ocaml/utils/cset.ml

104 lines
2.8 KiB
OCaml

(* Sets over ordered types *)
type 'a t = Empty | Node of 'a t * 'a * 'a t * int
let empty = Empty
(* Compute the size (number of nodes and leaves) of a tree. *)
let size = function
Empty -> 1
| Node(_, _, _, s) -> s
(* Creates a new node with left son l, value x and right son r.
l and r must be balanced and size l / size r must be between 1/N and N.
Inline expansion of size for better speed. *)
let new l x r =
let sl = match l with Empty -> 0 | Node(_,_,_,s) -> s in
let sr = match r with Empty -> 0 | Node(_,_,_,s) -> s in
Node(l, x, r, sl + sr + 1)
(* Same as new, but performs rebalancing if necessary.
Assumes l and r balanced, and size l / size r "reasonable".
Inline expansion of new for better speed in the most frequent case
where no rebalancing is required. *)
let bal l x r =
let sl = match l with Empty -> 0 | Node(_,_,_,s) -> s in
let sr = match r with Empty -> 0 | Node(_,_,_,s) -> s in
if sl > 3 * sr then begin
match l with
Empty -> invalid_arg "Cset.bal"
| Node(ll, lv, lr, _) ->
if size ll >= size lr then
new ll lv (new lr x r)
else begin
match lr with
Empty -> invalid_arg "Cset.bal"
| Node(lrl, lrv, lrr, _)->
new (new ll lv lrl) lrv (new lrr x r)
end
end else if sr > 3 * sl then begin
match r with
Empty -> invalid_arg "Cset.bal"
| Node(rl, rv, rr, _) ->
if size rr >= size rl then
new (new l x rl) rv rr
else begin
match rl with
Empty -> invalid_arg "Cset.bal"
| Node(rll, rlv, rlr, _) ->
new (new l x rll) rlv (new rlr rv rr)
end
end else
Node(l, x, r, sl + sr + 1)
(* Merge two trees l and r into one.
All elements of l must precede the elements of r.
Assumes size l / size r between 1/N and N. *)
let rec merge l r =
match (l, r) with
(Empty, t) -> t
| (t, Empty) -> t
| (Node(l1, v1, r1, h1), Node(l2, v2, r2, h2)) ->
bal l1 v1 (bal (merge r1 l2) v2 r2)
(* Insertion *)
let rec add x = function
Empty ->
Node(Empty, x, Empty, 1)
| Node(l, v, r, _) as t ->
let c = compare x v in
if c = 0 then t else
if c < 0 then bal (add x l) v r else bal l v (add x r)
(* Membership *)
let rec mem x = function
Empty ->
false
| Node(l, v, r, _) ->
let c = compare x v in
c = 0 or mem x (if c < 0 then l else r)
(* Removal *)
let rec remove x = function
Empty ->
Empty
| Node(l, v, r, _) ->
let c = compare x v in
if c = 0 then merge l r else
if c < 0 then bal (remove x l) v r else bal l v (remove x r)
(* Contents *)
let elements s =
let rec elements accu = function
Empty -> accu
| Node(l, v, r, _) -> elements (v :: elements accu r) l
in elements [] s