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### set_of Reference

#### Header "boost/bimap/set_of.hpp" synopsis

    namespace boost {
    namespace bimaps {

    template
    <
        class KeyType,
        class KeyCompare = std::less< KeyType >
    >
    struct set_of;

    template
    <
        class KeyCompare = std::less< _relation >
    >
    struct set_of_relation;

    } // namespace bimap
    } // namespace boost

#### Header "boost/bimap/multiset_of.hpp" synopsis

    namespace boost {
    namespace bimaps {

    template
    <
        class KeyType,
        class KeyCompare = std::less< KeyType >
    >
    struct multiset_of;

    template
    <
        class KeyCompare = std::less< _relation >
    >
    struct multiset_of_relation;

    } // namespace bimap
    } // namespace boost

#### Collection type specifiers set_of and multiset_of

These collection type specifiers allow for insertion of sets disallowing or allowing duplicate elements, respectively. The syntaxes of `set_of` and `multiset_of` coincide, so they are described together.

#### [multi]set_of Views

A [multi]set_of set view is a std::[multi]set signature-compatible interface to the underlying heap of elements contained in a `bimap`.

There are two variants: set_of, which does not allow duplicate elements (with respect to its associated comparison predicate) and multiset_of, which does accept those duplicates. The interface of these two variants is largely the same, so they are documented together with their differences explicitly noted where they exist.

If you look the bimap from a side, you will use a map view, and if you look at it as a whole, you will be using a set view.

    namespace boost {
    namespace bimaps {
    namespace views {

    template< -implementation defined parameter list- >
    class -implementation defined view name-
    {
        public:

        typedef -unspecified- key_type;
        typedef -unspecified- value_type;
        typedef -unspecified- key_compare;
        typedef -unspecified- value_compare;
        typedef -unspecified- allocator_type;
        typedef -unspecified- reference;
        typedef -unspecified- const_reference;
        typedef -unspecified- iterator;
        typedef -unspecified- const_iterator;
        typedef -unspecified- size_type;
        typedef -unspecified- difference_type;
        typedef -unspecified- pointer;
        typedef -unspecified- const_pointer;
        typedef -unspecified- reverse_iterator;
        typedef -unspecified- const_reverse_iterator;

        typedef -unspecified- info_type;

        this_type & operator=(const this_type & x);

        allocator_type get_allocator() const;

        // iterators

        iterator               begin();
        const_iterator         begin() const;

        iterator               end();
        const_iterator         end() const;

        reverse_iterator       rbegin();
        const_reverse_iterator rbegin() const;

        reverse_iterator       rend();
        const_reverse_iterator rend() const;

        // capacity

        bool      empty() const;

        size_type size() const;

        size_type max_size() const;

        // modifiers

        std::pair<iterator,bool> insert(const value_type & x);

        iterator insert(iterator position, const value_type & x);

        template< class InputIterator>
        void insert(InputIterator first,  InputIterator last);

        iterator erase(iterator position);

        template< class CompatibleKey >
        size_type erase(const CompatibleKey & x);

        iterator erase(iterator first,  iterator last);

        bool replace(iterator position, const value_type& x);

        // Only in map views
        // {

          template< class CompatibleKey >
          bool replace_key(iterator position, const CompatibleKey & x);

          template< class CompatibleData >
          bool replace_data(iterator position, const CompatibleData & x);

          template< class KeyModifier >
          bool modify_key(iterator position, KeyModifier mod);

          template< class DataModifier >
          bool modify_data(iterator position, DataModifier mod);

        // }

        void swap(this_type & x);

        void clear();

        // observers

        key_compare    key_comp() const;

        value_compare  value_comp() const;

        // set operations

        template< class CompatibleKey >
        iterator find(const CompatibleKey & x);

        template< class CompatibleKey >
        const_iterator find(const CompatibleKey & x) const;

        template< class CompatibleKey >
        size_type count(const CompatibleKey & x) const;

        template< class CompatibleKey >
        iterator lower_bound(const CompatibleKey & x);

        template< class CompatibleKey >
        const_iterator lower_bound(const CompatibleKey & x) const;

        template< class CompatibleKey >
        iterator upper_bound(const CompatibleKey & x);

        template< class CompatibleKey >
        const_iterator upper_bound(const CompatibleKey & x) const;

        template< class CompatibleKey >
        std::pair<iterator,iterator>
            equal_range(const CompatibleKey & x);

        template< class CompatibleKey >
        std::pair<const_iterator,const_iterator>
            equal_range(const CompatibleKey & x) const;

        // Only in maps views
        // {

        template< class LowerBounder, class UpperBounder>
        std::pair<iterator,iterator> range(
            LowerBounder lower, UpperBounder upper);

        template< class LowerBounder, class UpperBounder>
        std::pair<const_iterator,const_iterator> range(
            LowerBounder lower, UpperBounder upper) const;

        typedef -unspecified- data_type;

          // Only in for `set_of` collection type
          // {

          template< class CompatibleKey >
          const data_type & at(const CompatibleKey & k) const;

            // Only if the other collection type is mutable
            // {

            template< class CompatibleKey >
            data_type & operator[](const CompatibleKey & k);

            template< class CompatibleKey >
            data_type & at(const CompatibleKey & k);

            // }

            // Only if info_hook is used
            // {

            template< class CompatibleKey >
            info_type & info_at(const CompatibleKey & k);

            template< class CompatibleKey >
            const info_type & info_at(const CompatibleKey & k) const;

            // }

          // }

        // }
    };

    // view comparison

    bool operator==(const this_type & v1, const this_type & v2 );
    bool operator< (const this_type & v1, const this_type & v2 );
    bool operator!=(const this_type & v1, const this_type & v2 );
    bool operator> (const this_type & v1, const this_type & v2 );
    bool operator>=(const this_type & v1, const this_type & v2 );
    bool operator<=(const this_type & v1, const this_type & v2 );

    } // namespace views
    } // namespace bimap
    } // namespace boost

In the case of a `bimap< {multi}set_of<Left>, ... >`

In the set view:

    typedef signature-compatible with relation<       Left, ... > key_type;
    typedef signature-compatible with relation< const Left, ... > value_type;

In the left map view:

    typedef  Left  key_type;
    typedef  ...   data_type;

    typedef signature-compatible with std::pair< const Left, ... > value_type;

In the right map view:

    typedef  ...  key_type;
    typedef  Left data_type;

    typedef signature-compatible with std::pair< ... ,const Left > value_type;

##### Complexity signature

Here and in the descriptions of operations of this view, we adopt the scheme outlined in the complexity signature section. The complexity signature of [multi]set_of view is:

- copying: `c(n) = n * log(n)`,
- insertion: `i(n) = log(n)`,
- hinted insertion: `h(n) = 1` (constant) if the hint element precedes the point of insertion, `h(n) = log(n)` otherwise,
- deletion: `d(n) = 1` (amortized constant),
- replacement: `r(n) = 1` (constant) if the element position does not change, `r(n) = log(n)` otherwise,
- modifying: `m(n) = 1` (constant) if the element position does not change, `m(n) = log(n)` otherwise.

##### Instantiation types

Set views are instantiated internally to a `bimap`. Instantiations are dependent on the following types:

- `Value` from the set specifier,
- `Allocator` from `bimap`,
- `Compare` from the set specifier.

`Compare` is a Strict Weak Ordering on elements of `Value`.

##### Constructors, copy and assignment

Set views do not have public constructors or destructors. Assignment, on the other hand, is provided.

    this_type & operator=(const this_type & x);

- Effects: `a = b;` where a and b are the `bimap` objects to which `*this` and x belong, respectively.
- Returns: `*this`.

##### Modifiers

    std::pair<iterator,bool> insert(const value_type & x);

- Effects: Inserts `x` into the `bimap` to which the set view belongs if
  - the set view is non-unique OR no other element with equivalent key exists,
  - AND insertion is allowed by the other set specifications the `bimap`.
- Returns: The return value is a pair `p`. `p.second` is `true` if and only if insertion took place. On successful insertion, `p.first` points to the element inserted; otherwise, `p.first` points to an element that caused the insertion to be banned. Note that more than one element can be causing insertion not to be allowed.
- Complexity: O(I(n)).
- Exception safety: Strong.

    iterator insert(iterator position, const value_type & x);

- Requires: `position` is a valid iterator of the view.
- Effects: `position` is used as a hint to improve the efficiency of the operation. Inserts `x` into the `bimap` to which the view belongs if
  - the set view is non-unique OR no other element with equivalent key exists,
  - AND insertion is allowed by all other views of the `bimap`.
- Returns: On successful insertion, an iterator to the newly inserted element. Otherwise, an iterator to an element that caused the insertion to be banned. Note that more than one element can be causing insertion not to be allowed.
- Complexity: O(H(n)).
- Exception safety: Strong.

    template< class InputIterator >
    void insert(InputIterator first, InputIterator last);

- Requires: `InputIterator` is a model of Input Iterator over elements of type `value_type` or a type convertible to value_type. `first` and `last` are not iterators into any view of the `bimap` to which this index belongs. `last` is reachable from `first`.
- Effects: `iterator hint = end()`; `while( first != last ) hint = insert( hint, *first++ );`
- Complexity: O(m*H(n+m)), where m is the number of elements in `[first, last)`.
- Exception safety: Basic.

    iterator erase(iterator position);

- Requires: `position` is a valid dereferenceable iterator if the set view.
- Effects: Deletes the element pointed to by `position`.
- Returns: An iterator pointing to the element immediately following the one that was deleted, or `end()` if no such element exists.
- Complexity: O(D(n)).
- Exception safety: nothrow.

    template< class CompatibleKey >
    size_type erase(const CompatibleKey & x);

- Requires: `CompatibleKey` is a compatible key of `key_compare`.
- Effects: Deletes the elements with key equivalent to `x`.
- Returns: Number of elements deleted.
- Complexity: O(log(n) + m*D(n)), where m is the number of elements deleted.
- Exception safety: Basic.

    iterator erase(iterator first, iterator last);

- Requires: `[first,last)` is a valid range of the view.
- Effects: Deletes the elements in `[first,last)`.
- Returns: last.
- Complexity: O(log(n) + m*D(n)), where m is the number of elements in `[first,last)`.
- Exception safety: nothrow.

    bool replace(iterator position, const value_type& x);

- Requires: `position` is a valid dereferenceable iterator of the set view.
- Effects: Assigns the value `x` to the element pointed to by `position` into the `bimap` to which the set view belongs if, for the value `x`
  - the set view is non-unique OR no other element with equivalent key exists (except possibly `*position`),
  - AND replacing is allowed by all other views of the `bimap`.
- Postconditions: Validity of position is preserved in all cases.
- Returns: `true` if the replacement took place, `false` otherwise.
- Complexity: O(R(n)).
- Exception safety: Strong. If an exception is thrown by some user-provided operation, the `bimap` to which the set view belongs remains in its original state.

    template< class CompatibleKey >
    bool replace_key(iterator position, const CompatibleKey & x);

- Requires: `position` is a valid dereferenceable iterator of the set view. `CompatibleKey` can be assigned to `key_type`.
- Effects: Assigns the value `x` to `e.first`, where `e` is the element pointed to by `position` into the `bimap` to which the set view belongs if,
  - the map view is non-unique OR no other element with equivalent key exists (except possibly `*position`),
  - AND replacing is allowed by all other views of the `bimap`.
- Postconditions: Validity of position is preserved in all cases.
- Returns: `true` if the replacement took place, `false` otherwise.
- Complexity: O(R(n)).
- Exception safety: Strong. If an exception is thrown by some user-provided operation, the `bimap` to which the set view belongs remains in its original state.

    template< class CompatibleData >
    bool replace_data(iterator position, const CompatibleData & x);

- Requires: `position` is a valid dereferenceable iterator of the set view. `CompatibleKey` can be assigned to `data_type`.
- Effects: Assigns the value `x` to `e.second`, where `e` is the element pointed to by `position` into the `bimap` to which the set view belongs if,
  - the map view is non-unique OR no other element with equivalent key exists (except possibly `*position`),
  - AND replacing is allowed by all other views of the `bimap`.
- Postconditions: Validity of position is preserved in all cases.
- Returns: `true` if the replacement took place, `false` otherwise.
- Complexity: O(R(n)).
- Exception safety: Strong. If an exception is thrown by some user-provided operation, the `bimap` to which the set view belongs remains in its original state.

    template< class KeyModifier >
    bool modify_key(iterator position, KeyModifier mod);

- Requires: `KeyModifier` is a model of Unary Function accepting arguments of type: `key_type&`; `position` is a valid dereferenceable iterator of the view.
- Effects: Calls `mod(e.first)` where e is the element pointed to by position and rearranges `*position` into all the views of the `bimap`. If the rearrangement fails, the element is erased. Rearrangement is successful if
  - the map view is non-unique OR no other element with equivalent key exists,
  - AND rearrangement is allowed by all other views of the `bimap`.
- Postconditions: Validity of `position` is preserved if the operation succeeds.
- Returns: `true` if the operation succeeded, `false` otherwise.
- Complexity: O(M(n)).
- Exception safety: Basic. If an exception is thrown by some user-provided operation (except possibly mod), then the element pointed to by position is erased.
- Note: Only provided for map views.

    template< class DataModifier >
    bool modify_data(iterator position, DataModifier mod);

- Requires: `DataModifier` is a model of Unary Function accepting arguments of type: `data_type&`; `position` is a valid dereferenceable iterator of the view.
- Effects: Calls `mod(e.second)` where e is the element pointed to by position and rearranges `*position` into all the views of the `bimap`. If the rearrangement fails, the element is erased. Rearrangement is successful if
  - the oppositte map view is non-unique OR no other element with equivalent key in that view exists,
  - AND rearrangement is allowed by all other views of the `bimap`.
- Postconditions: Validity of `position` is preserved if the operation succeeds.
- Returns: `true` if the operation succeeded, `false` otherwise.
- Complexity: O(M(n)).
- Exception safety: Basic. If an exception is thrown by some user-provided operation (except possibly mod), then the element pointed to by position is erased.
- Note: Only provided for map views.

##### Set operations

`[multi]set_of` views provide the full lookup functionality required by Sorted Associative Container and Unique Associative Container, namely `find`, `count`, `lower_bound`, `upper_bound` and `equal_range`. Additionally, these member functions are templatized to allow for non-standard arguments, so extending the types of search operations allowed.

A type `CompatibleKey` is said to be a compatible key of `Compare` if `(CompatibleKey, Compare)` is a compatible extension of `Compare`. This implies that `Compare`, as well as being a strict weak ordering, accepts arguments of type `CompatibleKey`, which usually means it has several overloads of `operator()`.

    template< class CompatibleKey >
    iterator find(const CompatibleKey & x);

    template< class CompatibleKey >
    const_iterator find(const CompatibleKey & x) const;

- Requires: `CompatibleKey` is a compatible key of `key_compare`.
- Effects: Returns a pointer to an element whose key is equivalent to `x`, or `end()` if such an element does not exist.
- Complexity: O(log(n)).

    template< class CompatibleKey >
    size_type count(const key_type & x) const;

- Requires: `CompatibleKey` is a compatible key of `key_compare`.
- Effects: Returns the number of elements with key equivalent to `x`.
- Complexity: O(log(n) + count(x)).

    template< class CompatibleKey >
    iterator lower_bound(const key_type & x);

    template< class CompatibleKey >
    const_iterator lower_bound(const key_type & x) const;

- Requires: `CompatibleKey` is a compatible key of `key_compare`.
- Effects: Returns an iterator pointing to the first element with key not less than `x`, or `end()` if such an element does not exist.
- Complexity: O(log(n)).

    template< class CompatibleKey >
    iterator upper_bound(const key_type & x);

    template< class CompatibleKey >
    const_iterator upper_bound(const key_type & x) const;

- Requires: `CompatibleKey` is a compatible key of `key_compare`.
- Effects: Returns an iterator pointing to the first element with key greater than `x`, or `end()` if such an element does not exist.
- Complexity: O(log(n)).

    template< class CompatibleKey >
    std::pair<iterator,iterator>
        equal_range(const key_type & x);

    template< class CompatibleKey >
    std::pair<const_iterator,const_iterator>
        equal_range(const key_type & x) const;

- Requires: `CompatibleKey` is a compatible key of `key_compare`.
- Effects: Equivalent to `make_pair(lower_bound(x),upper_bound(x))`.
- Complexity: O(log(n)).

##### Range operations

The member function range is not defined for sorted associative containers, but `[multi]set_of` map views provide it as a convenient utility. A range or interval is defined by two conditions for the lower and upper bounds, which are modelled after the following concepts.

Consider a Strict Weak Ordering `Compare` over values of type Key. A type `LowerBounder` is said to be a lower bounder of `Compare` if

- `LowerBounder` is a `Predicate` over `Key`,
- if `lower(k1)` and `!comp(k2,k1)` then `lower(k2)`,

for every `lower` of type `LowerBounder`, `comp` of type `Compare`, and `k1`, `k2` of type `Key`. Similarly, an upper bounder is a type `UpperBounder` such that

- `UpperBounder` is a `Predicate` over `Key`,
- if `upper(k1)` and `!comp(k1,k2)` then `upper(k2)`,

for every `upper` of type `UpperBounder`, `comp` of type `Compare`, and `k1`, `k2` of type `Key`.

    template< class LowerBounder, class UpperBounder>
    std::pair<const_iterator,const_iterator> range(
        LowerBounder lower, UpperBounder upper) const;

- Requires: `LowerBounder` and `UpperBounder` are a lower and upper bounder of `key_compare`, respectively.
- Effects: Returns a pair of iterators pointing to the beginning and one past the end of the subsequence of elements satisfying lower and upper simultaneously. If no such elements exist, the iterators both point to the first element satisfying lower, or else are equal to `end()` if this latter element does not exist.
- Complexity: O(log(n)).
- Variants: In place of lower or upper (or both), the singular value `boost::bimap::unbounded` can be provided. This acts as a predicate which all values of type `key_type` satisfy.
- Note: Only provided for map views.

##### at(), info_at() and operator[] - set_of only

    template< class CompatibleKey >
    const data_type & at(const CompatibleKey & k) const;

- Requires: `CompatibleKey` is a compatible key of `key_compare`.
- Effects: Returns the `data_type` reference that is associated with `k`, or throws `std::out_of_range` if such key does not exist.
- Complexity: O(log(n)).
- Note: Only provided when `set_of` is used.

The symmetry of bimap imposes some constraints on `operator[]` and the non constant version of at() that are not found in `std::maps`. Tey are only provided if the other collection type is mutable (`list_of`, `vector_of` and `unconstrained_set_of`).

    template< class CompatibleKey >
    data_type & operator[](const CompatibleKey & k);

- Requires: `CompatibleKey` is a compatible key of `key_compare`.
- Effects: `return insert(value_type(k,data_type()))->second;`
- Complexity: O(log(n)).
- Note: Only provided when `set_of` is used and the other collection type is mutable.

    template< class CompatibleKey >
    data_type & at(const CompatibleKey & k);

- Requires: `CompatibleKey` is a compatible key of `key_compare`.
- Effects: Returns the `data_type` reference that is associated with `k`, or throws `std::out_of_range` if such key does not exist.
- Complexity: O(log(n)).
- Note: Only provided when `set_of` is used and the other collection type is mutable.

    template< class CompatibleKey >
    info_type & info_at(const CompatibleKey & k);

    template< class CompatibleKey >
    const info_type & info_at(const CompatibleKey & k) const;

- Requires: `CompatibleKey` is a compatible key of `key_compare`.
- Effects: Returns the `info_type` reference that is associated with `k`, or throws `std::out_of_range` if such key does not exist.
- Complexity: O(log(n)).
- Note: Only provided when `set_of` and `info_hook` are used

##### Serialization

Views cannot be serialized on their own, but only as part of the `bimap` into which they are embedded. In describing the additional preconditions and guarantees associated to `[multi]set_of` views with respect to serialization of their embedding containers, we use the concepts defined in the `bimap` serialization section.

- Requires: No additional requirements to those imposed by the container.

- Requires: In addition to the general requirements, `value_comp()` must be serialization-compatible with `m.get<i>().value_comp()`, where i is the position of the ordered view in the container.
- Postconditions: On successful loading, each of the elements of `[begin(), end())` is a restored copy of the corresponding element in `[m.get<i>().begin(), m.get<i>().end())`.

- Requires: `it` is a valid iterator of the view. The associated `bimap` has been previously saved.

- Postconditions: On successful loading, if it was dereferenceable then `*it`' is the restored copy of `*it`, otherwise `it`'`== end()`.
- Note: It is allowed that it be a `const_iterator` and the restored `it`' an iterator, or viceversa.