...one of the most highly
regarded and expertly designed C++ library projects in the
world.

— Herb Sutter and Andrei
Alexandrescu, C++
Coding Standards

- Header
`"boost/multi_index/hashed_index_fwd.hpp"`

synopsis - Header
`"boost/multi_index/hashed_index.hpp"`

synopsis

`"boost/multi_index/hashed_index_fwd.hpp"`

synopsisnamespace boost{ namespace multi_index{ // index specifiers hashed_unique and hashed_non_unique template<consult hashed_unique reference for arguments> struct hashed_unique; template<consult hashed_non_unique reference for arguments> struct hashed_non_unique; // indices namespace detail{ template<implementation defined> classindex name is implementation defined; } // namespace boost::multi_index::detail } // namespace boost::multi_index } // namespace boost

`hashed_index_fwd.hpp`

provides forward declarations for index specifiers
`hashed_unique`

and `hashed_non_unique`

and
their associated hashed index classes.

`"boost/multi_index/hashed_index.hpp"`

synopsis#include <initializer_list> namespace boost{ namespace multi_index{ // index specifiers hashed_unique and hashed_non_unique template<consult hashed_unique reference for arguments> struct hashed_unique; template<consult hashed_non_unique reference for arguments> struct hashed_non_unique; // indices namespace detail{ template<implementation defined> classindex class name implementation defined; // index comparison: //OPis any of ==,!= template<implementation defined> bool operator(constOPindex class name& x,constindex class name& y); // index specialized algorithms: template<implementation defined> void swap(index class name& x,index class name& y); } // namespace boost::multi_index::detail } // namespace boost::multi_index } // namespace boost

`hashed_unique`

and `hashed_non_unique`

These index specifiers allow
for insertion of hashed indices without and with
allowance of duplicate elements, respectively. The syntax of `hashed_unique`

and `hashed_non_unique`

coincide, thus we describe them in a grouped manner.
`hashed_unique`

and `hashed_non_unique`

can be instantiated in
two different forms, according to whether a tag list for the index is provided or not:

template< typename KeyFromValue, typename Hash=boost::hash<KeyFromValue::result_type>, typename Pred=std::equal_to<KeyFromValue::result_type> > struct (hashed_unique | hashed_non_unique); template< typename TagList, typename KeyFromValue, typename Hash=boost::hash<KeyFromValue::result_type>, typename Pred=std::equal_to<KeyFromValue::result_type> > struct (hashed_unique | hashed_non_unique);

If provided, `TagList`

must be an instantiation of the class template
`tag`

.
The template arguments are used by the corresponding index implementation,
refer to the hashed indices reference section for further
explanations on their acceptable type values.

A hashed index provides fast retrieval of elements of a `multi_index_container`

through hashing techniques.
A hashed index is particularized according to a given
`Key Extractor`

that retrieves keys from elements of `multi_index_container`

, a `Hash`

function object which returns hash values for the keys and a binary predicate `Pred`

acting as an equivalence relation on values of `Key`

.

There are two variants of hashed indices: *unique*, which do
not allow duplicate elements (with respect to its associated equality
predicate) and *non-unique*, which accept those duplicates.
The interface of these two variants is the same, so they are documented
together, with minor differences explicitly stated when they exist.

Except where noted or if the corresponding interface does not exist, hashed indices
(both unique and non-unique) satisfy the C++ requirements for unordered associative
containers at **[unord.req]** (supporting unique and equivalent keys, respectively.)
Iterators (including to the end of the index) and pointers and references to an element
remain valid during the lifetime of the associated container (which can change
upon swapping), or until the referred-to element is erased or extracted;
pointers and references to an extracted element, but not so for iterators,
become valid again once the element is re-inserted.
Occasionally, the exception safety guarantees provided
are actually stronger than required by the standard. We only provide descriptions of
those types and operations that do not exactly conform to or are not mandated by the standard
requirements.

namespace boost{ namespace multi_index{ namespace detail{ template<implementation defined: dependent on types Value, Allocator, TagList, KeyFromValue, Hash, Pred> classname is implementation defined{ public: // types: typedef typename KeyFromValue::result_type key_type; typedef Value value_type; typedef KeyFromValue key_from_value; typedef Hash hasher; typedef Pred key_equal; typedef boost::tuple< size_type,key_from_value,hasher,key_equal> ctor_args; typedef TagList tag_list; typedef Allocator allocator_type; typedef typename Allocator::pointer pointer; typedef typename Allocator::const_pointer const_pointer; typedef typename Allocator::reference reference; typedef typename Allocator::const_reference const_reference; typedefimplementation definedsize_type; typedefimplementation defineddifference_type; typedefimplementation definediterator; typedefimplementation definedconst_iterator; typedefimplementation definedlocal_iterator; typedefimplementation definedconst_local_iterator; typedefsame as owning containernode_type; typedeffollowing [container.insert.return] specinsert_return_type; // construct/destroy/copy:index class name& operator=(constindex class name& x);index class name& operator=(std::initializer_list<value_type> list); allocator_type get_allocator()const noexcept; // size and capacity: bool empty()const noexcept; size_type size()const noexcept; size_type max_size()const noexcept; // iterators: iterator begin()noexcept; const_iterator begin()const noexcept; iterator end()noexcept; const_iterator end()const noexcept; const_iterator cbegin()const; const_iterator cend()const; iterator iterator_to(const value_type& x); const_iterator iterator_to(const value_type& x)const; // modifiers: template<typename... Args> std::pair<iterator,bool> emplace(Args&&... args); template<typename... Args> iterator emplace_hint(iterator position,Args&&... args); std::pair<iterator,bool> insert(const value_type& x); std::pair<iterator,bool> insert(value_type&& x); iterator insert(iterator position,const value_type& x); iterator insert(iterator position,value_type&& x); template<typename InputIterator> void insert(InputIterator first,InputIterator last); void insert(std::initializer_list<value_type> list); insert_return_type insert(node_type&& nh); iterator insert(const_iterator position,node_type&& nh); node_type extract(const_iterator position); node_type extract(const key_type& x); iterator erase(iterator position); size_type erase(const key_type& x); iterator erase(iterator first,iterator last); bool replace(iterator position,const value_type& x); bool replace(iterator position,value_type&& x); template<typename Modifier> bool modify(iterator position,Modifier mod); template<typename Modifier,typename Rollback> bool modify(iterator position,Modifier mod,Rollback back); template<typename Modifier> bool modify_key(iterator position,Modifier mod); template<typename Modifier,typename Rollback> bool modify_key(iterator position,Modifier mod,Rollback back); void clear()noexcept; void swap(index class name& x); // observers: key_from_value key_extractor()const; hasher hash_function()const; key_equal key_eq()const; // lookup: template<typename CompatibleKey> iterator find(const CompatibleKey& x)const; template< typename CompatibleKey,typename CompatibleHash, typename CompatiblePred > iterator find( const CompatibleKey& x, const CompatibleHash& hash,const CompatiblePred& eq)const; template<typename CompatibleKey> size_type count(const CompatibleKey& x)const; template< typename CompatibleKey,typename CompatibleHash, typename CompatiblePred > size_type count( const CompatibleKey& x, const CompatibleHash& hash,const CompatiblePred& eq)const; template<typename CompatibleKey> std::pair<iterator,iterator> equal_range(const CompatibleKey& x)const; template< typename CompatibleKey,typename CompatibleHash, typename CompatiblePred > std::pair<iterator,iterator> equal_range( const CompatibleKey& x, const CompatibleHash& hash,const CompatiblePred& eq)const; // bucket interface: size_type bucket_count()const noexcept; size_type max_bucket_count()const noexcept; size_type bucket_size(size_type n)const; size_type bucket(const key_type& k)const; local_iterator begin(size_type n); const_local_iterator begin(size_type n)const; local_iterator end(size_type n); const_local_iterator end(size_type n)const; const_local_iterator cbegin(size_type n)const; const_local_iterator cend(size_type n)const; local_iterator local_iterator_to(const value_type& x); const_local_iterator local_iterator_to(const value_type& x)const; // hash policy: float load_factor()const noexcept; float max_load_factor()const noexcept; void max_load_factor(float z); void rehash(size_type n); void reserve(size_type n); }; // index comparison: template<implementation defined> bool operator==(constindex class name& x,constindex class name& y); template<implementation defined> bool operator!=(constindex class name& x,constindex class name& y) { return !(x==y); } // index specialized algorithms: template<implementation defined> void swap(index class name& x,index class name& y); } // namespace boost::multi_index::detail } // namespace boost::multi_index } // namespace boost

Here and in the descriptions of operations of hashed indices, we adopt the scheme outlined in the complexity signature section. The complexity signature of hashed indices is:

- copying:
`c(n)=n*log(n)`

, - insertion: average case
`i(n)=1`

(amortized constant), worst case`i(n)=n`

,_{dist} - hinted insertion: average case
`h(n)=1`

(amortized constant), worst case`h(n)=n`

,_{dist} - deletion:
`d(n)=1`

(constant), - replacement:
- if the new element key is equivalent to the original,
`r(n)=1`

(constant), - otherwise, average case
`r(n)=1`

(constant), worst case`r(n)=n`

,_{dist}

- if the new element key is equivalent to the original,
- modifying: average case
`m(n)=1`

(constant), worst case`m(n)=n`

,_{dist}

`n`_{dist}

is the number of non-equivalent elements out of
the total `n`

.
Hashed indices are instantiated internally to `multi_index_container`

and
specified by means of `indexed_by`

with index specifiers `hashed_unique`

and `hashed_non_unique`

. Instantiations are dependent on the
following types:

`Value`

from`multi_index_container`

,`Allocator`

from`multi_index_container`

,`TagList`

from the index specifier (if provided, otherwise`tag<>`

is assumed),`KeyFromValue`

from the index specifier,`Hash`

from the index specifier,`Pred`

from the index specifier.

`TagList`

must be an instantiation of
`tag`

. The type `KeyFromValue`

,
which determines the mechanism for extracting a key from `Value`

,
must be a model of
`Key Extractor`

from `Value`

. `Hash`

is a
`CopyConstructible`

unary function object
taking a single argument of type `KeyFromValue::result_type`

and returning a
value of type `std::size_t`

in the range
`[0, std::numeric_limits<std::size_t>::max())`

.
`Pred`

is a `CopyConstructible`

binary predicate inducing an equivalence relation
on elements of `KeyFromValue::result_type`

. It is required that
the `Hash`

object return the same value for keys
equivalent under `Pred`

.
`ctor_args`

The first element of this tuple indicates the minimum number of buckets set up by the index on construction time. If the default value 0 is used, an implementation defined number is used instead.

`iterator`

const_iterator

local_iterator

const_local_iterator

These types are forward iterators.

As explained in the index
concepts section, indices do not have public constructors or destructors.
Assignment, on the other hand, is provided. Upon construction,
`max_load_factor()`

is 1.0.

**index class name**& operator=(const **index class name**& x);

Effects:wherea=b;`a`

and`b`

are the`multi_index_container`

objects to which`*this`

and`x`

belong, respectively.

Returns:`*this`

.

**index class name**& operator=(std::initializer_list<value_type> list);

Effects:wherea=list;`a`

is the`multi_index_container`

object to which`*this`

belongs.

Returns:`*this`

.

`iterator iterator_to(const value_type& x);`

const_iterator iterator_to(const value_type& x)const;

Requires:`x`

is a reference to an element of the container.

Returns:An iterator to`x`

.

Complexity:Constant.

Exception safety:`nothrow`

.

`template<typename... Args>`

std::pair<iterator,bool> emplace(Args&&... args);

Requires:`value_type`

is`EmplaceConstructible`

into`multi_index_container`

from`args`

.

Effects:Inserts a`value_type`

object constructed with`std::forward<Args>(args)...`

into the`multi_index_container`

to which the index belongs if

- the index is non-unique OR no other element exists with equivalent key,
- AND insertion is allowed by all other indices of the
`multi_index_container`

.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, except that rehashing may occur even if the operation fails.

`template<typename... Args>`

iterator emplace_hint(iterator position, Args&&... args);

Requires:`value_type`

is`EmplaceConstructible`

into`multi_index_container`

from`args`

.`position`

is a valid iterator of the index.

Effects:Inserts a`value_type`

object constructed with`std::forward<Args>(args)...`

into the`multi_index_container`

to which the index belongs if

- the index is non-unique OR no other element exists with equivalent key,
- AND insertion is allowed by all other indices of the
`multi_index_container`

.`position`

is used as a hint to improve the efficiency of the operation.

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, except that rehashing may occur even if the operation fails.

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

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

Requires (first version):`value_type`

is`CopyInsertable`

into`multi_index_container`

.

Requires (second version):`value_type`

is`MoveInsertable`

into`multi_index_container`

.

Effects:Inserts`x`

into the`multi_index_container`

to which the index belongs if

- the index is non-unique OR no other element exists with equivalent key,
- AND insertion is allowed by all other indices of the
`multi_index_container`

.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, except that rehashing may occur even if the operation fails.

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

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

Requires (first version):`value_type`

is`CopyInsertable`

into`multi_index_container`

.`position`

is a valid iterator of the index.

Requires (second version):`value_type`

is`MoveInsertable`

into`multi_index_container`

.`position`

is a valid iterator of the index.

Effects:Inserts`x`

into the`multi_index_container`

to which the index belongs if

- the index is non-unique OR no other element exists with equivalent key,
- AND insertion is allowed by all other indices of the
`multi_index_container`

.`position`

is used as a hint to improve the efficiency of the operation.

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, except that rehashing may occur even if the operation fails.

`template<typename InputIterator>`

void insert(InputIterator first,InputIterator last);

Requires:`InputIterator`

is an input iterator.`value_type`

is`EmplaceConstructible`

into`multi_index_container`

from`*first`

.`first`

and`last`

are not iterators into any index of the`multi_index_container`

to which this index belongs.`last`

is reachable from`first`

.

Effects:For each element of [`first`

,`last`

), in this order, inserts it into the`multi_index_container`

to which this index belongs if

- the index is non-unique OR no other element exists with equivalent key,
- AND insertion is allowed by all other indices of the
`multi_index_container`

.Complexity:`O(m*I(n+m))`

, where`m`

is the number of elements in [`first`

,`last`

).

Exception safety:Basic.

`void insert(std::initializer_list<value_type> list);`

Effects:insert(list.begin(),list.end());

`insert_return_type insert(node_type&& nh);`

Requires:`nh.empty() || get_allocator()==nh.get_allocator()`

.

Effects:Does nothing if`nh`

is empty; otherwise, inserts the node owned by`nh`

into the`multi_index_container`

to which the index belongs if

- the index is non-unique OR no other element exists with equivalent key,
- AND insertion is allowed by all other indices of the
`multi_index_container`

.Postconditions:`nh`

is empty.

Returns:A value`p`

of type`insert_return_type`

. If`nh`

is empty,`p.position`

is`end()`

,`p.inserted`

is`false`

and`p.node`

is empty; on successful insertion,`p.position`

points to the element inserted,`p.inserted`

is`true`

and`p.node`

is empty; if the insertion failed,`p.position`

points to an element that caused the insertion to be banned,`p.inserted`

is`false`

and`p.node`

owns the original node. Note that more than one element can be causing insertion not to be allowed.

Complexity:`O(I(n))`

.

Exception safety:Strong, except that rehashing may occur even if the operation fails. If an exception is thrown,`nh`

is not changed.

`iterator insert(const_iterator position,node_type&& nh);`

Requires:`nh.empty() || get_allocator()==nh.get_allocator()`

.`position`

is a valid iterator of the index.

Effects:Does nothing if`nh`

is empty; otherwise, inserts the node owned by`nh`

into the`multi_index_container`

to which the index belongs if

- the index is non-unique OR no other element exists with equivalent key,
- AND insertion is allowed by all other indices of the
`multi_index_container`

.`position`

is used as a hint to improve the efficiency of the operation.

Postconditions:`nh`

is empty if insertion succeeds, and is not changed otherwise.

Returns:`end()`

if`nh`

is empty. 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, except that rehashing may occur even if the operation fails. If an exception is thrown,`nh`

is not changed.

`node_type extract(const_iterator position);`

Requires:`position`

is a valid dereferenceable iterator of the index.

Effects:Extracts the node of the element pointed to by`position`

.

Returns:A node handle owning the extracted node.

Complexity:`O(D(n))`

.

Exception safety:`nothrow`

.

`node_type extract(const key_type& x);`

Effects:Extracts the node of the first element with key equivalent to`x`

, if there is any.

Returns:A node handle owning the extracted node, or empty otherwise.

Complexity:Average case`O(1 + D(n))`

, worst case`O(n`

._{dist}+ D(n))

Exception safety:Strong.

`iterator erase(iterator position);`

Requires:`position`

is a valid dereferenceable iterator of the index.

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`

.

`size_type erase(const key_type& x);`

Effects:Deletes the elements with key equivalent to`x`

.

Returns:Number of elements deleted.

Complexity:Average case`O(1 + m*D(n))`

, worst case`O(n`

, where_{dist}+ m*D(n))`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 index.

Effects:Deletes the elements in [`first`

,`last`

).

Returns:`last`

.

Complexity:`O(m*D(n))`

, where`m`

is the number of elements in [`first`

,`last`

).

Exception safety:`nothrow`

.

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

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

Requires (first version):`value_type`

is`CopyAssignable`

.`position`

is a valid dereferenceable iterator of the index.

Requires (second version):`value_type`

is`MoveAssignable`

.`position`

is a valid dereferenceable iterator of the index.

Effects:Assigns the value`x`

to the element pointed to by`position`

into the`multi_index_container`

to which the index belongs if, for the value`x`

- the index is non-unique OR no other element exists (except possibly
`*position`

) with equivalent key,- AND replacing is allowed by all other indices of the
`multi_index_container`

.Postconditions:Validity of`position`

is preserved in all cases. If the key of the new value is equivalent to that of the replaced value, the position of the element does not change.

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`multi_index_container`

to which the index belongs remains in its original state.

`template<typename Modifier> bool modify(iterator position,Modifier mod);`

Requires:`mod`

is a unary function object accepting arguments of type`value_type&`

.`position`

is a valid dereferenceable iterator of the index. The execution of`mod(e)`

, where`e`

is the element pointed to by`position`

, does not invoke any operation of the`multi_index_container`

after`e`

is directly modified or, before modification, if the operation would invalidate`position`

.

Effects:Calls`mod(e)`

where`e`

is the element pointed to by`position`

and rearranges`*position`

into all the indices of the`multi_index_container`

. Rearrangement is successful ifIf the rearrangement fails, the element is erased.

- the index is non-unique OR no other element exists with equivalent key,
- AND rearrangement is allowed by all other indices of the
`multi_index_container`

.

Postconditions:Validity of`position`

is preserved if the operation succeeds. If the key of the modified value is equivalent to that of the original value, the position of the element does not change.

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 (including`mod`

), then the element pointed to by`position`

is erased.

`template<typename Modifier,typename Rollback>`

bool modify(iterator position,Modifier mod,Rollback back);

Requires:`mod`

and`back`

are unary function objects accepting arguments of type`value_type&`

.`position`

is a valid dereferenceable iterator of the index. The execution of`mod(e)`

, where`e`

is the element pointed to by`position`

, does not invoke any operation of the`multi_index_container`

after`e`

is directly modified or, before modification, if the operation would invalidate`position`

.`back(e)`

does not invoke any operation of the`multi_index_container`

.

Effects:Calls`mod(e)`

where`e`

is the element pointed to by`position`

and tries to rearrange`*position`

into all the indices of the`multi_index_container`

. Rearrangement is successful ifIf the rearrangement fails,

- the index is non-unique OR no other element exists with equivalent key,
- AND rearrangement is allowed by all other indices of the
`multi_index_container`

.`back(e)`

is invoked: if the resulting value of`e`

is consistent with its original position and constraints in all indices, the element is kept, otherwise it is erased.

Postconditions:Validity of`position`

is preserved except if the element is erased under the conditions described below. If the key of the modified value is equivalent to that of the original value, the position of the element does not change.

Returns:`true`

if the operation succeeded,`false`

otherwise.

Complexity:`O(M(n))`

.

Exception safety:Strong, except if`mod`

or`back`

throw an exception or`back(e)`

fails to properly restore the element or there is a throwing user-provided operation after invoking`back(e)`

, in which cases the modified element is erased. If`back`

throws inside the handling code executing after some other user-provided operation has thrown, it is the exception generated by`back`

that is rethrown.

`template<typename Modifier> bool modify_key(iterator position,Modifier mod);`

Requires:`key_from_value`

is a read/write`Key Extractor`

from`value_type`

.`mod`

is a unary function object accepting arguments of type`key_type&`

.`position`

is a valid dereferenceable iterator of the index. The execution of`mod(k)`

, where`k`

is the key of the element pointed to by`position`

, does not invoke any operation of the`multi_index_container`

after`k`

is directly modified or, before modification, if the operation would invalidate`position`

.

Effects:Equivalent to`modify(position,mod')`

, with`mod'`

defined in such a way that`mod'(x)`

is the same as`mod(key(x))`

, where`key`

is the internal`KeyFromValue`

object of the index.

`template<typename Modifier,typename Rollback>`

bool modify_key(iterator position,Modifier mod,Rollback back);

Requires:`key_from_value`

is a read/write`Key Extractor`

from`value_type`

.`mod`

and`back`

are unary function objects accepting arguments of type`key_type&`

.`position`

is a valid dereferenceable iterator of the index. The execution of`mod(k)`

, where`k`

is the key of the element pointed to by`position`

, does not invoke any operation of the`multi_index_container`

after`k`

is directly modified or, before modification, if the operation would invalidate`position`

.`back(k)`

does not invoke any operation of the`multi_index_container`

.

Effects:Equivalent to`modify(position,mod',back')`

, with`mod'`

and`back`

defined in such a way that`mod'(x)`

is the same as`mod(key(x))`

and`back'(x)`

is the same as`back(key(x))`

, where`key`

is the internal`KeyFromValue`

object of the index.

Apart from standard `hash_function`

and `key_eq`

,
hashed indices have a member function for retrieving the internal key extractor
used.

`key_from_value key_extractor()const;`

Returns a copy of the`key_from_value`

object used to construct the index.

Complexity:Constant.

Hashed indices provide the full lookup functionality required by
**[unord.req]**, namely `find`

,
`count`

, and `equal_range`

. Additionally,
these member functions are templatized to allow for non-standard
arguments, so extending the types of search operations allowed.
The kind of arguments permissible when invoking the lookup member
functions is defined by the following concept.

Consider a pair (`Hash`

, `Pred`

) where
`Hash`

is a hash functor over values of type `Key`

and `Pred`

is a binary predicate
inducing an equivalence relation
on `Key`

, with the additional constraint that equivalent
keys have the same hash value.
A triplet of types (`CompatibleKey`

, `CompatibleHash`

,
`CompatiblePred`

) is said to be a *compatible extension*
of (`Hash`

, `Pred`

) if

`CompatibleHash`

is a hash functor on values of type`CompatibleKey`

,`CompatiblePred`

is a binary predicate over (`Key`

,`CompatibleKey`

),`CompatiblePred`

is a binary predicate over (`CompatibleKey`

,`Key`

),- if
`c_eq(ck,k1)`

then`c_eq(k1,ck)`

, - if
`c_eq(ck,k1)`

and`eq(k1,k2)`

then`c_eq(ck,k2)`

, - if
`c_eq(ck,k1)`

and`c_eq(ck,k2)`

then`eq(k1,k2)`

, - if
`c_eq(ck,k1)`

then`c_hash(ck)==hash(k1)`

,

`c_hash`

of type `CompatibleHash`

,
`c_eq`

of type `CompatiblePred`

,
`hash`

of type `Hash`

,
`eq`

of type `Pred`

, `ck`

of type
`CompatibleKey`

and `k1`

, `k2`

of type
`Key`

.
Additionally, a type `CompatibleKey`

is said to be a
*compatible key* of (`Hash`

, `Pred`

) if
(`CompatibleKey`

, `Hash`

, `Pred`

)
is a compatible extension of (`Hash`

, `Pred`

).
This implies that `Hash`

and `Pred`

accept arguments
of type `CompatibleKey`

, which usually means they have
several overloads of their corresponding `operator()`

member functions.

In the context of a compatible extension or a compatible key, the expression "equivalent key" takes on its obvious interpretation.

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

Requires:`CompatibleKey`

is a compatible key of (`hasher`

,`key_equal`

).

Effects:Returns a pointer to an element whose key is equivalent to`x`

, or`end()`

if such an element does not exist.

Complexity:Average case`O(1)`

(constant), worst case`O(n`

._{dist})

`template<`

typename CompatibleKey,typename CompatibleHash, typename CompatiblePred

>

iterator find(

const CompatibleKey& x,

const CompatibleHash& hash,const CompatiblePred& eq)const;

Requires:(`CompatibleKey`

,`CompatibleHash`

,`CompatiblePred`

) is a compatible extension of (`hasher`

,`key_equal`

).

Effects:Returns a pointer to an element whose key is equivalent to`x`

, or`end()`

if such an element does not exist.

Complexity:Average case`O(1)`

(constant), worst case`O(n`

._{dist})

`template<typename CompatibleKey>`

size_type count(const CompatibleKey& x)const;

Requires:`CompatibleKey`

is a compatible key of (`hasher`

,`key_equal`

).

Effects:Returns the number of elements with key equivalent to`x`

.

Complexity:Average case`O(count(x))`

, worst case`O(count(x)+n`

._{dist})

`template<`

typename CompatibleKey,typename CompatibleHash, typename CompatiblePred

>

size_type count(

const CompatibleKey& x,

const CompatibleHash& hash,const CompatiblePred& eq)const;

Requires:(`CompatibleKey`

,`CompatibleHash`

,`CompatiblePred`

) is a compatible extension of (`hasher`

,`key_equal`

).

Effects:Returns the number of elements with key equivalent to`x`

.

Complexity:Average case`O(count(x,hash,eq))`

, worst case`O(count(x,hash,eq)+n`

._{dist})

`template<typename CompatibleKey>`

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

Requires:`CompatibleKey`

is a compatible key of (`hasher`

,`key_equal`

).

Effects:Returns a range containing all elements with keys equivalent to`x`

(and only those), or (`end()`

,`end()`

) if no such elements exist.

Complexity:Average case`O(1)`

(constant), worst case`O(n`

._{dist})

`template<`

typename CompatibleKey,typename CompatibleHash, typename CompatiblePred

>

std::pair<iterator,iterator> equal_range(

const CompatibleKey& x,

const CompatibleHash& hash,const CompatiblePred& eq)const;

Requires:(`CompatibleKey`

,`CompatibleHash`

,`CompatiblePred`

) is a compatible extension of (`hasher`

,`key_equal`

).

Effects:Returns a range containing all elements with keys equivalent to`x`

(and only those), or (`end()`

,`end()`

) if no such elements exist.

Complexity:Average case`O(1)`

(constant), worst case`O(n`

._{dist})

`local_iterator local_iterator_to(const value_type& x);`

const_local_iterator local_iterator_to(const value_type& x)const;

Requires:`x`

is a reference to an element of the container.

Returns:An iterator to`x`

.

Complexity:Constant.

Exception safety:`nothrow`

.

`void rehash(size_type n);`

Effects:Increases if necessary the number of internal buckets so that`size()/bucket_count()`

does not exceed the maximum load factor, and`bucket_count()>=n`

.

Postconditions:Validity of iterators and references to the elements contained is preserved.

Complexity:`O(m)`

, where`m`

is the number of non-equivalent elements in the index.

Exception safety:Strong.

`void reserve(size_type n);`

Effects:rehash(std::ceil(n/max_load_factor()));

`template<`*implementation defined*>

bool operator==(const *index class name*& x,const *index class name*& y);

Requires:`x.key_extractor()`

,`x.hash_function()`

and`x.key_eq()`

have the same behavior as the corresponding objects in`y`

. For any two elements`e1`

,`e2`

in`x`

or`y`

, if`e1==e2`

then their keys are equivalent.

Returns:`true`

iff`x`

and`y`

have the same size and for each key`k`

present in`x`

the range`x.equal_range(k)`

is equal (considering the`==`

operator of`value_type`

) to`y.equal_range(k)`

under permutations of the elements.

Complexity:Let`k`

,...,_{1}`k`

be the different keys present in_{m}`x`

:

(For unique indices, the formulas above reduce to average case

- If, for each
`k`

,_{i}`x.equal_range(k`

is arranged in the same order as_{i})`y.equal_range(k`

, average case is_{i})`O(x.size())`

, worst case`O(x.size()`

.^{2})- Otherwise, average case is
`O(Σ(x.count(k`

, worst case_{i})^{2}))`O(x.size()`

.^{2})`O(x.size())`

, worst case`O(x.size()`

.)^{2})

Indices cannot be serialized on their own, but only as part of the
`multi_index_container`

into which they are embedded. In describing
the additional preconditions and guarantees associated to hashed indices
with respect to serialization of their embedding containers, we
use the concepts defined in the `multi_index_container`

serialization section.

`multi_index_container`

`m`

to an
output archive (XML archive) `ar`

.
Operation: loading of aRequires:No additional requirements to those imposed by the container.

`multi_index_container`

`m'`

from an
input archive (XML archive) `ar`

.
Operation: saving of anRequires:Additionally to the general requirements,`key_eq()`

must be serialization-compatible with`m.get<i>().key_eq()`

, where`i`

is the position of the hashed index in the container.

Postconditions:On successful loading, the range [`begin()`

,`end()`

) contains restored copies of every element in [`m.get<i>().begin()`

,`m.get<i>().end()`

), though not necessarily in the same order.

`iterator`

or `const_iterator`

`it`

to an output archive (XML archive) `ar`

.
Operation: loading of anRequires:`it`

is a valid iterator of the index. The associated`multi_index_container`

has been previously saved.

`iterator`

or `const_iterator`

`it'`

from an input archive (XML archive) `ar`

.
Operation: saving of aPostconditions: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 vice versa.

`local_iterator`

or
`const_local_iterator`

`it`

to an output archive (XML archive) `ar`

.
Operation: loading of aRequires:`it`

is a valid local iterator of the index. The associated`multi_index_container`

has been previously saved.

`local_iterator`

or
`const_local_iterator`

`it'`

from an input archive (XML archive) `ar`

.
Postconditions:On successful loading, if`it`

was dereferenceable then`*it'`

is the restored copy of`*it`

; if`it`

was`m.get<i>().end(n)`

for some`n`

, then`it'==m'.get<i>().end(n)`

(where`m`

is the original`multi_index_container`

,`m'`

its restored copy and`i`

is the ordinal of the index.)

Note:It is allowed that`it`

be a`const_local_iterator`

and the restored`it'`

a`local_iterator`

, or vice versa.

Revised May 9th 2020

© Copyright 2003-2020 Joaquín M López Muñoz. Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)