Source file mapExtPoly.ml
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(** Maps with polymorphic keys and values *)
type ('k,'a) map =
Empty
| Node of ('k,'a) map * 'k * 'a * ('k,'a) map * int
type 'k compare = 'k -> 'k -> int
type ('k,'a) t = {
map: ('k,'a) map;
compare: 'k compare;
}
(** {2 Internal functions with compare parameter} *)
(** ********************************************* *)
let height_ = function
Empty -> 0
| Node(_,_,_,_,h) -> h
let create_ l x d r =
let hl = height_ l and hr = height_ r in
Node(l, x, d, r, (if hl >= hr then hl + 1 else hr + 1))
let singleton_ x d = Node(Empty, x, d, Empty, 1)
let bal_ l x d 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 "Mapext.bal"
| Node(ll, lv, ld, lr, _) ->
if height_ ll >= height_ lr then
create_ ll lv ld (create_ lr x d r)
else begin
match lr with
Empty -> invalid_arg "Mapext.bal"
| Node(lrl, lrv, lrd, lrr, _)->
create_ (create_ ll lv ld lrl) lrv lrd (create_ lrr x d r)
end
end else if hr > hl + 2 then begin
match r with
Empty -> invalid_arg "Mapext.bal"
| Node(rl, rv, rd, rr, _) ->
if height_ rr >= height_ rl then
create_ (create_ l x d rl) rv rd rr
else begin
match rl with
Empty -> invalid_arg "Mapext.bal"
| Node(rll, rlv, rld, rlr, _) ->
create_ (create_ l x d rll) rlv rld (create_ rlr rv rd rr)
end
end else
Node(l, x, d, r, (if hl >= hr then hl + 1 else hr + 1))
let empty_ = Empty
let is_empty_ = function Empty -> true | _ -> false
let is_singleton_ = function Node(Empty, _, _, Empty, _) -> true | _ -> false
let rec add_ compare x data m = match m with
Empty ->
Node(Empty, x, data, Empty, 1)
| Node(l, v, d, r, h) ->
let c = compare x v in
if c = 0 then
if d == data then m else Node(l, x, data, r, h)
else if c < 0 then
let ll = add_ compare x data l in
if l == ll then m else bal_ ll v d r
else
let rr = add_ compare x data r in
if r == rr then m else bal_ l v d rr
let rec find_ compare x = function
Empty ->
raise Not_found
| Node(l, v, d, r, _) ->
let c = compare x v in
if c = 0 then d
else find_ compare x (if c < 0 then l else r)
let rec find_opt_ compare x = function
Empty ->
None
| Node(l, v, d, r, _) ->
let c = compare x v in
if c = 0 then Some d
else find_opt_ compare x (if c < 0 then l else r)
let rec mem_ compare x = function
Empty ->
false
| Node(l, v, d, r, _) ->
let c = compare x v in
c = 0 || mem_ compare x (if c < 0 then l else r)
let rec min_binding_ = function
Empty -> raise Not_found
| Node(Empty, x, d, r, _) -> (x, d)
| Node(l, x, d, r, _) -> min_binding_ l
let rec max_binding_ = function
Empty -> raise Not_found
| Node(l, x, d, Empty, _) -> (x, d)
| Node(l, x, d, r, _) -> max_binding_ r
let rec remove_min_binding_ = function
Empty -> invalid_arg "Mapext.remove_min_elt"
| Node(Empty, x, d, r, _) -> r
| Node(l, x, d, r, _) -> bal_ (remove_min_binding_ l) x d r
let merge_ t1 t2 =
match (t1, t2) with
(Empty, t) -> t
| (t, Empty) -> t
| (_, _) ->
let (x, d) = min_binding_ t2 in
bal_ t1 x d (remove_min_binding_ t2)
let rec remove_ compare x m = match m with
Empty ->
Empty
| Node(l, v, d, r, h) ->
let c = compare x v in
if c = 0 then
merge_ l r
else if c < 0 then
let ll = remove_ compare x l in if l == ll then m else bal_ ll v d r
else
let rr = remove_ compare x r in if r == rr then m else bal_ l v d rr
let rec iter_ f = function
Empty -> ()
| Node(l, v, d, r, _) ->
iter_ f l; f v d; iter_ f r
let rec map_ f = function
Empty ->
Empty
| Node(l, v, d, r, h) ->
let l' = map_ f l in
let d' = f d in
let r' = map_ f r in
Node(l', v, d', r', h)
let rec mapi_ f = function
Empty ->
Empty
| Node(l, v, d, r, h) ->
let l' = mapi_ f l in
let d' = f v d in
let r' = mapi_ f r in
Node(l', v, d', r', h)
let rec fold_ f m accu =
match m with
Empty -> accu
| Node(l, v, d, r, _) ->
fold_ f r (f v d (fold_ f l accu))
let rec for_all_ p = function
Empty -> true
| Node(l, v, d, r, _) -> for_all_ p l && p v d && for_all_ p r
let rec exists_ p = function
Empty -> false
| Node(l, v, d, r, _) -> exists_ p l || p v d || exists_ p r
let filter_ compare p s =
fold_ (fun k d a -> if p k d then add_ compare k d a else a) s Empty
let partition_ compare p s =
let rec part (t, f as accu) = function
| Empty -> accu
| Node(l, v, d, r, _) ->
part (part (if p v d then (add_ compare v d t, f) else (t, add_ compare v d f)) l) r in
part (Empty, Empty) s
let rec join_ compare l v d r =
match (l, r) with
(Empty, _) -> add_ compare v d r
| (_, Empty) -> add_ compare v d l
| (Node(ll, lv, ld, lr, lh), Node(rl, rv, rd, rr, rh)) ->
if lh > rh + 2 then bal_ ll lv ld (join_ compare lr v d r) else
if rh > lh + 2 then bal_ (join_ compare l v d rl) rv rd rr else
create_ l v d r
let concat_ compare t1 t2 =
match (t1, t2) with
(Empty, t) -> t
| (t, Empty) -> t
| (_, _) ->
let (x, d) = min_binding_ t2 in
join_ compare t1 x d (remove_min_binding_ t2)
let concat_or_join_ compare t1 v d t2 =
match d with
| Some d -> join_ compare t1 v d t2
| None -> concat_ compare t1 t2
let of_list_ compare l =
List.fold_left (fun acc (k,x) -> add_ compare k x acc) empty_ l
let rec cut_ compare k = function
Empty -> Empty,None,Empty
| Node (l1,k1,d1,r1,h1) ->
let c = compare k k1 in
if c < 0 then
let l2,d2,r2 = cut_ compare k l1 in (l2,d2,Node (r2,k1,d1,r1,h1))
else if c > 0 then
let l2,d2,r2 = cut_ compare k r1 in (Node (l1,k1,d1,l2,h1),d2,r2)
else (l1,Some d1,r1)
let rec for_all2zo_ compare f1 f2 f m1 m2 =
(m1 == m2) ||
(match m1 with
| Empty -> for_all_ f2 m2
| Node (l1,k,d1,r1,h1) ->
let l2, d2, r2 = cut_ compare k m2 in
(for_all2zo_ compare f1 f2 f l1 l2) &&
(match d2 with None -> f1 k d1 | Some d2 -> d1 == d2 || f k d1 d2) &&
(for_all2zo_ compare f1 f2 f r1 r2)
)
let rec map2zo_ compare f1 f2 f m1 m2 =
if m1 == m2 then m1 else
match m1 with
| Empty -> mapi_ f2 m2
| Node (l1,k,d1,r1,h1) ->
let l2, d2, r2 = cut_ compare k m2 in
let l = map2zo_ compare f1 f2 f l1 l2 in
let d = match d2 with
| None -> f1 k d1
| Some d2 -> if d1 == d2 then d1 else f k d1 d2
in
let r = map2zo_ compare f1 f2 f r1 r2 in
join_ compare l k d r
let rec split_ compare x = function
Empty ->
(Empty, None, Empty)
| Node(l, v, d, r, _) ->
let c = compare x v in
if c = 0 then (l, Some d, r)
else if c < 0 then
let (ll, pres, rl) = split_ compare x l in (ll, pres, join_ compare rl v d r)
else
let (lr, pres, rr) = split_ compare x r in (join_ compare l v d lr, pres, rr)
let rec merge_ compare f s1 s2 =
match (s1, s2) with
(Empty, Empty) -> Empty
| (Node (l1, v1, d1, r1, h1), _) when h1 >= height_ s2 ->
let (l2, d2, r2) = split_ compare v1 s2 in
concat_or_join_ compare (merge_ compare f l1 l2) v1 (f v1 (Some d1) d2) (merge_ compare f r1 r2)
| (_, Node (l2, v2, d2, r2, h2)) ->
let (l1, d1, r1) = split_ compare v2 s1 in
concat_or_join_ compare (merge_ compare f l1 l2) v2 (f v2 d1 (Some d2)) (merge_ compare f r1 r2)
| _ ->
assert false
let rec bindings_aux_ accu = function
Empty -> accu
| Node(l, v, d, r, _) -> bindings_aux_ ((v, d) :: bindings_aux_ accu r) l
let bindings_ s =
bindings_aux_ [] s
let rec cardinal_ = function
Empty -> 0
| Node(l, _, _, r, _) -> cardinal_ l + 1 + cardinal_ r
let rec fold2zo_ compare f1 f2 f m1 m2 acc =
if m1 == m2 then acc else
match m1 with
| Empty -> fold_ f2 m2 acc
| Node (l1,k,d1,r1,h1) ->
let l2, d2, r2 = cut_ compare k m2 in
let acc = fold2zo_ compare f1 f2 f l1 l2 acc in
let acc = match d2 with
| None -> f1 k d1 acc
| Some d2 -> if d1 == d2 then acc else f k d1 d2 acc
in
fold2zo_ compare f1 f2 f r1 r2 acc
let rec fold2o_ compare f1 f2 f m1 m2 acc =
match m1 with
| Empty -> fold_ f2 m2 acc
| Node (l1,k,d1,r1,h1) ->
let l2, d2, r2 = cut_ compare k m2 in
let acc = fold2o_ compare f1 f2 f l1 l2 acc in
let acc = match d2 with
| None -> f1 k d1 acc | Some d2 -> f k d1 d2 acc
in
fold2o_ compare f1 f2 f r1 r2 acc
let rec iter_ f = function
Empty -> ()
| Node(l, v, d, r, _) ->
iter_ f l; f v d; iter_ f r
let rec iter2zo_ compare f1 f2 f m1 m2 =
if m1 == m2 then () else
match m1 with
| Empty -> iter_ f2 m2
| Node (l1,k,d1,r1,h1) ->
let l2, d2, r2 = cut_ compare k m2 in
iter2zo_ compare f1 f2 f l1 l2;
(match d2 with
| None -> f1 k d1
| Some d2 -> if d1 != d2 then f k d1 d2);
iter2zo_ compare f1 f2 f r1 r2
let compare_ compare cmp m1 m2 =
let r = ref 0 in
try
iter2zo_ compare
(fun _ _ -> r := 1; raise Exit)
(fun _ _ -> r := -1; raise Exit)
(fun _ x y -> r := cmp x y; if !r <> 0 then raise Exit)
m1 m2;
!r
with Exit -> !r
(** {2 Exported functions} *)
(** ********************** *)
let singleton ~compare x d = { map = singleton_ x d; compare }
let empty ~compare = { map = empty_; compare }
let is_empty m = is_empty_ m.map
let is_singleton m = is_singleton_ m.map
let add x data m =
let map = add_ m.compare x data m.map in
if m.map == map then m else { m with map }
let find x m = find_ m.compare x m.map
let find_opt x m = find_opt_ m.compare x m.map
let mem x m = mem_ m.compare x m.map
let min_binding m = min_binding_ m.map
let remove_min_binding m = { m with map = remove_min_binding_ m.map }
let remove x m =
let map = remove_ m.compare x m.map in
if map == m.map then m else { m with map }
let max_binding m = max_binding_ m.map
let iter f m = iter_ f m.map
let map f m = { m with map = map_ f m.map }
let mapi f m = { m with map = mapi_ f m.map }
let fold f m accu = fold_ f m.map accu
let for_all p m = for_all_ p m.map
let exists p m = exists_ p m.map
let filter p s =
let map = filter_ s.compare p s.map in
if map == s.map then s else { s with map }
let partition p s =
let map1,map2 = partition_ s.compare p s.map in
(if map1 == s.map then s else { s with map = map1 }),
(if map2 == s.map then s else { s with map = map2 })
let for_all2zo f1 f2 f m1 m2 =
for_all2zo_ m1.compare f1 f2 f m1.map m2.map
let map2zo f1 f2 f m1 m2 =
let map = map2zo_ m1.compare f1 f2 f m1.map m2.map in
if map == m1.map then m1
else if map == m2.map then m2
else { map; compare = m1.compare }
let merge f m1 m2 =
let map = merge_ m1.compare f m1.map m2.map in
{ map; compare = m1.compare }
let bindings s = bindings_ s.map
let cardinal s = cardinal_ s.map
let fold2zo f1 f2 f m1 m2 acc =
fold2zo_ m1.compare f1 f2 f m1.map m2.map acc
let fold2o f1 f2 f m1 m2 acc =
fold2o_ m1.compare f1 f2 f m1.map m2.map acc
let compare cmp m1 m2 = compare_ m1.compare cmp m1.map m2.map
let of_list compare l = {map = of_list_ compare l; compare}
let choose = min_binding