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(*
This file is part of licht.
licht is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
licht is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with licht. If not, see <http://www.gnu.org/licenses/>.
*)
module type KEY = sig
type 'a t
(** Parametrized comparator *)
val comp: 'a t -> 'b t -> ('a, 'b) Tools.cmp
val repr: Format.formatter -> 'a t -> unit
end
module Make (El : KEY) = struct
type container = C : ('a El.t * 'a) -> container [@@unboxed]
type leaf (** Fantom type for typing the tree *)
type node (** Fantom type for typing the tree *)
type 'a branch =
| Leaf : leaf branch
| Node : _ branch * ('a El.t * 'a) * _ branch -> node branch
type t = T : 'a branch ref -> t [@@unboxed]
let empty = T (ref Leaf)
let isEmpty (T tree) = match !tree with
| Leaf -> true
| _ -> false
let rec splay : type a. a El.t -> node branch -> node branch = fun x t -> begin
let Node (l, y, r) = t in
begin match El.comp x (fst y) with
| Tools.Eq -> t
| Tools.Lt ->
begin match l with
| Leaf -> t
| Node (ll, z, rr) ->
begin match El.comp x (fst z) with
| Tools.Eq -> Node (ll, z, Node (rr, y, r))
| Tools.Lt ->
begin match ll with
| Leaf -> Node (ll, z, Node (rr, y, r))
| Node _ as ll ->
let Node (newL, newV, newR) = splay x ll
in Node (newL, newV, Node (newR, z, Node (rr, y, r)))
end
| Tools.Gt ->
begin match rr with
| Leaf -> Node (ll, z, Node (rr, y, r))
| Node _ as rr ->
let Node (newL, newV, newR) = splay x rr
in Node (Node (ll, z, newL), newV, Node (newR, y, r))
end
end
end
| Tools.Gt ->
begin match r with
| Leaf -> t
| Node (ll, z, rr) ->
begin match El.comp x (fst z) with
| Tools.Eq -> Node (Node (l, y, ll), z, rr)
| Tools.Lt ->
begin match ll with
| Leaf -> Node (Node (l, y, ll), z, rr)
| Node _ as ll ->
let Node (newL, newV, newR) = splay x ll
in Node (Node (l, y, newL), newV, Node (newR, z, rr))
end
| Tools.Gt ->
begin match rr with
| Leaf -> Node (Node (l, y, ll), z, rr)
| Node _ as rr ->
let Node (newL, newV, newR) = splay x rr
in Node (Node (Node(l, y, ll), z, newL), newV, newR)
end
end
end
end
end
let member: type a. a El.t -> t -> bool = fun x (T t) -> match !t with
| Leaf -> false
| Node _ as root ->
let root' = splay x root in
t := root';
let Node (_, c', _) = root' in
begin match El.comp (fst c') x with
| Tools.Eq -> true
| _ -> false
end
let find: type a. a El.t -> t -> a = fun x (T t) -> match !t with
| Leaf -> raise Not_found
| Node _ as root ->
let root' = splay x root in
t := root';
let Node (_, c', _) = root' in
begin match El.comp (fst c') x with
| Tools.Eq -> snd c'
| _ -> raise Not_found
end
let add: type a. a El.t -> a -> t -> t = fun key value (T t) -> match !t with
| Leaf -> T (ref (Node (Leaf, (key, value), Leaf)))
| Node _ as root ->
let root' = splay key root in
let Node (l, y, r) = root' in
begin match El.comp key (fst y) with
| Tools.Eq -> T (ref (Node(l, (key, value), r)))
| Tools.Lt -> T (ref (Node (l, (key, value), Node (Leaf, y, r))))
| Tools.Gt -> T (ref (Node (Node (l, y, Leaf), (key, value), r)))
end
let rec _subtree_maximum:type a. a branch -> a branch = fun t -> begin match t with
| Leaf -> Leaf
| Node (_, _, (Node (_, _, _) as x)) -> _subtree_maximum x
| Node (_, (key, value), Leaf) -> splay key t
end
let rec _subtree_minimum: type a. a branch -> a branch = fun t -> begin match t with
| Leaf -> Leaf
| Node ((Node (_, _, _) as x), _, _) -> _subtree_minimum x
| Node (Leaf, (key, value), _) -> splay key t
end
let remove: type a. a El.t -> t -> t = fun key (T t) -> begin match !t with
| Leaf -> empty
| Node _ as root ->
let root' = splay key root in
let Node (l, c', r) = root' in
begin match El.comp (fst c') key with
| Tools.Eq -> begin match _subtree_maximum l with
| Node(l, c, Leaf) -> T (ref (Node(l, c, r)))
| Node(l, c, _) -> raise Not_found
| Leaf -> begin match _subtree_minimum r with
| Leaf -> empty
| Node(Leaf, c, r) -> T (ref (Node(l, c, r)))
| Node(_, c, r) -> raise Not_found
end
end
(* The key is not present, return the splayed tree *)
| _ -> T (ref root')
end
end
(** Existencial type for the branches *)
type exBranch = Branch : _ branch -> exBranch [@@unboxed]
let fold f init (T t) = begin
let rec _fold : type b. (container * exBranch) list -> 'a -> b branch -> 'a = begin
fun acc v -> function
(* We have a node : we accumulate the right part, and process the left branch *)
| Node (left, (key, value), right) ->
let c = C (key, value) in
(_fold [@tailcall]) ((c, Branch right)::acc) v left
(* We have nothing left, we process the values delayed *)
| Leaf -> begin match acc with
| [] -> v
| (c, (Branch right))::tl -> (_fold [@tailcall]) tl (f v c) right
end
end in
_fold [] init !t
end
let choose (T tree) = begin match (_subtree_minimum !tree) with
| Leaf -> raise Not_found
| Node (left, (key, value), right) -> C (key, value)
end
let repr formatter (T t) = begin
let repr_edge from formatter dest = begin
Format.fprintf formatter "\"%a\" -> \"%a\"\n"
El.repr from
El.repr dest
end in
let rec repr': type a b. a El.t -> Format.formatter -> b branch -> unit = fun parent formatter -> function
| Leaf -> ()
| Node (l, c, r) ->
let key = fst c in
Format.fprintf formatter "%a%a%a"
(repr_edge parent) key
(repr' key) l
(repr' key) r in
begin match !t with
| Leaf -> Format.fprintf formatter "digraph G {}"
| Node (l, c, r) ->
let key = fst c in
Format.fprintf formatter "digraph G {\n%a%a}"
(repr' key) l
(repr' key) r
end
end
end
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