Source file splay_tree0.ml
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open Core_kernel
open Int.Replace_polymorphic_compare
include Splay_tree0_intf
module Make_with_reduction
(Key : Key)
(Data : Data)
(R : Reduction_operation with type key = Key.t and type data = Data.t) =
struct
type key = Key.t [@@deriving sexp]
type data = Data.t [@@deriving sexp]
type accum = R.accum
module Kernel : sig
(** tree size *)
type size
type t = private
| Empty
| Node of
{ left : t
; key : key
; data : data
; right : t
; size : size
; accum : accum
}
val length : t -> int
val node : t -> key -> data -> t -> t
val empty : t
val accum : t -> accum
end = struct
type size = int
type t =
| Empty
| Node of
{ left : t
; key : key
; data : data
; right : t
; size : int
; accum : accum
}
let length = function
| Empty -> 0
| Node { size; _ } -> size
;;
let accum = function
| Empty -> R.identity
| Node { accum; _ } -> accum
;;
let node left key data right =
Node
{ left
; key
; data
; right
; size = length left + length right + 1
; accum =
R.combine (R.combine (accum left) (R.singleton ~key ~data)) (accum right)
}
;;
let empty = Empty
end
module Tree = struct
include Kernel
let is_empty = function
| Empty -> true
| Node _ -> false
;;
type ctx =
| Top
| Fst of ctx * key * data * t
| Snd of t * key * data * ctx
let rec _plug t = function
| Top -> t
| Fst (ctx, k, v, r) -> _plug (node t k v r) ctx
| Snd (l, k, v, ctx) -> _plug (node l k v t) ctx
;;
let find_ctx : t -> key -> ctx * t =
fun t x ->
let rec loop ctx this =
match this with
| Empty -> ctx, this
| Node { left; key; data; right; _ } ->
let cmp = Key.compare x key in
if cmp < 0
then loop (Fst (ctx, key, data, right)) left
else if cmp > 0
then loop (Snd (left, key, data, ctx)) right
else ctx, this
in
loop Top t
;;
let find_leftmost_ctx t =
let rec loop t ctx =
match t with
| Empty -> ctx
| Node { left; key; data; right; _ } -> loop left (Fst (ctx, key, data, right))
in
loop t Top
;;
let find_rightmost_ctx t =
let rec loop ctx t =
match t with
| Empty -> ctx
| Node { left; key; data; right; _ } -> loop (Snd (left, key, data, ctx)) right
in
loop Top t
;;
let nth_ctx t i =
let rec loop ctx this i =
match this with
| Empty -> ctx, this
| Node { left; key; data; right; _ } ->
let lsize = length left in
if i < lsize
then loop (Fst (ctx, key, data, right)) left i
else if i = lsize
then ctx, this
else
loop (Snd (left, key, data, ctx)) right (i - lsize - 1)
in
loop Top t i
;;
let search_ctx t ~f =
let rec loop ctx this ~left:left_ctx ~right:right_ctx =
match this with
| Empty -> ctx, this
| Node { left; key; data; right; _ } ->
let left_combined = R.combine left_ctx (accum left) in
let right_combined = R.combine right_ctx (accum right) in
let right_with_node = R.combine (R.singleton ~key ~data) right_combined in
(match f ~left:left_combined ~right:right_with_node with
| `Left ->
loop (Fst (ctx, key, data, right)) left ~left:left_ctx ~right:right_with_node
| `Right ->
let left_with_node = R.combine left_combined (R.singleton ~key ~data) in
(match f ~left:left_with_node ~right:right_combined with
| `Left -> ctx, this
| `Right ->
loop
(Snd (left, key, data, ctx))
right
~left:left_with_node
~right:right_ctx))
in
loop Top t ~left:R.identity ~right:R.identity
;;
let rec splay l r = function
| Top -> l, r
| Fst (Top, y, yv, c) ->
let a = l in
let b = r in
a, node b y yv c
| Snd (a, y, yv, Top) ->
let b = l in
let c = r in
node a y yv b, c
| Fst (Fst (ctx, z, zv, d), y, yv, c) ->
let a = l in
let b = r in
splay a (node b y yv (node c z zv d)) ctx
| Snd (b, y, yv, Snd (a, z, zv, ctx)) ->
let c = l in
let d = r in
splay (node (node a z zv b) y yv c) d ctx
| Snd (a, y, yv, Fst (ctx, z, zv, d)) | Fst (Snd (a, y, yv, ctx), z, zv, d) ->
let b = l in
let c = r in
splay (node a y yv b) (node c z zv d) ctx
;;
let splay_node l k v r ctx =
let l, r = splay l r ctx in
node l k v r
;;
let splay_empty ctx =
match ctx with
| Top -> empty
| Fst (ctx, k, v, r) -> splay_node empty k v r ctx
| Snd (l, k, v, ctx) -> splay_node l k v empty ctx
;;
let splay_to_triple found =
let inject v (left, right) = left, v, right in
match found with
| ctx, Node { left; key; data; right; _ } ->
inject (Some (key, data)) (splay left right ctx)
| ctx, Empty -> inject None (splay empty empty ctx)
;;
let splay_split_leq_gt = function
| ctx, Node { left; key; data; right; _ } ->
let l, r = splay left right ctx in
node l key data empty, r
| ctx, Empty -> splay empty empty ctx
;;
let splay_split_lt_geq = function
| ctx, Node { left; key; data; right; _ } ->
let l, r = splay left right ctx in
l, node empty key data r
| ctx, Empty -> splay empty empty ctx
;;
let splay_to_tree = function
| ctx, Node { left; key; data; right; _ } -> splay_node left key data right ctx
| ctx, Empty -> splay_empty ctx
;;
let splay_to_result = function
| ctx, Node { left; key; data; right; _ } ->
splay_node left key data right ctx, Some (key, data)
| ctx, Empty -> splay_empty ctx, None
;;
let set t ~key ~data =
let l, _, r = find_ctx t key |> splay_to_triple in
node l key data r
;;
let add t ~key ~data =
match find_ctx t key |> splay_to_triple with
| l, None, r -> Some (node l key data r)
| _, Some _, _ -> None
;;
let remove_min t =
match find_leftmost_ctx t with
| Top -> None
| Snd _ ->
assert false
| Fst (ctx, x, xv, right) ->
(match splay empty right ctx with
| Empty, r -> Some (x, xv, r)
| Node _, _ ->
assert false)
;;
let remove_max t =
match find_rightmost_ctx t with
| Top -> None
| Fst _ ->
assert false
| Snd (left, x, xv, ctx) ->
(match splay left empty ctx with
| l, Empty ->
Some (x, xv, l)
| _, Node _ ->
assert false)
;;
let concat_unchecked left right =
match remove_min right with
| None -> left
| Some (x, xv, right) -> node left x xv right
;;
let concat_value_unchecked left key data right =
match data with
| None -> concat_unchecked left right
| Some data -> node left key data right
;;
let concat_triple_unchecked left kv right =
match kv with
| None -> concat_unchecked left right
| Some (k, v) -> node left k v right
;;
let remove t k =
match find_ctx t k with
| ctx, Empty -> splay_empty ctx
| ctx, Node { left; right; _ } ->
splay_to_tree (ctx, concat_unchecked left right)
;;
let remove_before t k =
let before, at, after = find_ctx t k |> splay_to_triple in
match remove_max before with
| Some (res_k, res_v, before) ->
First (res_k, res_v, concat_triple_unchecked before at after)
| None -> Second (concat_triple_unchecked before at after)
;;
let remove_after t k =
let before, at, after = find_ctx t k |> splay_to_triple in
match remove_min after with
| Some (res_k, res_v, after) ->
First (res_k, res_v, concat_triple_unchecked before at after)
| None -> Second (concat_triple_unchecked before at after)
;;
let fold_right : 'b. t -> init:'b -> f:(key:key -> data:data -> 'b -> 'b) -> 'b =
fun t ~init ~f ->
let rec loop acc = function
| [] -> acc
| `Elem (key, data) :: to_visit -> loop (f ~key ~data acc) to_visit
| `Tree Empty :: to_visit -> loop acc to_visit
| `Tree (Node { left; key; data; right; _ }) :: to_visit ->
loop acc (`Tree right :: `Elem (key, data) :: `Tree left :: to_visit)
in
loop init [ `Tree t ]
;;
let data t = fold_right t ~init:[] ~f:(fun ~key:_ ~data acc -> data :: acc)
let keys t = fold_right t ~init:[] ~f:(fun ~key ~data:_ acc -> key :: acc)
let mem t x =
let t, res = find_ctx t x |> splay_to_result in
t, Option.is_some res
;;
let find t x =
let t, res = find_ctx t x |> splay_to_result in
t, Option.map ~f:snd res
;;
let nth t n = nth_ctx t n |> splay_to_result
let rank t key =
let t = find_ctx t key |> splay_to_tree in
let result =
match t with
| Empty -> 0
| Node { left; key = root; _ } ->
if Key.compare root key < 0 then length left + 1 else length left
in
t, result
;;
let search t ~f = search_ctx t ~f |> splay_to_result
let to_alist t = fold_right t ~init:[] ~f:(fun ~key ~data acc -> (key, data) :: acc)
let of_alist l =
List.fold_result l ~init:empty ~f:(fun t (key, data) ->
match add t ~key ~data with
| None -> error_s [%message "Duplicate key" (key : Key.t)]
| Some t -> Ok t)
;;
let of_alist_exn l = Or_error.ok_exn (of_alist l)
let t_of_sexp sexp = of_alist_exn ([%of_sexp: (key * data) list] sexp)
let sexp_of_t t =
Sexp.List
(fold_right t ~init:[] ~f:(fun ~key ~data acc ->
Sexp.List [ sexp_of_key key; sexp_of_data data ] :: acc))
;;
module Partition = struct
type nonrec t =
{ lt : t
; mid : t
; gt : t
}
end
let partition ?min_key ?max_key t =
let lt, geq =
match min_key with
| None -> empty, t
| Some min_key -> find_ctx t min_key |> splay_split_lt_geq
in
let mid, gt =
match max_key with
| None -> geq, empty
| Some max_key -> find_ctx geq max_key |> splay_split_leq_gt
in
{ Partition.lt; mid; gt }
;;
let subrange ?min_key ?max_key t = (partition ?min_key ?max_key t).mid
let rec merge left right ~f =
match left, right with
| Empty, Empty -> empty
| Empty, Node { left; key; data; right; _ } ->
let l' = merge ~f empty left in
let v' = f ~key (`Right data) in
let r' = merge ~f empty right in
concat_value_unchecked l' key v' r'
| Node { left; key; data; right; _ }, Empty ->
let l' = merge ~f left empty in
let v' = f ~key (`Left data) in
let r' = merge ~f right empty in
concat_value_unchecked l' key v' r'
| Node { left = l1; key; data = v1; right = r1; _ }, Node _ ->
let l2, kv2, r2 = find_ctx right key |> splay_to_triple in
let v =
match kv2 with
| None -> `Left v1
| Some (k2, v2) ->
assert (Key.compare key k2 = 0);
`Both (v1, v2)
in
let l' = merge ~f l1 l2 in
let v' = f ~key v in
let r' = merge ~f r1 r2 in
concat_value_unchecked l' key v' r'
;;
let split t k =
let l, v, r = find_ctx t k |> splay_to_triple in
l, Option.map ~f:snd v, r
;;
let join l r =
match find_rightmost_ctx l, remove_min r with
| _, None -> Ok l
| Top, _ -> Ok r
| Fst _, _ ->
assert false
| Snd (_, k1, _, _), Some (k2, v2, r) ->
if Key.compare k1 k2 >= 0
then
error_s
[%message
"Trees were overlapping" ~left_max:(k1 : key) ~right_min:(k2 : key)]
else Ok (node l k2 v2 r)
;;
let join_exn l r = Or_error.ok_exn (join l r)
let rec map_cps : 'r. t -> f:(data -> data) -> (t -> 'r) -> 'r =
fun t ~f k ->
match t with
| Empty -> k empty
| Node { left; key; data; right; _ } ->
map_cps left ~f (fun l ->
let data = f data in
map_cps right ~f (fun r -> k (node l key data r)))
;;
let map t ~f = map_cps t ~f Fn.id
let map_range t ~min_key ~max_key ~f =
let old_range, t =
let { Partition.lt; mid; gt } = partition ~min_key ~max_key t in
to_alist mid, concat_unchecked lt gt
in
let new_range = f old_range in
List.fold new_range ~init:t ~f:(fun t (key, data) -> set t ~key ~data)
;;
end
module T : sig
type t [@@deriving sexp]
val create : Tree.t -> t
val update : t -> Tree.t * 'a -> 'a
val pack : t -> Tree.t -> t
val unpack : t -> Tree.t
end = struct
type t = { mutable tree : Tree.t } [@@deriving sexp]
let create tree = { tree }
let pack (_ : t) tree = { tree }
let update t (tree, res) =
t.tree <- tree;
res
;;
let unpack t = t.tree
end
open Tree
include T
let empty = create empty
let of_alist l = Or_error.map ~f:create (of_alist l)
let of_alist_exn l = create (of_alist_exn l)
let to_alist t = to_alist (unpack t)
let is_empty t = is_empty (unpack t)
let length t = length (unpack t)
let accum t = accum (unpack t)
let keys t = keys (unpack t)
let data t = data (unpack t)
let mem t k = update t (mem (unpack t) k)
let find t k = update t (find (unpack t) k)
let set t ~key ~data = pack t (set (unpack t) ~key ~data)
let remove t k = pack t (remove (unpack t) k)
let pack_remove t = function
| None -> None
| Some (a, b, tree) -> Some (a, b, pack t tree)
;;
let remove_min t = pack_remove t (remove_min (unpack t))
let remove_max t = pack_remove t (remove_max (unpack t))
let pack_remove_either t = function
| First (a, b, tree) -> Some (a, b, pack t tree)
| Second tree -> update t (tree, None)
;;
let remove_after t k = pack_remove_either t (remove_after (unpack t) k)
let remove_before t k = pack_remove_either t (remove_before (unpack t) k)
let map t ~f = pack t (map (unpack t) ~f)
let map_range t ~min_key ~max_key ~f =
pack t (map_range (unpack t) ~min_key ~max_key ~f)
;;
let nth t idx = update t (nth (unpack t) idx)
let rank t key = update t (rank (unpack t) key)
let search t ~f = update t (search (unpack t) ~f)
module Partition = struct
type nonrec t =
{ lt : t
; mid : t
; gt : t
}
end
let partition ?min_key ?max_key t =
let { Tree.Partition.lt; mid; gt } = partition ?min_key ?max_key (unpack t) in
{ Partition.lt = pack t lt; mid = pack t mid; gt = pack t gt }
;;
let subrange ?min_key ?max_key t = pack t (subrange ?min_key ?max_key (unpack t))
let split t k =
let l, v, r = split (unpack t) k in
pack t l, v, pack t r
;;
let merge a b ~f = create (merge ~f (unpack a) (unpack b))
let join a b = Or_error.map ~f:create (join (unpack a) (unpack b))
let join_exn a b = create (join_exn (unpack a) (unpack b))
end
module Make_without_reduction (Key : Key) (Data : Data) :
S with type key = Key.t and type data = Data.t and type accum = unit =
Make_with_reduction (Key) (Data)
(struct
type key = Key.t
type data = Data.t
type accum = unit
let identity = ()
let singleton ~key:_ ~data:_ = ()
let combine () () = ()
end)
module Reduction_operations = struct
let reduce2
(type k d a b)
(module R1 : Reduction_operation
with type key = k
and type data = d
and type accum = a)
(module R2 : Reduction_operation
with type key = k
and type data = d
and type accum = b)
=
(module struct
type key = k
type data = d
type accum = a * b
let identity = R1.identity, R2.identity
let singleton ~key ~data = R1.singleton ~key ~data, R2.singleton ~key ~data
let combine (l1, l2) (r1, r2) = R1.combine l1 r1, R2.combine l2 r2
end : Reduction_operation
with type key = k
and type data = d
and type accum = a * b)
;;
end