-spec add_element(Element, Ordset1) -> Ordset2
                     when Element :: E, Ordset1 :: ordset(T), Ordset2 :: ordset(T | E).

Returns a new ordered set formed from Ordset1 with Element inserted.

Examples

1> S0 = ordsets:new().
[]
2> S1 = ordsets:add_element(7, S0).
[7]
3> S2 = ordsets:add_element(42, S1).
[7,42]
4> ordsets:add_element(42, S2).
[7,42]

-spec del_element(Element, Ordset1) -> Ordset2
                     when Element :: term(), Ordset1 :: ordset(T), Ordset2 :: ordset(T).

Returns a copy of Ordset1 with Element removed.

Examples

1> S = ordsets:from_list([a,b,c]).
2> ordsets:del_element(c, S).
[a,b]
3> ordsets:del_element(x, S).
[a,b,c]

-spec filter(Pred, Ordset1) -> Ordset2
                when
                    Pred :: fun((Element :: T) -> boolean()), Ordset1 :: ordset(T), Ordset2 :: ordset(T).

Filters elements in Ordset1 using predicate function Pred.

Examples

1> S = ordsets:from_list([1,2,3,4,5,6,7]).
2> IsEven = fun(N) -> N rem 2 =:= 0 end.
3> ordsets:filter(IsEven, S).
[2,4,6]

-spec filtermap(Fun, Ordset1) -> Ordset2
                   when
                       Fun :: fun((Element1 :: T1) -> boolean | {true, Element2 :: T2}),
                       Ordset1 :: ordset(T1),
                       Ordset2 :: ordset(T1 | T2).

Calls Fun(Elem) for each Elem of Ordset1 to update or remove elements from Ordset1.

Fun/1 must return either a Boolean or a tuple {true, Value}. The function returns the set of elements for which Fun returns a new value, with true being equivalent to {true, Elem}.

ordsets:filtermap/2 behaves as if it were defined as follows:

filtermap(Fun, Ordset1) ->
    ordsets:from_list(lists:filtermap(Fun, Ordset1)).

Examples

1> S = ordsets:from_list([2,4,5,6,8,9])
2> F = fun(X) ->
           case X rem 2 of
               0 -> {true, X div 2};
               1 -> false
           end
        end.
3> ordsets:filtermap(F, S).
[1,2,3,4]

-spec fold(Function, Acc0, Ordset) -> Acc1
              when
                  Function :: fun((Element :: T, AccIn :: term()) -> AccOut :: term()),
                  Ordset :: ordset(T),
                  Acc0 :: term(),
                  Acc1 :: term().

Folds Function over every element in Ordset and returns the final value of the accumulator.

Examples

1> S = ordsets:from_list([1,2,3,4]).
2> Plus = fun erlang:'+'/2.
3> ordsets:fold(Plus, 0, S).
10

-spec from_list(List) -> Ordset when List :: [T], Ordset :: ordset(T).

Returns an ordered set of the elements in List.

Examples

1> ordsets:from_list([a,b,a,b,b,c]).
[a,b,c]

-spec intersection(OrdsetList) -> Ordset when OrdsetList :: [ordset(_), ...], Ordset :: ordset(_).

Returns the intersection of the non-empty list of sets.

The intersection of multiple sets is a new set that contains only the elements that are present in all sets.

Examples

1> S0 = ordsets:from_list([a,b,c,d]).
2> S1 = ordsets:from_list([d,e,f]).
3> S2 = ordsets:from_list([q,r])
4> Sets = [S0, S1, S2].
5> ordsets:intersection([S0, S1, S2]).
[]
6> ordsets:intersection([S0, S1]).
[d]
7> ordsets:intersection([]).
** exception error: no function clause matching ordsets:intersection([])

-spec intersection(Ordset1, Ordset2) -> Ordset3
                      when Ordset1 :: ordset(_), Ordset2 :: ordset(_), Ordset3 :: ordset(_).

Returns the intersection of Ordset1 and Ordset2.

The intersection of two sets is a new set that contains only the elements that are present in both sets.

Examples

1> S0 = ordsets:from_list([a,b,c,d]).
2> S1 = ordsets:from_list([c,d,e,f]).
3> S2 = ordsets:from_list([q,r]).
4> ordsets:intersection(S0, S1).
[c,d]
5> ordsets:intersection(S1, S2).
[]

-spec is_disjoint(Ordset1, Ordset2) -> boolean() when Ordset1 :: ordset(_), Ordset2 :: ordset(_).

Returns true if Ordset1 and Ordset2 are disjoint; otherwise, returns false.

Two sets are disjoint if they have no elements in common.

This function is equivalent to ordsets:intersection(Ordset1, Ordset2) =:= [], but faster.

Examples

1> S0 = ordsets:from_list([a,b,c,d]).
2> S1 = ordsets:from_list([d,e,f]).
3> S2 = ordsets:from_list([q,r])
4> ordsets:is_disjoint(S0, S1).
false
5> ordsets:is_disjoint(S1, S2).
true

-spec is_element(Element, Ordset) -> boolean() when Element :: term(), Ordset :: ordset(_).

Returns true if Element is an element of Ordset; otherwise, returns false.

Examples

1> S = ordsets:from_list([a,b,c]).
2> ordsets:is_element(42, S).
false
3> ordsets:is_element(b, S).
true

-spec is_empty(Ordset) -> boolean() when Ordset :: ordset(_).

Returns true if Ordset is an empty set; otherwise, returns false.

Examples

1> ordsets:is_empty(ordsets:new()).
true
2> ordsets:is_empty(ordsets:from_list([1])).
false

-spec is_equal(Ordset1, Ordset2) -> boolean() when Ordset1 :: ordset(_), Ordset2 :: ordset(_).

Returns true if Ordset1 and Ordset2 are equal, that is, if every element of one set is also a member of the other set; otherwise, returns false.

Examples

1> Empty = ordsets:new().
2> S = ordsets:from_list([a,b]).
3> ordsets:is_equal(S, S)
true
4> ordsets:is_equal(S, Empty)
false

-spec is_set(Ordset) -> boolean() when Ordset :: term().

Returns true if Ordset is an ordered set of elements; otherwise, returns false.

Examples

1> ordsets:is_set(ordsets:from_list([a,x,13,{p,q}])).
true
2> ordsets:is_set([a,b,c]).
true
3> ordsets:is_set([z,a]).
false
4> ordsets:is_set({a,b}).
false

-spec is_subset(Ordset1, Ordset2) -> boolean() when Ordset1 :: ordset(_), Ordset2 :: ordset(_).

Returns true when every element of Ordset1 is also a member of Ordset2; otherwise, returns false.

Examples

1> S0 = ordsets:from_list([a,b,c,d]).
2> S1 = ordsets:from_list([c,d]).
3> ordsets:is_subset(S1, S0).
true
4> ordsets:is_subset(S0, S1).
false
5> ordsets:is_subset(S0, S0).
true

-spec map(Fun, Ordset1) -> Ordset2
             when
                 Fun :: fun((Element1 :: T1) -> Element2 :: T2),
                 Ordset1 :: ordset(T1),
                 Ordset2 :: ordset(T2).

Maps elements in Ordset1 with mapping function Fun.

Examples

1> S = ordsets:from_list([1,2,3,4,5,6,7]).
2> F = fun(N) -> N div 2 end.
3> ordsets:map(F, S).
[0,1,2,3]

-spec new() -> [].

Returns a new empty ordered set.

Examples

1> ordsets:new()
[]

-spec size(Ordset) -> non_neg_integer() when Ordset :: ordset(_).

Returns the number of elements in Ordset.

Examples

1> ordsets:size(ordsets:new()).
0
2> ordsets:size(ordsets:from_list([4,5,6])).
3

-spec subtract(Ordset1, Ordset2) -> Ordset3
                  when Ordset1 :: ordset(_), Ordset2 :: ordset(_), Ordset3 :: ordset(_).

Returns the elements of Ordset1 that are not elements in Ordset2.

Examples

1> S0 = ordsets:from_list([a,b,c,d]).
2> S1 = ordsets:from_list([c,d,e,f]).
3> ordsets:subtract(S0, S1).
[a,b]
4> ordsets:subtract(S1, S0).
[e,f]

-spec to_list(Ordset) -> List when Ordset :: ordset(T), List :: [T].

Returns the elements of Ordset as a list.

Examples

1> S = ordsets:from_list([a,b]).
2> ordsets:to_list(S).
[a,b]

-spec union(OrdsetList) -> Ordset when OrdsetList :: [ordset(T)], Ordset :: ordset(T).

Returns the union of a list of sets.

The union of multiple sets is a new set that contains all the elements from all sets, without duplicates.

Examples

1> S0 = ordsets:from_list([a,b,c,d]).
2> S1 = ordsets:from_list([d,e,f]).
3> S2 = ordsets:from_list([q,r])
4> Sets = [S0, S1, S2].
5> ordsets:union(Sets).
[a,b,c,d,e,f,q,r]

-spec union(Ordset1, Ordset2) -> Ordset3
               when Ordset1 :: ordset(T1), Ordset2 :: ordset(T2), Ordset3 :: ordset(T1 | T2).

Returns the union of Ordset1 and Ordset2.

The union of two sets is a new set that contains all the elements from both sets, without duplicates.

Examples

1> S0 = ordsets:from_list([a,b,c,d]).
2> S1 = ordsets:from_list([c,d,e,f]).
3> ordsets:union(S0, S1).
[a,b,c,d,e,f]