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|
(***********************************************************************)
(* *)
(* Objective Caml *)
(* *)
(* Xavier Leroy, projet Cristal, INRIA Rocquencourt *)
(* *)
(* Copyright 1996 Institut National de Recherche en Informatique et *)
(* Automatique. Distributed only by permission. *)
(* *)
(***********************************************************************)
(* $Id$ *)
module type OrderedType =
sig
type t
val compare: t -> t -> int
end
module type S =
sig
type key
type 'a t
val empty: 'a t
val add: key -> 'a -> 'a t -> 'a t
val find: key -> 'a t -> 'a
val remove: key -> 'a t -> 'a t
val mem: key -> 'a t -> bool
val iter: (key -> 'a -> unit) -> 'a t -> unit
val map: ('a -> 'b) -> 'a t -> 'b t
val fold: (key -> 'a -> 'b -> 'b) -> 'a t -> 'b -> 'b
end
module Make(Ord: OrderedType) = struct
type key = Ord.t
type 'a t =
Empty
| Node of 'a t * key * 'a * 'a t * int
let empty = Empty
let height = function
Empty -> 0
| Node(_,_,_,_,h) -> h
let create l x d r =
let hl = height l and hr = height r in
Node(l, x, d, r, (if hl >= hr then hl + 1 else hr + 1))
let bal l x d r =
let hl = match l with Empty -> 0 | Node(_,_,_,_,h) -> h in
let hr = match r with Empty -> 0 | Node(_,_,_,_,h) -> h in
if hl > hr + 2 then begin
match l with
Empty -> invalid_arg "Map.bal"
| Node(ll, lv, ld, lr, _) ->
if height ll >= height lr then
create ll lv ld (create lr x d r)
else begin
match lr with
Empty -> invalid_arg "Map.bal"
| Node(lrl, lrv, lrd, lrr, _)->
create (create ll lv ld lrl) lrv lrd (create lrr x d r)
end
end else if hr > hl + 2 then begin
match r with
Empty -> invalid_arg "Map.bal"
| Node(rl, rv, rd, rr, _) ->
if height rr >= height rl then
create (create l x d rl) rv rd rr
else begin
match rl with
Empty -> invalid_arg "Map.bal"
| Node(rll, rlv, rld, rlr, _) ->
create (create l x d rll) rlv rld (create rlr rv rd rr)
end
end else
Node(l, x, d, r, (if hl >= hr then hl + 1 else hr + 1))
let rec add x data = function
Empty ->
Node(Empty, x, data, Empty, 1)
| Node(l, v, d, r, h) as t ->
let c = Ord.compare x v in
if c = 0 then
Node(l, x, data, r, h)
else if c < 0 then
bal (add x data l) v d r
else
bal l v d (add x data r)
let rec find x = function
Empty ->
raise Not_found
| Node(l, v, d, r, _) ->
let c = Ord.compare x v in
if c = 0 then d
else find x (if c < 0 then l else r)
let rec mem x = function
Empty ->
false
| Node(l, v, d, r, _) ->
let c = Ord.compare x v in
c = 0 || mem x (if c < 0 then l else r)
let rec merge t1 t2 =
match (t1, t2) with
(Empty, t) -> t
| (t, Empty) -> t
| (Node(l1, v1, d1, r1, h1), Node(l2, v2, d2, r2, h2)) ->
bal l1 v1 d1 (bal (merge r1 l2) v2 d2 r2)
let rec remove x = function
Empty ->
Empty
| Node(l, v, d, r, h) as t ->
let c = Ord.compare x v in
if c = 0 then
merge l r
else if c < 0 then
bal (remove x l) v d r
else
bal l v d (remove x r)
let rec iter f = function
Empty -> ()
| Node(l, v, d, r, _) ->
iter f l; f v d; iter f r
let rec map f = function
Empty -> Empty
| Node(l, v, d, r, h) -> Node(map f l, v, f d, map f r, h)
let rec fold f m accu =
match m with
Empty -> accu
| Node(l, v, d, r, _) ->
fold f l (f v d (fold f r accu))
end
|
