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
159 let n = (x) lsr 24 in
160 if n != 0 then hbit.(n) lsl 24
161 else let n = (x) lsr 16 in if n != 0 then hbit.(n) lsl 16
162 else let n = (x) lsr 8 in if n != 0 then hbit.(n) lsl 8
165 _ -> raise (Invalid_argument ("highest_bit " ^ (string_of_int x)))
167 let highest_bit64 x =
168 let n = x lsr 32 in if n != 0 then highest_bit n lsl 32
171 let branching_bit p0 p1 = highest_bit64 (p0 lxor p1)
173 let join p0 t0 p1 t1 =
174 let m = branching_bit p0 p1 in
175 if zero_bit p0 m then
176 branch (mask p0 m) m t0 t1
178 branch (mask p0 m) m t1 t0
180 let match_prefix k p m = (mask k m) == p
183 let kid = Uid.to_int (H.uid k) in
185 let rec ins n = match Node.node n with
187 | Leaf j -> if j == k then n else join kid (leaf k) (Uid.to_int (H.uid j)) n
188 | Branch (p,m,t0,t1) ->
189 if match_prefix kid p m then
190 if zero_bit kid m then
191 branch p m (ins t0) t1
193 branch p m t0 (ins t1)
195 join kid (leaf k) p n
200 let kid = Uid.to_int(H.uid k) in
201 let rec rmv n = match Node.node n with
203 | Leaf j -> if k == j then empty else n
204 | Branch (p,m,t0,t1) ->
205 if match_prefix kid p m then
206 if zero_bit kid m then
207 branch_ne p m (rmv t0) t1
209 branch_ne p m t0 (rmv t1)
215 (* should run in O(1) thanks to Hash consing *)
217 let equal a b = Node.equal a b
219 let compare a b = (Uid.to_int (Node.uid a)) - (Uid.to_int (Node.uid b))
222 if (equal s t) (* This is cheap thanks to hash-consing *)
225 match Node.node s, Node.node t with
228 | Leaf k, _ -> add k t
229 | _, Leaf k -> add k s
230 | Branch (p,m,s0,s1), Branch (q,n,t0,t1) ->
231 if m == n && match_prefix q p m then
232 branch p m (merge s0 t0) (merge s1 t1)
233 else if m > n && match_prefix q p m then
235 branch p m (merge s0 t) s1
237 branch p m s0 (merge s1 t)
238 else if m < n && match_prefix p q n then
240 branch q n (merge s t0) t1
242 branch q n t0 (merge s t1)
244 (* The prefixes disagree. *)
250 let rec subset s1 s2 = (equal s1 s2) ||
251 match (Node.node s1,Node.node s2) with
254 | Leaf k1, _ -> mem k1 s2
255 | Branch _, Leaf _ -> false
256 | Branch (p1,m1,l1,r1), Branch (p2,m2,l2,r2) ->
257 if m1 == m2 && p1 == p2 then
258 subset l1 l2 && subset r1 r2
259 else if m1 < m2 && match_prefix p1 p2 m2 then
260 if zero_bit p1 m2 then
261 subset l1 l2 && subset r1 l2
263 subset l1 r2 && subset r1 r2
268 let union s1 s2 = merge s1 s2
269 (* Todo replace with e Memo Module *)
270 module MemUnion = Hashtbl.Make(
274 let equal (x,y) (z,t) = (equal x z)&&(equal y t)
275 let equal a b = equal a b || equal b a
276 let hash (x,y) = (* commutative hash *)
280 if x < y then HASHINT2(x,y) else HASHINT2(y,x)
282 let h_mem = MemUnion.create MED_H_SIZE
284 let mem_union s1 s2 =
285 try MemUnion.find h_mem (s1,s2)
287 let r = merge s1 s2 in MemUnion.add h_mem (s1,s2) r;r
290 let rec inter s1 s2 =
294 match (Node.node s1,Node.node s2) with
297 | Leaf k1, _ -> if mem k1 s2 then s1 else empty
298 | _, Leaf k2 -> if mem k2 s1 then s2 else empty
299 | Branch (p1,m1,l1,r1), Branch (p2,m2,l2,r2) ->
300 if m1 == m2 && p1 == p2 then
301 merge (inter l1 l2) (inter r1 r2)
302 else if m1 > m2 && match_prefix p2 p1 m1 then
303 inter (if zero_bit p2 m1 then l1 else r1) s2
304 else if m1 < m2 && match_prefix p1 p2 m2 then
305 inter s1 (if zero_bit p1 m2 then l2 else r2)
313 match (Node.node s1,Node.node s2) with
316 | Leaf k1, _ -> if mem k1 s2 then empty else s1
317 | _, Leaf k2 -> remove k2 s1
318 | Branch (p1,m1,l1,r1), Branch (p2,m2,l2,r2) ->
319 if m1 == m2 && p1 == p2 then
320 merge (diff l1 l2) (diff r1 r2)
321 else if m1 > m2 && match_prefix p2 p1 m1 then
322 if zero_bit p2 m1 then
323 merge (diff l1 s2) r1
325 merge l1 (diff r1 s2)
326 else if m1 < m2 && match_prefix p1 p2 m2 then
327 if zero_bit p1 m2 then diff s1 l2 else diff s1 r2
332 (*s All the following operations ([cardinal], [iter], [fold], [for_all],
333 [exists], [filter], [partition], [choose], [elements]) are
334 implemented as for any other kind of binary trees. *)
336 let rec cardinal n = match Node.node n with
339 | Branch (_,_,t0,t1) -> cardinal t0 + cardinal t1
341 let rec iter f n = match Node.node n with
344 | Branch (_,_,t0,t1) -> iter f t0; iter f t1
346 let rec fold f s accu = match Node.node s with
349 | Branch (_,_,t0,t1) -> fold f t0 (fold f t1 accu)
352 let rec for_all p n = match Node.node n with
355 | Branch (_,_,t0,t1) -> for_all p t0 && for_all p t1
357 let rec exists p n = match Node.node n with
360 | Branch (_,_,t0,t1) -> exists p t0 || exists p t1
362 let rec filter pr n = match Node.node n with
364 | Leaf k -> if pr k then n else empty
365 | Branch (p,m,t0,t1) -> branch_ne p m (filter pr t0) (filter pr t1)
368 let rec part (t,f as acc) n = match Node.node n with
370 | Leaf k -> if p k then (add k t, f) else (t, add k f)
371 | Branch (_,_,t0,t1) -> part (part acc t0) t1
373 part (empty, empty) s
375 let rec choose n = match Node.node n with
376 | Empty -> raise Not_found
378 | Branch (_, _,t0,_) -> choose t0 (* we know that [t0] is non-empty *)
382 let coll k (l, b, r) =
383 if k < x then add k l, b, r
384 else if k > x then l, b, add k r
387 fold coll s (empty, false, empty)
389 (*s Additional functions w.r.t to [Set.S]. *)
391 let rec intersect s1 s2 = (equal s1 s2) ||
392 match (Node.node s1,Node.node s2) with
395 | Leaf k1, _ -> mem k1 s2
396 | _, Leaf k2 -> mem k2 s1
397 | Branch (p1,m1,l1,r1), Branch (p2,m2,l2,r2) ->
398 if m1 == m2 && p1 == p2 then
399 intersect l1 l2 || intersect r1 r2
400 else if m1 < m2 && match_prefix p2 p1 m1 then
401 intersect (if zero_bit p2 m1 then l1 else r1) s2
402 else if m1 > m2 && match_prefix p1 p2 m2 then
403 intersect s1 (if zero_bit p1 m2 then l2 else r2)
409 let rec uncons n = match Node.node n with
410 | Empty -> raise Not_found
411 | Leaf k -> (k,empty)
412 | Branch (p,m,s,t) -> let h,ns = uncons s in h,branch_ne p m ns t
414 let from_list l = List.fold_left (fun acc e -> add e acc) empty l
420 include S with type elt = int
421 val print : Format.formatter -> t -> unit
425 include Make ( struct type t = int
427 external hash : t -> int = "%identity"
428 external uid : t -> Uid.t = "%identity"
429 external equal : t -> t -> bool = "%eq"
430 external make : t -> int = "%identity"
431 external node : t -> int = "%identity"
432 external stats : unit -> unit = "%identity"
436 Format.pp_print_string ppf "{ ";
437 iter (fun i -> Format.fprintf ppf "%i " i) s;
438 Format.pp_print_string ppf "}";
439 Format.pp_print_flush ppf ()