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Diffstat (limited to 'ocaml-binary-annot/stdlib/set.ml')
| -rw-r--r-- | ocaml-binary-annot/stdlib/set.ml | 330 |
1 files changed, 330 insertions, 0 deletions
diff --git a/ocaml-binary-annot/stdlib/set.ml b/ocaml-binary-annot/stdlib/set.ml new file mode 100644 index 0000000000..375fc5d0e4 --- /dev/null +++ b/ocaml-binary-annot/stdlib/set.ml @@ -0,0 +1,330 @@ +(***********************************************************************) +(* *) +(* Objective Caml *) +(* *) +(* Xavier Leroy, projet Cristal, INRIA Rocquencourt *) +(* *) +(* Copyright 1996 Institut National de Recherche en Informatique et *) +(* en Automatique. All rights reserved. This file is distributed *) +(* under the terms of the GNU Library General Public License, with *) +(* the special exception on linking described in file ../LICENSE. *) +(* *) +(***********************************************************************) + +(* $Id$ *) + +(* 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 singleton: elt -> 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 subset: t -> t -> bool + val iter: (elt -> unit) -> t -> unit + val fold: (elt -> 'a -> 'a) -> t -> 'a -> 'a + val for_all: (elt -> bool) -> t -> bool + val exists: (elt -> bool) -> t -> bool + val filter: (elt -> bool) -> t -> t + val partition: (elt -> bool) -> t -> t * t + val cardinal: t -> int + val elements: t -> elt list + val min_elt: t -> elt + val max_elt: t -> elt + val choose: t -> elt + val split: elt -> t -> t * bool * t + end + +module Make(Ord: OrderedType) = + 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 v and right son r. + We must have all elements of l < v < all elements of r. + l and r must be balanced and | height l - height r | <= 2. + Inline expansion of height for better speed. *) + + let create l v 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, v, r, (if hl >= hr then hl + 1 else hr + 1)) + + (* Same as create, but performs one step of rebalancing if necessary. + Assumes l and r balanced and | height l - height r | <= 3. + Inline expansion of create for better speed in the most frequent case + where no rebalancing is required. *) + + let bal l v 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 + create ll lv (create lr v r) + else begin + match lr with + Empty -> invalid_arg "Set.bal" + | Node(lrl, lrv, lrr, _)-> + create (create ll lv lrl) lrv (create lrr v 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 + create (create l v rl) rv rr + else begin + match rl with + Empty -> invalid_arg "Set.bal" + | Node(rll, rlv, rlr, _) -> + create (create l v rll) rlv (create rlr rv rr) + end + end else + Node(l, v, r, (if hl >= hr then hl + 1 else hr + 1)) + + (* Insertion of one element *) + + 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) + + (* Same as create and bal, but no assumptions are made on the + relative heights of l and r. *) + + let rec join l v r = + match (l, r) with + (Empty, _) -> add v r + | (_, Empty) -> add v l + | (Node(ll, lv, lr, lh), Node(rl, rv, rr, rh)) -> + if lh > rh + 2 then bal ll lv (join lr v r) else + if rh > lh + 2 then bal (join l v rl) rv rr else + create l v r + + (* Smallest and greatest element of a set *) + + let rec min_elt = function + Empty -> raise Not_found + | Node(Empty, v, r, _) -> v + | Node(l, v, r, _) -> min_elt l + + let rec max_elt = function + Empty -> raise Not_found + | Node(l, v, Empty, _) -> v + | Node(l, v, r, _) -> max_elt r + + (* Remove the smallest element of the given set *) + + let rec remove_min_elt = function + Empty -> invalid_arg "Set.remove_min_elt" + | Node(Empty, v, r, _) -> r + | Node(l, v, r, _) -> bal (remove_min_elt l) v r + + (* Merge two trees l and r into one. + All elements of l must precede the elements of r. + Assume | height l - height r | <= 2. *) + + let merge t1 t2 = + match (t1, t2) with + (Empty, t) -> t + | (t, Empty) -> t + | (_, _) -> bal t1 (min_elt t2) (remove_min_elt t2) + + (* Merge two trees l and r into one. + All elements of l must precede the elements of r. + No assumption on the heights of l and r. *) + + let concat t1 t2 = + match (t1, t2) with + (Empty, t) -> t + | (t, Empty) -> t + | (_, _) -> join t1 (min_elt t2) (remove_min_elt t2) + + (* Splitting. split x s returns a triple (l, present, r) where + - l is the set of elements of s that are < x + - r is the set of elements of s that are > x + - present is false if s contains no element equal to x, + or true if s contains an element equal to x. *) + + let rec split x = function + Empty -> + (Empty, false, Empty) + | Node(l, v, r, _) -> + let c = Ord.compare x v in + if c = 0 then (l, true, r) + else if c < 0 then + let (ll, pres, rl) = split x l in (ll, pres, join rl v r) + else + let (lr, pres, rr) = split x r in (join l v lr, pres, 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 + c = 0 || mem x (if c < 0 then l else r) + + let singleton x = Node(Empty, x, Empty, 1) + + 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, h1), Node(l2, v2, r2, h2)) -> + if h1 >= h2 then + if h2 = 1 then add v2 s1 else begin + let (l2, _, r2) = split v1 s2 in + join (union l1 l2) v1 (union r1 r2) + end + else + if h1 = 1 then add v1 s2 else begin + let (l1, _, r1) = split v2 s1 in + join (union l1 l2) v2 (union r1 r2) + end + + 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, false, r2) -> + concat (inter l1 l2) (inter r1 r2) + | (l2, true, 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, false, r2) -> + join (diff l1 l2) v1 (diff r1 r2) + | (l2, true, r2) -> + concat (diff l1 l2) (diff r1 r2) + + type enumeration = End | More of elt * t * enumeration + + let rec cons_enum s e = + match s with + Empty -> e + | Node(l, v, r, _) -> cons_enum l (More(v, r, e)) + + let rec compare_aux e1 e2 = + match (e1, e2) with + (End, End) -> 0 + | (End, _) -> -1 + | (_, End) -> 1 + | (More(v1, r1, e1), More(v2, r2, e2)) -> + let c = Ord.compare v1 v2 in + if c <> 0 + then c + else compare_aux (cons_enum r1 e1) (cons_enum r2 e2) + + let compare s1 s2 = + compare_aux (cons_enum s1 End) (cons_enum s2 End) + + let equal s1 s2 = + compare s1 s2 = 0 + + let rec subset s1 s2 = + match (s1, s2) with + Empty, _ -> + true + | _, Empty -> + false + | Node (l1, v1, r1, _), (Node (l2, v2, r2, _) as t2) -> + let c = Ord.compare v1 v2 in + if c = 0 then + subset l1 l2 && subset r1 r2 + else if c < 0 then + subset (Node (l1, v1, Empty, 0)) l2 && subset r1 t2 + else + subset (Node (Empty, v1, r1, 0)) r2 && subset l1 t2 + + 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 r (f v (fold f l accu)) + + let rec for_all p = function + Empty -> true + | Node(l, v, r, _) -> p v && for_all p l && for_all p r + + let rec exists p = function + Empty -> false + | Node(l, v, r, _) -> p v || exists p l || exists p r + + let filter p s = + let rec filt accu = function + | Empty -> accu + | Node(l, v, r, _) -> + filt (filt (if p v then add v accu else accu) l) r in + filt Empty s + + let partition p s = + let rec part (t, f as accu) = function + | Empty -> accu + | Node(l, v, r, _) -> + part (part (if p v then (add v t, f) else (t, add v f)) l) r in + part (Empty, Empty) s + + let rec cardinal = function + Empty -> 0 + | Node(l, v, r, _) -> cardinal l + 1 + cardinal r + + 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 choose = min_elt + + end |