1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
|
%%
%% %CopyrightBegin%
%%
%% Copyright Ericsson AB 2000-2015. All Rights Reserved.
%%
%% Licensed under the Apache License, Version 2.0 (the "License");
%% you may not use this file except in compliance with the License.
%% You may obtain a copy of the License at
%%
%% http://www.apache.org/licenses/LICENSE-2.0
%%
%% Unless required by applicable law or agreed to in writing, software
%% distributed under the License is distributed on an "AS IS" BASIS,
%% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
%% See the License for the specific language governing permissions and
%% limitations under the License.
%%
%% %CopyrightEnd%
%%
-module(cerl_sets).
%% Standard interface.
-export([new/0,is_set/1,size/1,to_list/1,from_list/1]).
-export([is_element/2,add_element/2,del_element/2]).
-export([union/2,union/1,intersection/2,intersection/1]).
-export([is_disjoint/2]).
-export([subtract/2,is_subset/2]).
-export([fold/3,filter/2]).
-export_type([set/0, set/1]).
%%------------------------------------------------------------------------------
-type set() :: set(_).
-opaque set(Element) :: #{Element => 'ok'}.
%%------------------------------------------------------------------------------
%% new() -> Set
-spec new() -> set().
new() -> #{}.
%% is_set(Set) -> boolean().
%% Return 'true' if Set is a set of elements, else 'false'.
-spec is_set(Set) -> boolean() when
Set :: term().
is_set(S) when is_map(S) -> true;
is_set(_) -> false.
%% size(Set) -> int().
%% Return the number of elements in Set.
-spec size(Set) -> non_neg_integer() when
Set :: set().
size(S) -> maps:size(S).
%% to_list(Set) -> [Elem].
%% Return the elements in Set as a list.
-spec to_list(Set) -> List when
Set :: set(Element),
List :: [Element].
to_list(S) -> maps:keys(S).
%% from_list([Elem]) -> Set.
%% Build a set from the elements in List.
-spec from_list(List) -> Set when
List :: [Element],
Set :: set(Element).
from_list(Ls) -> maps:from_list([{K,ok}||K<-Ls]).
%% is_element(Element, Set) -> boolean().
%% Return 'true' if Element is an element of Set, else 'false'.
-spec is_element(Element, Set) -> boolean() when
Set :: set(Element).
is_element(E,S) ->
case S of
#{E := _} -> true;
_ -> false
end.
%% add_element(Element, Set) -> Set.
%% Return Set with Element inserted in it.
-spec add_element(Element, Set1) -> Set2 when
Set1 :: set(Element),
Set2 :: set(Element).
add_element(E,S) -> S#{E=>ok}.
-spec del_element(Element, Set1) -> Set2 when
Set1 :: set(Element),
Set2 :: set(Element).
%% del_element(Element, Set) -> Set.
%% Return Set but with Element removed.
del_element(E,S) -> maps:remove(E,S).
%% union(Set1, Set2) -> Set
%% Return the union of Set1 and Set2.
-spec union(Set1, Set2) -> Set3 when
Set1 :: set(Element),
Set2 :: set(Element),
Set3 :: set(Element).
union(S1,S2) -> maps:merge(S1,S2).
%% union([Set]) -> Set
%% Return the union of the list of sets.
-spec union(SetList) -> Set when
SetList :: [set(Element)],
Set :: set(Element).
union([S1,S2|Ss]) ->
union1(union(S1, S2), Ss);
union([S]) -> S;
union([]) -> new().
union1(S1, [S2|Ss]) ->
union1(union(S1, S2), Ss);
union1(S1, []) -> S1.
%% intersection(Set1, Set2) -> Set.
%% Return the intersection of Set1 and Set2.
-spec intersection(Set1, Set2) -> Set3 when
Set1 :: set(Element),
Set2 :: set(Element),
Set3 :: set(Element).
intersection(S1, S2) ->
filter(fun (E) -> is_element(E, S1) end, S2).
%% intersection([Set]) -> Set.
%% Return the intersection of the list of sets.
-spec intersection(SetList) -> Set when
SetList :: [set(Element),...],
Set :: set(Element).
intersection([S1,S2|Ss]) ->
intersection1(intersection(S1, S2), Ss);
intersection([S]) -> S.
intersection1(S1, [S2|Ss]) ->
intersection1(intersection(S1, S2), Ss);
intersection1(S1, []) -> S1.
%% is_disjoint(Set1, Set2) -> boolean().
%% Check whether Set1 and Set2 are disjoint.
-spec is_disjoint(Set1, Set2) -> boolean() when
Set1 :: set(Element),
Set2 :: set(Element).
is_disjoint(S1, S2) when map_size(S1) > map_size(S2) ->
is_disjoint_1(S1, maps:iterator(S2));
is_disjoint(S1, S2) ->
is_disjoint_1(S2, maps:iterator(S1)).
is_disjoint_1(Set, Iter) ->
case maps:next(Iter) of
{K, _, NextIter} ->
case Set of
#{K := _} -> false;
#{} -> is_disjoint_1(Set, NextIter)
end;
none ->
true
end.
%% subtract(Set1, Set2) -> Set.
%% Return all and only the elements of Set1 which are not also in
%% Set2.
-spec subtract(Set1, Set2) -> Set3 when
Set1 :: set(Element),
Set2 :: set(Element),
Set3 :: set(Element).
subtract(S1, S2) ->
filter(fun (E) -> not is_element(E, S2) end, S1).
%% is_subset(Set1, Set2) -> boolean().
%% Return 'true' when every element of Set1 is also a member of
%% Set2, else 'false'.
-spec is_subset(Set1, Set2) -> boolean() when
Set1 :: set(Element),
Set2 :: set(Element).
is_subset(S1, S2) when map_size(S1) > map_size(S2) ->
false;
is_subset(S1, S2) ->
is_subset_1(S2, maps:iterator(S1)).
is_subset_1(Set, Iter) ->
case maps:next(Iter) of
{K, _, NextIter} ->
case Set of
#{K := _} -> is_subset_1(Set, NextIter);
#{} -> false
end;
none ->
true
end.
%% fold(Fun, Accumulator, Set) -> Accumulator.
%% Fold function Fun over all elements in Set and return Accumulator.
-spec fold(Function, Acc0, Set) -> Acc1 when
Function :: fun((Element, AccIn) -> AccOut),
Set :: set(Element),
Acc0 :: Acc,
Acc1 :: Acc,
AccIn :: Acc,
AccOut :: Acc.
fold(Fun, Init, Set) ->
fold_1(Fun, Init, maps:iterator(Set)).
fold_1(Fun, Acc, Iter) ->
case maps:next(Iter) of
{K, _, NextIter} ->
fold_1(Fun, Fun(K,Acc), NextIter);
none ->
Acc
end.
%% filter(Fun, Set) -> Set.
%% Filter Set with Fun.
-spec filter(Pred, Set1) -> Set2 when
Pred :: fun((Element) -> boolean()),
Set1 :: set(Element),
Set2 :: set(Element).
filter(Fun, Set) ->
maps:from_list(filter_1(Fun, maps:iterator(Set))).
filter_1(Fun, Iter) ->
case maps:next(Iter) of
{K, _, NextIter} ->
case Fun(K) of
true ->
[{K,ok} | filter_1(Fun, NextIter)];
false ->
filter_1(Fun, NextIter)
end;
none ->
[]
end.
|
