1 (* Copied from OCaml's set.ml *)
3 type 'a set = Empty | Node of 'a set * 'a * 'a set * int
7 let is_empty = function Empty -> true | Node _ -> false
11 | Node(_, _, _, h) -> h
14 let hl = match l with Empty -> 0 | Node(_,_,_,h) -> h in
15 let hr = match r with Empty -> 0 | Node(_,_,_,h) -> h in
16 Node(l, v, r, (if hl >= hr then hl + 1 else hr + 1))
19 let hl = match l with Empty -> 0 | Node(_,_,_,h) -> h in
20 let hr = match r with Empty -> 0 | Node(_,_,_,h) -> h in
21 if hl > hr + 2 then begin
23 Empty -> invalid_arg "Set.bal"
24 | Node(ll, lv, lr, _) ->
25 if height ll >= height lr then
26 create ll lv (create lr v r)
29 Empty -> invalid_arg "Set.bal"
30 | Node(lrl, lrv, lrr, _)->
31 create (create ll lv lrl) lrv (create lrr v r)
33 end else if hr > hl + 2 then begin
35 Empty -> invalid_arg "Set.bal"
36 | Node(rl, rv, rr, _) ->
37 if height rr >= height rl then
38 create (create l v rl) rv rr
41 Empty -> invalid_arg "Set.bal"
42 | Node(rll, rlv, rlr, _) ->
43 create (create l v rll) rlv (create rlr rv rr)
46 Node(l, v, r, (if hl >= hr then hl + 1 else hr + 1))
48 let rec add x = function
49 Empty -> Node(Empty, x, Empty, 1)
50 | Node(l, v, r, _) as t ->
51 let c = compare x v in
53 if c < 0 then bal (add x l) v r else bal l v (add x r)
55 let singleton elt = add elt Empty
57 let rec min_elt = function
58 Empty -> raise Not_found
59 | Node(Empty, v, r, _) -> v
60 | Node(l, v, r, _) -> min_elt l
62 let rec remove_min_elt = function
63 Empty -> invalid_arg "Set.remove_min_elt"
64 | Node(Empty, v, r, _) -> r
65 | Node(l, v, r, _) -> bal (remove_min_elt l) v r
71 | (_, _) -> bal t1 (min_elt t2) (remove_min_elt t2)
73 let rec remove x = function
76 let c = compare x v in
77 if c = 0 then merge l r else
78 if c < 0 then bal (remove x l) v r else bal l v (remove x r)
80 let rec fold f s accu =
83 | Node(l, v, r, _) -> fold f r (f v (fold f l accu))
85 let rec iter f = function
87 | Node(l, v, r, _) -> iter f l; f v; iter f r
89 let rec cardinal = function
91 | Node(l, v, r, _) -> cardinal l + 1 + cardinal r
96 | (_, Empty) -> add v l
97 | (Node(ll, lv, lr, lh), Node(rl, rv, rr, rh)) ->
98 if lh > rh + 2 then bal ll lv (join lr v r) else
99 if rh > lh + 2 then bal (join l v rl) rv rr else
102 let rec split x = function
104 (Empty, false, Empty)
105 | Node(l, v, r, _) ->
106 let c = compare x v in
107 if c = 0 then (l, true, r)
109 let (ll, pres, rl) = split x l in (ll, pres, join rl v r)
111 let (lr, pres, rr) = split x r in (join l v lr, pres, rr)
113 let rec union s1 s2 =
117 | (Node(l1, v1, r1, h1), Node(l2, v2, r2, h2)) ->
119 if h2 = 1 then add v2 s1 else begin
120 let (l2, _, r2) = split v1 s2 in
121 join (union l1 l2) v1 (union r1 r2)
124 if h1 = 1 then add v1 s2 else begin
125 let (l1, _, r1) = split v2 s1 in
126 join (union l1 l2) v2 (union r1 r2)
133 | (_, _) -> join t1 (min_elt t2) (remove_min_elt t2)
135 let rec mem x = function
137 | Node(l, v, r, _) ->
138 let c = compare x v in
139 c = 0 || mem x (if c < 0 then l else r)
141 let rec for_all p = function
143 | Node(l, v, r, _) -> p v && for_all p l && for_all p r
145 let rec exists p = function
147 | Node(l, v, r, _) -> p v || exists p l || exists p r
149 let rec subset s1 s2 =
155 | Node (l1, v1, r1, _), (Node (l2, v2, r2, _) as t2) ->
156 let c = compare v1 v2 in
158 subset l1 l2 && subset r1 r2
160 subset (Node (l1, v1, Empty, 0)) l2 && subset r1 t2
162 subset (Node (Empty, v1, r1, 0)) r2 && subset l1 t2
168 | (Node(l1, v1, r1, _), t2) ->
169 match split v1 t2 with
171 join (diff l1 l2) v1 (diff r1 r2)
173 concat (diff l1 l2) (diff r1 r2)
175 type 'a enumeration = End | More of 'a * 'a set * 'a enumeration
177 let rec cons_enum s e =
180 | Node(l, v, r, _) -> cons_enum l (More(v, r, e))
182 let rec compare_aux e1 e2 =
187 | (More(v1, r1, e1), More(v2, r2, e2)) ->
188 let c = compare v1 v2 in
191 else compare_aux (cons_enum r1 e1) (cons_enum r2 e2)
194 compare_aux (cons_enum s1 End) (cons_enum s2 End)