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Diffstat (limited to 'stdlib/set.ml')
| -rw-r--r-- | stdlib/set.ml | 226 |
1 files changed, 0 insertions, 226 deletions
diff --git a/stdlib/set.ml b/stdlib/set.ml deleted file mode 100644 index 84a8a942c8..0000000000 --- a/stdlib/set.ml +++ /dev/null @@ -1,226 +0,0 @@ -(* Sets over ordered types *) - -module type OrderedType = - sig - type t - val compare: t -> t -> int - end - -module type S = - sig - type elt - type t - val empty: t - val is_empty: t -> bool - val mem: elt -> t -> bool - val add: elt -> t -> t - val remove: elt -> t -> t - val union: t -> t -> t - val inter: t -> t -> t - val diff: t -> t -> t - val compare: t -> t -> int - val equal: t -> t -> bool - val iter: (elt -> 'a) -> t -> unit - val fold: (elt -> 'a -> 'a) -> t -> 'a -> 'a - val elements: t -> elt list - val choose: t -> elt - end - -module Make(Ord: OrderedType): (S with elt = Ord.t) = - struct - type elt = Ord.t - type t = Empty | Node of t * elt * t * int - - (* Sets are represented by balanced binary trees (the heights of the - children differ by at most 2 *) - - let height = function - Empty -> 0 - | Node(_, _, _, h) -> h - - (* Creates a new node with left son l, value x and right son r. - l and r must be balanced and | height l - height r | <= 2. - Inline expansion of height for better speed. *) - - let new l x r = - let hl = match l with Empty -> 0 | Node(_,_,_,h) -> h in - let hr = match r with Empty -> 0 | Node(_,_,_,h) -> h in - Node(l, x, r, (if hl >= hr then hl + 1 else hr + 1)) - - (* Same as new, but performs one step of rebalancing if necessary. - Assumes l and r balanced. - Inline expansion of new for better speed in the most frequent case - where no rebalancing is required. *) - - let bal l x 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 "Set.bal" - | Node(ll, lv, lr, _) -> - if height ll >= height lr then - new ll lv (new lr x r) - else begin - match lr with - Empty -> invalid_arg "Set.bal" - | Node(lrl, lrv, lrr, _)-> - new (new ll lv lrl) lrv (new lrr x r) - end - end else if hr > hl + 2 then begin - match r with - Empty -> invalid_arg "Set.bal" - | Node(rl, rv, rr, _) -> - if height rr >= height rl then - new (new l x rl) rv rr - else begin - match rl with - Empty -> invalid_arg "Set.bal" - | Node(rll, rlv, rlr, _) -> - new (new l x rll) rlv (new rlr rv rr) - end - end else - Node(l, x, r, (if hl >= hr then hl + 1 else hr + 1)) - - (* Same as bal, but repeat rebalancing until the final result - is balanced. *) - - let rec join l x r = - match bal l x r with - Empty -> invalid_arg "Set.join" - | Node(l', x', r', _) as t' -> - let d = height l' - height r' in - if d < -2 or d > 2 then join l' x' r' else t' - - (* Merge two trees l and r into one. - All elements of l must precede the elements of r. - Assumes | height l - height r | <= 2. *) - - let rec merge t1 t2 = - match (t1, t2) 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) - - (* Same as merge, but does not assume anything about l and r. *) - - let rec concat t1 t2 = - match (t1, t2) with - (Empty, t) -> t - | (t, Empty) -> t - | (Node(l1, v1, r1, h1), Node(l2, v2, r2, h2)) -> - join l1 v1 (join (concat r1 l2) v2 r2) - - (* Splitting *) - - let rec split x = function - Empty -> - (Empty, None, Empty) - | Node(l, v, r, _) -> - let c = Ord.compare x v in - if c = 0 then (l, Some v, r) - else if c < 0 then - let (ll, vl, rl) = split x l in (ll, vl, join rl v r) - else - let (lr, vr, rr) = split x r in (join l v lr, vr, rr) - - (* Implementation of the set operations *) - - let empty = Empty - - let is_empty = function Empty -> true | _ -> false - - let rec mem x = function - Empty -> false - | Node(l, v, r, _) -> - let c = Ord.compare x v in - if c = 0 then true else - if c < 0 then mem x l else mem x r - - let rec add x = function - Empty -> Node(Empty, x, Empty, 1) - | Node(l, v, r, _) as t -> - let c = Ord.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) - - let rec remove x = function - Empty -> Empty - | Node(l, v, r, _) -> - let c = Ord.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) - - let rec union s1 s2 = - match (s1, s2) with - (Empty, t2) -> t2 - | (t1, Empty) -> t1 - | (Node(l1, v1, r1, _), t2) -> - let (l2, _, r2) = split v1 t2 in - join (union l1 l2) v1 (union r1 r2) - - let rec inter s1 s2 = - match (s1, s2) with - (Empty, t2) -> Empty - | (t1, Empty) -> Empty - | (Node(l1, v1, r1, _), t2) -> - match split v1 t2 with - (l2, None, r2) -> - concat (inter l1 l2) (inter r1 r2) - | (l2, Some _, r2) -> - join (inter l1 l2) v1 (inter r1 r2) - - let rec diff s1 s2 = - match (s1, s2) with - (Empty, t2) -> Empty - | (t1, Empty) -> t1 - | (Node(l1, v1, r1, _), t2) -> - match split v1 t2 with - (l2, None, r2) -> - join (diff l1 l2) v1 (diff r1 r2) - | (l2, Some _, r2) -> - concat (diff l1 l2) (diff r1 r2) - - let rec compare_aux l1 l2 = - match (l1, l2) with - ([], []) -> 0 - | ([], _) -> -1 - | (_, []) -> 1 - | (Empty :: t1, Empty :: t2) -> - compare_aux t1 t2 - | (Node(Empty, v1, r1, _) :: t1, Node(Empty, v2, r2, _) :: t2) -> - let c = Ord.compare v1 v2 in - if c <> 0 then c else compare_aux (r1::t1) (r2::t2) - | (Node(l1, v1, r1, _) :: t1, t2) -> - compare_aux (l1 :: Node(Empty, v1, r1, 0) :: t1) t2 - | (t1, Node(l2, v2, r2, _) :: t2) -> - compare_aux t1 (l2 :: Node(Empty, v2, r2, 0) :: t2) - - let compare s1 s2 = - compare_aux [s1] [s2] - - let equal s1 s2 = - compare s1 s2 = 0 - - let rec iter f = function - Empty -> () - | Node(l, v, r, _) -> iter f l; f v; iter f r - - let rec fold f s accu = - match s with - Empty -> accu - | Node(l, v, r, _) -> fold f l (f v (fold f r accu)) - - let rec elements_aux accu = function - Empty -> accu - | Node(l, v, r, _) -> elements_aux (v :: elements_aux accu r) l - - let elements s = - elements_aux [] s - - let rec choose = function - Empty -> raise Not_found - | Node(Empty, v, r, _) -> v - | Node(l, v, r, _) -> choose l - end |