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
|
%%
%% %CopyrightBegin%
%%
%% Copyright Ericsson AB 1998-2010. All Rights Reserved.
%%
%% The contents of this file are subject to the Erlang Public License,
%% Version 1.1, (the "License"); you may not use this file except in
%% compliance with the License. You should have received a copy of the
%% Erlang Public License along with this software. If not, it can be
%% retrieved online at http://www.erlang.org/.
%%
%% Software distributed under the License is distributed on an "AS IS"
%% basis, WITHOUT WARRANTY OF ANY KIND, either express or implied. See
%% the License for the specific language governing rights and limitations
%% under the License.
%%
%% %CopyrightEnd%
%%
%%
%% Copyright (C) 1991, Ellemtel Telecommunications Systems Laboratories
%% File : ordsets.erl
%% Author : Robert Virding
%% Purpose : Functions for manipulating sets as ordered lists.
%% As yet some of these are not very efficiently written.
-module(ordsets1).
-export([new_set/0,is_set/1,set_to_list/1,list_to_set/1]).
-export([is_element/2,add_element/2,del_element/2]).
-export([union/2,union/1,intersection/2,intersection/1]).
-export([subtract/2,subset/2]).
%% new_set()
%% Return a new empty ordered set.
new_set() ->
[].
%% is_set(Set)
%% Return 'true' if Set is an ordered set of elements, else 'false'.
is_set([E|Es]) ->
is_set(Es, E);
is_set([]) ->
true.
is_set([E2|Es], E1) when E1 < E2 ->
is_set(Es, E2);
is_set([E2|Es], E1) ->
false;
is_set([], E1) ->
true.
%% set_to_list(OrdSet)
%% Return the elements in OrdSet as a list.
set_to_list(S) ->
S.
%% list_to_set(List)
%% Build an ordered set from the elements in List.
list_to_set([E|Es]) ->
add_element(E, list_to_set(Es));
list_to_set([]) ->
[].
%% is_element(Element, OrdSet)
%% Return 'true' if Element is an element of OrdSet, else 'false'.
is_element(E, [H|Es]) when E < H ->
false;
is_element(E, [H|Es]) when E == H ->
true;
is_element(E, [H|Es]) when E > H ->
is_element(E, Es);
is_element(E, []) ->
false.
%% add_element(Element, OrdSet)
%% Return OrdSet with Element inserted in it.
add_element(E, [H|Es]) when E < H ->
[E,H|Es];
add_element(E, [H|Es]) when E == H ->
[H|Es];
add_element(E, [H|Es]) when E > H ->
[H|add_element(E, Es)];
add_element(E, []) ->
[E].
%% del_element(Element, OrdSet)
%% Return OrdSet but with Element removed.
del_element(E, [H|Es]) when E < H ->
[H|Es];
del_element(E, [H|Es]) when E == H ->
Es;
del_element(E, [H|Es]) when E > H ->
[H|del_element(E, Es)];
del_element(E, []) ->
[].
%% union(Set1, Set2)
%% Return the union of Set1 and Set2.
union([H1|Es1], [H2|Es2]) when H1 < H2 ->
[H1|union(Es1, [H2|Es2])];
union([H1|Es1], [H2|Es2]) when H1 == H2 ->
[H1|union(Es1, Es2)];
union([H1|Es1], [H2|Es2]) when H1 > H2 ->
[H2|union([H1|Es1], Es2)];
union([], Es2) ->
Es2;
union(Es1, []) ->
Es1.
%% union(OrdSets)
%% Return the union of the list of sets.
union([S1,S2|Ss]) ->
union1(union(S1,S2), Ss);
union([S]) ->
S;
union([]) ->
[].
union1(S1, [S2|Ss]) ->
union1(union(S1, S2), Ss);
union1(S1, []) ->
S1.
%% intersection(Set1, Set2)
%% Return the intersection of Set1 and Set2.
intersection([H1|Es1], [H2|Es2]) when H1 < H2 ->
intersection(Es1, [H2|Es2]);
intersection([H1|Es1], [H2|Es2]) when H1 == H2 ->
[H1|intersection(Es1, Es2)];
intersection([H1|Es1], [H2|Es2]) when H1 > H2 ->
intersection([H1|Es1], Es2);
intersection([], Es2) ->
[];
intersection(Es1, []) ->
[].
%% intersection(OrdSets)
%% Return the intersection of the list of sets.
intersection([S1,S2|Ss]) ->
intersection1(intersection(S1,S2), Ss);
intersection([S]) ->
S;
intersection([]) ->
[].
intersection1(S1, [S2|Ss]) ->
intersection1(intersection(S1, S2), Ss);
intersection1(S1, []) ->
S1.
%% subtract(Set1, Set2)
%% Return all and only the elements of Set1 which are not also in Set2.
subtract([H1|Es1], [H2|Es2]) when H1 < H2 ->
[H1|subtract(Es1, [H2|Es2])];
subtract([H1|Es1], [H2|Es2]) when H1 == H2 ->
subtract(Es1, Es2);
subtract([H1|Es1], [H2|Es2]) when H1 > H2 ->
subtract([H1|Es1], Es2);
subtract([], Es2) ->
[];
subtract(Es1, []) ->
Es1.
%% subset(Set1, Set2)
%% Return 'true' when every element of Set1 is also a member of Set2,
%% else 'false'.
subset([H1|Es1], [H2|Es2]) when H1 < H2 -> %H1 not in Set2
false;
subset([H1|Es1], [H2|Es2]) when H1 == H2 ->
subset(Es1, Es2);
subset([H1|Es1], [H2|Es2]) when H1 > H2 ->
subset([H1|Es1], Es2);
subset([], Es2) ->
true;
subset(Es1, []) ->
false.
|
