x2,y2)) ->
                let w = x2 -. x1 in
                let h = y2 -. y1 in
                    w *. h;;    

let center = function
  | Point p -> p
  | Circle (p,_) -> p
  | Rect ((x1,y1),(x2,y2)) ->
      ((x2 -. x1) /. 2.0, 
       (y2 -. y1) /. 2.0);;

type int_btree =
| Empty
| Node of int_btree * int * int_btree;;

type 'a btree =
| Empty
| Node of 'a btree * 'a *  'a btree;;

let rec insert x t =
        match t with 
        | Empty -> Node(Empty, x, Empty)
        | Node(left, value, right) -> 
                if (x <= value) then Node(insert x left, value, right)
        else Node(left, value, insert x right)
;;

let rec mem x t =
        match t with
        | Empty -> false
        | Node(left,v,right) -> 
                if (x = v) then true
                else if (x < v) then mem x left
                else mem x right;;