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### Bimap Reference

#### View concepts

`bimap` instantiations comprise two side views and an view of the relation specified at compile time. Each view allows read-write access to the elements contained in a definite manner, mathing an STL container signature.

Views are not isolated objects and so cannot be constructed on their own; rather they are an integral part of a `bimap`. The name of the view class implementation proper is never directly exposed to the user, who has access only to the associated view type specifier.

Insertion and deletion of elements are always performed through the appropriate interface of any of the three views of the `bimap`; these operations do, however, have an impact on all other views as well: for instance, insertion through a given view may fail because there exists another view that forbids the operation in order to preserve its invariant (such as uniqueness of elements). The global operations performed jointly in the any view can be reduced to six primitives:

- copying
- insertion of an element
- hinted insertion, where a pre-existing element is suggested in order to improve the efficiency of the operation
- deletion of an element
- replacement of the value of an element, which may trigger the rearrangement of this element in one or more views, or may forbid the replacement
- modification of an element, and its subsequent rearrangement/banning by the various views

The last two primitives deserve some further explanation: in order to guarantee the invariants associated to each view (e.g. some definite ordering) elements of a `bimap` are not mutable. To overcome this restriction, the views expose member functions for updating and modifying, which allows for the mutation of elements in a controlled fashion.

#### Complexity signature

Some member functions of a view interface are implemented by global primitives from the above list. The complexity of these operations thus depends on all views of a given `bimap`, not just the currently used view.

In order to establish complexity estimates, a view is characterised by its complexity signature, consisting of the following associated functions on the number of elements:

- `c(n)`: copying
- `i(n)`: insertion
- `h(n)`: hinted insertion
- `d(n)`: deletion
- `r(n)`: replacement
- `m(n)`: modifying

If the collection type of the relation is `left_based` or `right_based`, and we use an `l` subscript to denote the left view and an `r` for the right view, then the insertion of an element in such a container is of complexity `O(i_l(n)+i_r(n))`, where n is the number of elements. If the collection type of relation is not side-based, then there is an additional term to add that is contributed by the collection type of relation view. Using `a` to denote the above view, the complexity of insertion will now be `O(i_l(n)+i_r(n)+i_a(n))`. To abbreviate the notation, we adopt the following definitions:

- `C(n) = c_l(n) + c_r(n) [ + c_a(n) ]`
- `I(n) = i_l(n) + i_r(n) [ + i_a(n) ]`
- `H(n) = h_l(n) + h_r(n) [ + h_a(n) ]`
- `D(n) = d_l(n) + d_r(n) [ + d_a(n) ]`
- `R(n) = r_l(n) + r_r(n) [ + r_a(n) ]`
- `M(n) = m_l(n) + m_r(n) [ + m_a(n) ]`

#### Set type specification

Set type specifiers are passed as instantiation arguments to `bimap` and provide the information needed to incorporate the corresponding views. Currently, Boost.Bimap provides the collection type specifiers. The side collection type specifiers define the constraints of the two map views of the bimap. The collection type of relation specifier defines the main set view constraints. If `left_based` (the default parameter) or `right_based` is used, then the collection type of relation will be based on the left or right collection type correspondingly.

Side collection type | Collection type of relation | Include
--- | --- | ---
`set_of` | `set_of_relation` | `boost/bimap/set_of.hpp`
`multiset_of` | `multiset_of_relation` | `boost/bimap/multiset_of.hpp`
`unordered_set_of` | `unordered_set_of_relation` | `boost/bimap/unordered_set_of.hpp`
`unordered_multiset_of` | `unordered_multiset_of_relation` | `boost/bimap/unordered_multiset_of.hpp`
`list_of` | `list_of_relation` | `boost/bimap/list_of.hpp`
`vector_of` | `vector_of_relation` | `boost/bimap/vector_of.hpp`
`unconstrained_set_of` | `unconstrained_set_of_relation` | `boost/bimap/unconstrained_set_of.hpp`
| `left_based` | `boost/bimap/bimap.hpp`
| `right_based` | `boost/bimap/bimap.hpp`

#### Tags

Tags are just conventional types used as mnemonics for the types stored in a `bimap`. Boost.Bimap uses the tagged idiom to let the user specify this tags.

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

    namespace boost {
    namespace bimaps {

    template< class Type, typename Tag >
    struct tagged;

    // bimap template class

    template
    <
        class LeftCollectionType, class RightCollectionType,

        class AdditionalParameter_1 = detail::not_specified,
        class AdditionalParameter_2 = detail::not_specified
    >
    class bimap - implementation defined { : public SetView } -
    {
        public:

        // Metadata

        typedef -unspecified- left_tag;
        typedef -unspecified- left_map;

        typedef -unspecified- right_tag;
        typedef -unspecified- right_map;

        // Shortcuts
        // typedef -side-_map::-type- -side-_-type-;

        typedef -unspecified- info_type;

        // Map views

         left_map  left;
        right_map right;

        // Constructors

        bimap();

        template< class InputIterator >
        bimap(InputIterator first,InputIterator last);

        bimap(const bimap &);

        bimap& operator=(const bimap& b);

        // Projection of iterators

        template< class IteratorType >
        left_iterator project_left(IteratorType iter);

        template< class IteratorType >
        left_const_iterator project_left(IteratorType iter) const;

        template< class IteratorType >
        right_iterator project_right(IteratorType iter);

        template< class IteratorType >
        right_const_iterator project_right(IteratorType iter) const;

        template< class IteratorType >
        iterator project_up(IteratorType iter);

        template< class IteratorType >
        const_iterator project_up(IteratorType iter) const;

        // Support for tags

        template< class Tag >
        struct map_by;

        template< class Tag >
        map_by<Tag>::type by();

        template< class Tag >
        const map_by<Tag>::type & by() const;

        template< class Tag, class IteratorType >
        map_by<Tag>::iterator project(IteratorType iter);

        template< class Tag, class IteratorType >
        map_by<Tag>::const_iterator project(IteratorType iter) const

    };

    } // namespace bimap
    } // namespace boost

#### Class template bimap

This is the main component of Boost.Bimap.

##### Complexity

In the descriptions of the operations of `bimap`, we adopt the scheme outlined in the complexity signature section.

##### Instantiation types

`bimap` is instantiated with the following types:

1. LeftCollectionType and RightCollectionType are collection type specifications optionally tagged, or any type optionally tagged, in which case that side acts as a set.
2. AdditionalParameter_{1/2} can be any ordered subset of:
   - CollectionTypeOfRelation specification
   - Allocator

##### Nested types

    left_tag, right_tag

> Tags for each side of the bimap. If the user has not specified any tag the tags default to `member_at::left` and `member_at::right`.

    left_key_type, right_key_type

> Key type of each side. In a `bimap<A,B>` `left_key_type` is `A` and `right_key_type` is `B`. If there are tags, it is better to use: `Bimap::map_by<Tag>::key_type`.

    left_data_type, right_data_type

> Data type of each side. In a bimap<A,B> left_key_type is B and right_key_type is A. If there are tags, it is better to use: `Bimap::map_by<Tag>::data_type`.

    left_value_type, right_value_type

> Value type used for the views. If there are tags, it is better to use: `Bimap::map_by<Tag>::value_type`.

    left_iterator, right_iterator
    left_const_iterator, right_const_iterator

> Iterators of the views. If there are tags, it is better to use: `Bimap::map_by<Tag>::iterator` and `Bimap::map_by<Tag>::const_iterator`

    left_map, right_map

> Map view type of each side. If there are tags, it is better to use: `Bimap::map_by<Tag>::type`.

##### Constructors, copy and assignment

    bimap();

- Effects: Constructs an empty `bimap`.
- Complexity: Constant.

    template<typename InputIterator>
    bimap(InputIterator first,InputIterator last);

- Requires: `InputIterator` is a model of Input Iterator over elements of type `relation` or a type convertible to `relation`. last is reachable from `first`.
- Effects: Constructs an empty `bimap` and fills it with the elements in the range `[first,last)`. Insertion of each element may or may not succeed depending on acceptance by the collection types of the `bimap`.
- Complexity: O(m*H(m)), where m is the number of elements in `[first,last)`.

    bimap(const bimap & x);

- Effects: Constructs a copy of x, copying its elements as well as its internal objects (key extractors, comparison objects, allocator.)
- Postconditions: `*this == x`. The order of the views of the `bimap` is preserved as well.
- Complexity: O(x.size()*log(x.size()) + C(x.size()))

    ~bimap()

- Effects: Destroys the `bimap` and all the elements contained. The order in which the elements are destroyed is not specified.
- Complexity: O(n).

    bimap& operator=(const bimap& x);

- Effects: Replaces the elements and internal objects of the `bimap` with copies from x.
- Postconditions: `*this==x`. The order on the views of the `bimap` is preserved as well.
- Returns: `*this`.
- Complexity: O(n + x.size()*log(x.size()) + C(x.size())).
- Exception safety: Strong, provided the copy and assignment operations of the types of `ctor_args_list` do not throw.

##### Projection operations

Given a `bimap` with views v1 and v2, we say than an v1-iterator it1 and an v2-iterator it2 are equivalent if:

- `it1 == i1.end()` AND `it2 == i2.end()`,
- OR `it1` and `it2` point to the same element.

    template< class IteratorType >
    left_iterator project_left(IteratorType iter);

    template< class IteratorType >
    left_const_iterator project_left(IteratorType iter) const;

- Requires: `IteratorType` is a bimap view iterator. it is a valid iterator of some view of `*this` (i.e. does not refer to some other `bimap`.)
- Effects: Returns a left map view iterator equivalent to `it`.
- Complexity: Constant.
- Exception safety: nothrow.

    template< class IteratorType >
    right_iterator project_right(IteratorType iter);

    template< class IteratorType >
    right_const_iterator project_right(IteratorType iter) const;

- Requires: `IteratorType` is a bimap view iterator. it is a valid iterator of some view of `*this` (i.e. does not refer to some other `bimap`.)
- Effects: Returns a right map view iterator equivalent to `it`.
- Complexity: Constant.
- Exception safety: nothrow.

    template< class IteratorType >
    iterator project_up(IteratorType iter);

    template< class IteratorType >
    const_iterator project_up(IteratorType iter) const;

- Requires: `IteratorType` is a bimap view iterator. it is a valid iterator of some view of `*this` (i.e. does not refer to some other `bimap`.)
- Effects: Returns a collection of relations view iterator equivalent to `it`.
- Complexity: Constant.
- Exception safety: nothrow.

##### Support for user defined names

    template< class Tag >
    struct map_by;

- `map_by<Tag>::type` yields the type of the map view tagged with `Tag`. `map_by<Tag>::`-type name- is the same as `map_by<Tag>::type::`-type name-.
- Requires: `Tag` is a valid user defined name of the bimap.

    template< class Tag >
    map_by<Tag>::type by();

    template< class Tag >
    const map_by<Tag>::type & by() const;

- Requires: `Tag` is a valid user defined name of the bimap.
- Effects: Returns a reference to the map view tagged with `Tag` held by `*this`.
- Complexity: Constant.
- Exception safety: nothrow.

    template< class Tag, class IteratorType >
    map_by<Tag>::iterator project(IteratorType iter);

    template< class Tag, class IteratorType >
    map_by<Tag>::const_iterator project(IteratorType iter) const

- Requires: `Tag` is a valid user defined name of the bimap. `IteratorType` is a bimap view iterator. it is a valid iterator of some view of `*this` (i.e. does not refer to some other `bimap`.)
- Effects: Returns a reference to the map view tagged with `Tag` held by `*this`.
- Complexity: Constant.
- Exception safety: nothrow.

##### Serialization

A `bimap` can be archived and retrieved by means of Boost.Serialization. Boost.Bimap does not expose a public serialisation interface, as this is provided by Boost.Serialization itself. Both regular and XML archives are supported.

Each of the set specifications comprising a given `bimap` contributes its own preconditions as well as guarantees on the retrieved containers. In describing these, the following concepts are used. A type `T` is serializable (resp. XML-serializable) if any object of type `T` can be saved to an output archive (XML archive) and later retrieved from an input archive (XML archive) associated to the same storage. If `x`' of type `T` is loaded from the serialization information saved from another object x, we say that x' is a restored copy of x. Given a Binary Predicate `Pred` over `(T, T)`, and objects `p` and `q` of type `Pred`, we say that `q` is serialization-compatible with `p` if

- `p(x,y) == q(x`'`,y`'`)`

for every `x` and `y` of type `T` and `x`' and `y`' being restored copies of `x` and `y`, respectively.

- Requires: Value is serializable (XML-serializable). Additionally, each of the views of b can impose other requirements.
- Exception safety: Strong with respect to `b`. If an exception is thrown, ar may be left in an inconsistent state.

- Requires: Value is serializable (XML-serializable). Additionally, each of the views of `b`' can impose other requirements.
- Exception safety: Basic. If an exception is thrown, ar may be left in an inconsistent state.