restructure + lecutre 07

lectures/06/functor/_build/bstree.ml

@@ -0,0 +1,86 @@
+module type OrderedType = sig
+  type t
+  val compare : t -> t -> int
+end
+
+module type S = sig
+  type elt
+  type t
+
+  val size : t -> int
+  val height : t -> int
+  val empty : t
+  val is_empty : t -> bool
+  val insert : elt -> t -> t
+  val of_list : elt list -> t
+  val mem : elt -> t -> bool
+  val delete : elt -> t -> t
+end
+
+module Make(Ord : OrderedType) = struct
+  type elt = Ord.t;;
+  type t = L | N of elt * t * t;;
+
+  let rec size t =
+    match t with
+    | L -> 0
+    | N (_, l, r) ->
+      1 + size l + size r;;
+
+  let rec height t =
+    match t with
+    | L -> 0
+    | N (_, l, r) ->
+      1 + max (height l) (height r);;
+
+  let empty = L;;
+
+  let is_empty t = t = L;;
+
+  let rec insert x t =
+    match t with
+    | L -> N (x, L, L)
+    | N (x', l, r) when Ord.compare x x' < 0 ->
+      N (x', insert  x l, r)
+    | N (x', l, r) when Ord.compare x x' > 0 ->
+      N (x', l, insert  x r)
+    | _ -> t;;
+
+  let of_list l =
+    List.fold_left (Fun.flip insert) L l;;
+
+  let rec mem x t =
+    match t with
+    | L -> false
+    | N (x', l, _) when Ord.compare x x' < 0 ->
+      mem  x l
+    | N (x', _, r) when Ord.compare x x' > 0 ->
+      mem  x r
+    | _ -> true;;
+
+  let rec largest t =
+    match t with
+    | L -> failwith "largest: empty tree"
+    | N (x, _, L) -> x
+    | N (_, _, r) -> largest r;;
+
+  let rec smallest t =
+    match t with
+    | L -> failwith "smallest: empty tree"
+    | N (x, L, _) -> x
+    | N (_, l, _) -> smallest l;;
+
+  let rec delete x t =
+    match t with
+    | L -> L
+    | N (x', l, r) when Ord.compare x x' < 0 ->
+      N (x', delete  x l, r)
+    | N (x', l, r) when Ord.compare x x' > 0 ->
+      N (x', l, delete  x r)
+    | N (_, L, L) -> L (* this does not need to be here, its a special case but ill leave it for clarity *)
+    | N (_, l, L) -> l
+    | N (_, L, r) -> r
+    | N (_, l, r) ->
+      let succ = largest l in
+      N (succ, delete  succ l, r);;
+end