# Boost.MultiIndex Hashed indices reference

Ordered indices
Boost.MultiIndex reference
Sequenced indices

## Contents

- Header `"boost/multi_index/hashed_index_fwd.hpp"` synopsis
- Header `"boost/multi_index/hashed_index.hpp"` synopsis
  - Index specifiers `hashed_unique` and `hashed_non_unique`
  - Hashed indices
    - Complexity signature
    - Instantiation types
    - Nested types
    - Constructors, copy and assignment
    - Modifiers
    - Observers
    - Lookup
    - Hash policy
    - Serialization

## Header `"boost/multi_index/hashed_index_fwd.hpp"` synopsis

>     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> class index 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.

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

>     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> class index class name implementation defined;

>     // 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

### Index specifiers `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.

### Hashed indices

A hashed index provides fast retrieval of elements of a `multi_index_container` through hashing tecnhiques. The interface and semantics of hashed indices are modeled according to the proposal for unordered associative containers given in the C++ Proposed Draft Tecnhical Report on Standard Library Extensions, also known as TR1. 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, hashed indices (both unique and non-unique) are models of `Unordered Associative Container`, in the spirit of `std::tr1::unordered_set`s. Validity of iterators and references to elements is preserved in all cases. Occasionally, the exception safety guarantees provided are actually stronger than required by the extension draft. We only provide descriptions of those types and operations that are either not present in the concepts modeled or do not exactly conform to the requirements for unordered associative containers.

>     namespace boost{

>     namespace multi_index{

>     namespace detail{

>     template<implementation defined: dependent on types Value, Allocator,
>       TagList, KeyFromValue, Hash, Pred>
>     class name 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 tuple<
>         size_type,key_from_value,hasher,key_equal>       ctor_args;
>       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;
>       typedef implementation defined                     size_type;
>       typedef implementation defined                     difference_type;
>       typedef implementation defined                     iterator;
>       typedef implementation defined                     const_iterator;
>       typedef implementation defined                     local_iterator;
>       typedef implementation defined                     const_local_iterator;

>       // construct/destroy/copy:

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

>       allocator_type get_allocator()const;

>       // size and capacity:

>       bool      empty()const;
>       size_type size()const;
>       size_type max_size()const;

>       // iterators:

>       iterator       begin();
>       const_iterator begin()const;
>       iterator       end();
>       const_iterator end()const;

>       // modifiers:

>       std::pair<iterator,bool> insert(const value_type& x);
>       iterator insert(iterator position,const value_type& x);
>       template<typename InputIterator>
>       void insert(InputIterator first,InputIterator last);

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

>       void clear();
>       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;
>       size_type max_bucket_count()const;
>       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;

>       // hash policy:

>       float load_factor()const;
>       float max_load_factor()const;
>       void  max_load_factor(float z);
>       void  rehash(size_type n);
>     };

>     // 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

#### Complexity signature

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` (constant), worst case `i(n)=n`,
- hinted insertion: average case `h(n)=1` (constant), worst case `h(n)=n`,
- deletion: average case `d(n)=1` (constant), worst case `d(n)=n`,
- 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`,
- modifying: average case `m(n)=1` (constant), worst case `m(n)=n`.

#### Instantiation types

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),
- `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 `Unary Function` 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 `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`.

#### Nested types

`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 models of `Forward Iterator`.

#### Constructors, copy and assignment

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:

> >     a=b;

> where `a` and `b` are the `multi_index_container` 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 `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.

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

> Requires: `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.

`template<typename 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 index of the `multi_index_container` 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 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 + 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 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);`

> Requires: `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.
> 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: `Modifier` is a model of `Unary Function` accepting arguments of type `value_type&`. `position` is a valid dereferenceable iterator of the index. 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 if
> - 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`.
> If the rearrangement fails, the element is erased.
> 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.

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

> Requires: `key_from_value` is a read/write `Key Extractor` from `value_type`. `Modifier` is a model of `Unary Function` accepting arguments of type `key_type&`. `position` is a valid dereferenceable iterator of the index. Effects: Calls `mod(k)` where `k` is the key obtained by the internal `KeyFromValue` object of the index from the element pointed to by `position`, and rearranges `*position` into all the indices of the `multi_index_container`. Rearrangement is successful if
> - 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`.
> If the rearrangement fails, the element is erased.
> 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.

#### Observers

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.

#### Lookup

Hashed indices provide the full lookup functionality required by unordered associative containers, 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

1. `CompatibleHash` is a hash functor on values of type `CompatibleKey`,
2. `CompatiblePred` is a `Binary Predicate` over (`Key`, `CompatibleKey`),
3. `CompatiblePred` is a `Binary Predicate` over (`CompatibleKey`, `Key`),
4. if `c_eq(ck,k1)` then `c_eq(k1,ck)`,
5. if `c_eq(ck,k1)` and `eq(k1,k2)` then `c_eq(ck,k2)`,
6. if `c_eq(ck,k1)` and `c_eq(ck,k2)` then `eq(k1,k2)`,
7. if `c_eq(ck,k1)` then `c_hash(ck)==hash(k1)`,

for every `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 therir 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)`.

`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)`.

`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(n)`.

`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(n)`.

`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).
> Complexity: Average case `O(count(x))`, worst case `O(n)`.

`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).
> Complexity: Average case `O(count(x,hash,eq))`, worst case `O(n)`.

#### Hash policy

`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: Average case `O(size())`, worst case `O(size(n)2)`.
> Exception safety: Strong.

#### Serialization

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.

Operation: saving of a `multi_index_container` `m` to an output archive (XML archive) `ar`.

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

Operation: loading of a `multi_index_container` `m'` from an input archive (XML archive) `ar`.

> Requires: 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 succesful 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.

Operation: saving of an `iterator` or `const_iterator` `it` to an output archive (XML archive) `ar`.

> Requires: `it` is a valid iterator of the index. The associated `multi_index_container` has been previously saved.

Operation: loading of an `iterator` or `const_iterator` `it'` from an input archive (XML archive) `ar`.

> Postconditions: On succesful 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.

Operation: saving of a `local_iterator` or `const_local_iterator` `it` to an output archive (XML archive) `ar`.

> Requires: `it` is a valid local iterator of the index. The associated `multi_index_container` has been previously saved.

Operation: loading of a `local_iterator` or `const_local_iterator` `it'` from an input archive (XML archive) `ar`.

> Postconditions: On succesful 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 viceversa.

Ordered indices
Boost.MultiIndex reference
Sequenced indices

Revised July 13th 2006

© Copyright 2003-2006 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)