1 (***************************************************************************)
2 (* Implementation for sets of positive integers implemented as deeply hash-*)
3 (* consed Patricia trees. Provide fast set operations, fast membership as *)
4 (* well as fast min and max elements. Hash consing provides O(1) equality *)
7 (***************************************************************************)
15 include Hcons.S with type data = Data.t
19 Hashtbl.HashedType with type t = Node.t node
26 val is_empty : t -> bool
27 val mem : elt -> t -> bool
28 val add : elt -> t -> t
29 val singleton : elt -> t
30 val remove : elt -> t -> t
31 val union : t -> t -> t
32 val inter : t -> t -> t
33 val diff : t -> t -> t
34 val compare : t -> t -> int
35 val equal : t -> t -> bool
36 val subset : t -> t -> bool
37 val iter : (elt -> unit) -> t -> unit
38 val fold : (elt -> 'a -> 'a) -> t -> 'a -> 'a
39 val for_all : (elt -> bool) -> t -> bool
40 val exists : (elt -> bool) -> t -> bool
41 val filter : (elt -> bool) -> t -> t
42 val partition : (elt -> bool) -> t -> t * t
43 val cardinal : t -> int
44 val elements : t -> elt list
45 val min_elt : t -> elt
46 val max_elt : t -> elt
48 val split : elt -> t -> t * bool * t
50 val intersect : t -> t -> bool
51 val is_singleton : t -> bool
52 val mem_union : t -> t -> t
55 val uncons : t -> elt*t
56 val from_list : elt list -> t
59 val stats : unit -> unit
62 module Make ( H : Hcons.SA ) : S with type elt = H.t =
68 | Branch of int * int * 'a * 'a
70 module rec Node : Hcons.S with type data = Data.t = Hcons.Make (Data)
71 and Data : Hashtbl.HashedType with type t = Node.t node =
77 | Leaf k1, Leaf k2 -> k1 == k2
78 | Branch(b1,i1,l1,r1),Branch(b2,i2,l2,r2) ->
79 b1 == b2 && i1 == i2 &&
85 | Leaf i -> HASHINT2(HALF_MAX_INT,Uid.to_int (H.uid i))
86 | Branch (b,i,l,r) -> HASHINT4(b,i,Uid.to_int l.Node.id, Uid.to_int r.Node.id)
91 let stats = Node.stats
95 let node _ = failwith "node"
96 let empty = Node.make Empty
98 let is_empty s = (Node.node s) == Empty
100 let branch p m l r = Node.make (Branch(p,m,l,r))
102 let leaf k = Node.make (Leaf k)
104 (* To enforce the invariant that a branch contains two non empty sub-trees *)
105 let branch_ne p m t0 t1 =
106 if (is_empty t0) then t1
107 else if is_empty t1 then t0 else branch p m t0 t1
109 (********** from here on, only use the smart constructors *************)
111 let zero_bit k m = (k land m) == 0
113 let singleton k = leaf k
116 match Node.node n with Leaf _ -> true
120 let kid = Uid.to_int (H.uid k) in
121 let rec loop n = match Node.node n with
124 | Branch (p, _, l, r) -> if kid <= p then loop l else loop r
127 let rec min_elt n = match Node.node n with
128 | Empty -> raise Not_found
130 | Branch (_,_,s,_) -> min_elt s
132 let rec max_elt n = match Node.node n with
133 | Empty -> raise Not_found
135 | Branch (_,_,_,t) -> max_elt t
138 let rec elements_aux acc n = match Node.node n with
141 | Branch (_,_,l,r) -> elements_aux (elements_aux acc r) l
145 let mask k m = (k lor (m-1)) land (lnot m)
147 let naive_highest_bit x =
150 if i = 0 then 1 else if x lsr i = 1 then 1 lsl i else loop (i-1)
154 let hbit = Array.init 256 naive_highest_bit
156 external clz : int -> int = "caml_clz" "noalloc"
157 external leading_bit : int -> int = "caml_leading_bit" "noalloc"
160 let n = (x) lsr 24 in
161 if n != 0 then hbit.(n) lsl 24
162 else let n = (x) lsr 16 in if n != 0 then hbit.(n) lsl 16
163 else let n = (x) lsr 8 in if n != 0 then hbit.(n) lsl 8
166 _ -> raise (Invalid_argument ("highest_bit " ^ (string_of_int x)))
168 let highest_bit64 x =
169 let n = x lsr 32 in if n != 0 then highest_bit n lsl 32
172 let branching_bit p0 p1 = leading_bit (p0 lxor p1)
174 let join p0 t0 p1 t1 =
175 let m = branching_bit p0 p1 in
176 let msk = mask p0 m in
177 if zero_bit p0 m then
178 branch_ne msk m t0 t1
180 branch_ne msk m t1 t0
182 let match_prefix k p m = (mask k m) == p
185 let kid = Uid.to_int (H.uid k) in
187 let rec ins n = match Node.node n with
189 | Leaf j -> if j == k then n else join kid (leaf k) (Uid.to_int (H.uid j)) n
190 | Branch (p,m,t0,t1) ->
191 if match_prefix kid p m then
192 if zero_bit kid m then
193 branch_ne p m (ins t0) t1
195 branch_ne p m t0 (ins t1)
197 join kid (leaf k) p n
202 let kid = Uid.to_int(H.uid k) in
203 let rec rmv n = match Node.node n with
205 | Leaf j -> if k == j then empty else n
206 | Branch (p,m,t0,t1) ->
207 if match_prefix kid p m then
208 if zero_bit kid m then
209 branch_ne p m (rmv t0) t1
211 branch_ne p m t0 (rmv t1)
217 (* should run in O(1) thanks to Hash consing *)
219 let equal a b = Node.equal a b
221 let compare a b = (Uid.to_int (Node.uid a)) - (Uid.to_int (Node.uid b))
224 if (equal s t) (* This is cheap thanks to hash-consing *)
227 match Node.node s, Node.node t with
230 | Leaf k, _ -> add k t
231 | _, Leaf k -> add k s
232 | Branch (p,m,s0,s1), Branch (q,n,t0,t1) ->
233 if m == n && match_prefix q p m then
234 branch p m (merge s0 t0) (merge s1 t1)
235 else if m > n && match_prefix q p m then
237 branch_ne p m (merge s0 t) s1
239 branch_ne p m s0 (merge s1 t)
240 else if m < n && match_prefix p q n then
242 branch_ne q n (merge s t0) t1
244 branch_ne q n t0 (merge s t1)
246 (* The prefixes disagree. *)
252 let rec subset s1 s2 = (equal s1 s2) ||
253 match (Node.node s1,Node.node s2) with
256 | Leaf k1, _ -> mem k1 s2
257 | Branch _, Leaf _ -> false
258 | Branch (p1,m1,l1,r1), Branch (p2,m2,l2,r2) ->
259 if m1 == m2 && p1 == p2 then
260 subset l1 l2 && subset r1 r2
261 else if m1 < m2 && match_prefix p1 p2 m2 then
262 if zero_bit p1 m2 then
263 subset l1 l2 && subset r1 l2
265 subset l1 r2 && subset r1 r2
270 let union s1 s2 = merge s1 s2
271 (* Todo replace with e Memo Module *)
272 module MemUnion = Hashtbl.Make(
276 let equal (x,y) (z,t) = (equal x z)&&(equal y t)
277 let equal a b = equal a b || equal b a
278 let hash (x,y) = (* commutative hash *)
282 if x < y then HASHINT2(x,y) else HASHINT2(y,x)
284 let h_mem = MemUnion.create MED_H_SIZE
286 let mem_union s1 s2 =
287 try MemUnion.find h_mem (s1,s2)
289 let r = merge s1 s2 in MemUnion.add h_mem (s1,s2) r;r
292 let rec inter s1 s2 =
296 match (Node.node s1,Node.node s2) with
299 | Leaf k1, _ -> if mem k1 s2 then s1 else empty
300 | _, Leaf k2 -> if mem k2 s1 then s2 else empty
301 | Branch (p1,m1,l1,r1), Branch (p2,m2,l2,r2) ->
302 if m1 == m2 && p1 == p2 then
303 merge (inter l1 l2) (inter r1 r2)
304 else if m1 > m2 && match_prefix p2 p1 m1 then
305 inter (if zero_bit p2 m1 then l1 else r1) s2
306 else if m1 < m2 && match_prefix p1 p2 m2 then
307 inter s1 (if zero_bit p1 m2 then l2 else r2)
315 match (Node.node s1,Node.node s2) with
318 | Leaf k1, _ -> if mem k1 s2 then empty else s1
319 | _, Leaf k2 -> remove k2 s1
320 | Branch (p1,m1,l1,r1), Branch (p2,m2,l2,r2) ->
321 if m1 == m2 && p1 == p2 then
322 merge (diff l1 l2) (diff r1 r2)
323 else if m1 > m2 && match_prefix p2 p1 m1 then
324 if zero_bit p2 m1 then
325 merge (diff l1 s2) r1
327 merge l1 (diff r1 s2)
328 else if m1 < m2 && match_prefix p1 p2 m2 then
329 if zero_bit p1 m2 then diff s1 l2 else diff s1 r2
334 (*s All the following operations ([cardinal], [iter], [fold], [for_all],
335 [exists], [filter], [partition], [choose], [elements]) are
336 implemented as for any other kind of binary trees. *)
338 let rec cardinal n = match Node.node n with
341 | Branch (_,_,t0,t1) -> cardinal t0 + cardinal t1
343 let rec iter f n = match Node.node n with
346 | Branch (_,_,t0,t1) -> iter f t0; iter f t1
348 let rec fold f s accu = match Node.node s with
351 | Branch (_,_,t0,t1) -> fold f t0 (fold f t1 accu)
354 let rec for_all p n = match Node.node n with
357 | Branch (_,_,t0,t1) -> for_all p t0 && for_all p t1
359 let rec exists p n = match Node.node n with
362 | Branch (_,_,t0,t1) -> exists p t0 || exists p t1
364 let rec filter pr n = match Node.node n with
366 | Leaf k -> if pr k then n else empty
367 | Branch (p,m,t0,t1) -> branch_ne p m (filter pr t0) (filter pr t1)
370 let rec part (t,f as acc) n = match Node.node n with
372 | Leaf k -> if p k then (add k t, f) else (t, add k f)
373 | Branch (_,_,t0,t1) -> part (part acc t0) t1
375 part (empty, empty) s
377 let rec choose n = match Node.node n with
378 | Empty -> raise Not_found
380 | Branch (_, _,t0,_) -> choose t0 (* we know that [t0] is non-empty *)
384 let coll k (l, b, r) =
385 if k < x then add k l, b, r
386 else if k > x then l, b, add k r
389 fold coll s (empty, false, empty)
391 (*s Additional functions w.r.t to [Set.S]. *)
393 let rec intersect s1 s2 = (equal s1 s2) ||
394 match (Node.node s1,Node.node s2) with
397 | Leaf k1, _ -> mem k1 s2
398 | _, Leaf k2 -> mem k2 s1
399 | Branch (p1,m1,l1,r1), Branch (p2,m2,l2,r2) ->
400 if m1 == m2 && p1 == p2 then
401 intersect l1 l2 || intersect r1 r2
402 else if m1 < m2 && match_prefix p2 p1 m1 then
403 intersect (if zero_bit p2 m1 then l1 else r1) s2
404 else if m1 > m2 && match_prefix p1 p2 m2 then
405 intersect s1 (if zero_bit p1 m2 then l2 else r2)
411 let rec uncons n = match Node.node n with
412 | Empty -> raise Not_found
413 | Leaf k -> (k,empty)
414 | Branch (p,m,s,t) -> let h,ns = uncons s in h,branch_ne p m ns t
416 let from_list l = List.fold_left (fun acc e -> add e acc) empty l
422 include S with type elt = int
423 val print : Format.formatter -> t -> unit
427 include Make ( struct type t = int
429 external hash : t -> int = "%identity"
430 external uid : t -> Uid.t = "%identity"
431 external equal : t -> t -> bool = "%eq"
432 external make : t -> int = "%identity"
433 external node : t -> int = "%identity"
434 external stats : unit -> unit = "%identity"
438 Format.pp_print_string ppf "{ ";
439 iter (fun i -> Format.fprintf ppf "%i " i) s;
440 Format.pp_print_string ppf "}";
441 Format.pp_print_flush ppf ()