# Boost.MultiIndex Sequenced indices reference

Hashed indices
Boost.MultiIndex reference
Random access indices

## Contents

- Header `"boost/multi_index/sequenced_index_fwd.hpp"` synopsis
- Header `"boost/multi_index/sequenced_index.hpp"` synopsis
  - `sequenced` index specifier
  - Sequenced indices
    - Complexity signature
    - Instantiation types
    - Constructors, copy and assignment
    - Iterators
    - Capacity operations
    - Modifiers
    - List operations
    - Rearrange operations
    - Serialization

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

>     namespace boost{

>     namespace multi_index{

>     // sequenced index specifier

>     template<typename TagList=tag<> > struct sequenced;

>     // indices

>     namespace detail{

>     template<implementation defined> class index class name implementation defined;

>     } // namespace boost::multi_index::detail

>     } // namespace boost::multi_index

>     } // namespace boost

`sequenced_index_fwd.hpp` provides forward declarations for the `sequenced` index specifier and its associated sequenced index class.

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

>     namespace boost{

>     namespace multi_index{

>     // sequenced index specifier

>     template<typename TagList=tag<> > struct sequenced;

>     // indices

>     namespace detail{

>     template<implementation defined> class index class name implementation defined;

>     // index comparison:

>     // OP is any of ==,<,!=,>,>=,<=

>     template<arg set 1,arg set 2>
>     bool operator OP(
>       const index class name<arg set 1>& x,const index class name<arg set 2>& 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

### `sequenced` index specifier

This index specifier allows for insertion of a sequenced index.

>     template<typename TagList=tag<> > struct sequenced;

If provided, `TagList` must be an instantiation of `tag`.

### Sequenced indices

Sequenced indices are modeled after the semantics of a bidirectional list like `std::list`. Elements in a sequenced index are by default sorted according to their order of insertion: this means that new elements inserted through a different index of the `multi_index_container` are appended to the end of the sequenced index. Additionally, the index allows for free reordering of elements in the same vein as `std::list` does. Validity of iterators and references to elements is preserved in all operations.

There are a number of differences with respect to `std::lists`:

- Sequenced indices are not `Assignable` (like any other index.)
- Unlike as in `std::list`, insertions into a sequenced index may fail due to clashings with other indices. This alters the semantics of the operations provided with respect to their analogues in `std::list`.
- Elements in a sequenced index are not mutable, and can only be changed by means of `replace` and `modify` member functions.

Having these restrictions into account, sequenced indices are models of `Reversible Container`, `Front Insertion Sequence` and `Back Insertion Sequence`. 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 these types of containers.

>     namespace boost{

>     namespace multi_index{

>     namespace detail{

>     template<implementation defined: dependent on types Value, Allocator, TagList>
>     class name is implementation defined
>     {
>     public:
>       // types:

>       typedef typename node_type::value_type             value_type;
>       typedef tuples::null_type                          ctor_args;
>       typedef TagList                                    tag_list;
>       typedef Allocator                                  allocator_type;
>       typedef typename allocator_type::reference         reference;
>       typedef typename allocator_type::const_reference   const_reference;
>       typedef implementation defined                     iterator;
>       typedef implementation defined                     const_iterator;
>       typedef std::size_t                                size_type;
>       typedef std::ptrdiff_t                             difference_type;
>       typedef typename allocator_type::pointer           pointer;
>       typedef typename allocator_type::const_pointer     const_pointer;
>       typedef equivalent to
>         std::reverse_iterator<iterator>                  reverse_iterator;
>       typedef equivalent to
>         std::reverse_iterator<const_iterator>            const_reverse_iterator;

>       // construct/copy/destroy:

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

>       template <class InputIterator>
>       void assign(InputIterator first,InputIterator last);
>       void assign(size_type n,const value_type& value);

>       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;
>       const_iterator         cbegin()const;
>       const_iterator         cend()const;
>       const_reverse_iterator crbegin()const;
>       const_reverse_iterator crend()const;

>       iterator       iterator_to(const value_type& x);
>       const_iterator iterator_to(const value_type& x)const;

>       // capacity:

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

>       void resize(size_type n,const value_type& x=value_type());

>       // access:

>       const_reference front()const;
>       const_reference back()const;

>       // modifiers:

>       std::pair<iterator,bool> push_front(const value_type& x);
>       void                     pop_front();
>       std::pair<iterator,bool> push_back(const value_type& x);
>       void                     pop_back();

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

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

>       void swap(index class name& x);

>       void clear();

>       // list operations:

>       void splice(iterator position,index class name& x);
>       void splice(iterator position,index class name& x,iterator i);
>       void splice(
>         iterator position,index class name& x,iterator first,iterator last);

>       void remove(const value_type& value);
>       template<typename Predicate> void remove_if(Predicate pred);

>       void unique();
>       template <class BinaryPredicate>
>       void unique(BinaryPredicate binary_pred);

>       void merge(index class name& x);
>       template <typename Compare> void merge(index class name& x,Compare comp);

>       void sort();
>       template <typename Compare> void sort(Compare comp);

>       void reverse();

>       // rearrange operations:

>       void relocate(iterator position,iterator i);
>       void relocate(iterator position,iterator first,iterator last);
>       template<typename InputIterator> void rearrange(InputIterator first);
>     }

>     // index comparison:

>     template<arg set 1,arg set 2>
>     bool operator==(
>       const index class name<arg set 1>& x,
>       const index class name<arg set 2>& y)
>     {
>       return x.size()==y.size()&&std::equal(x.begin(),x.end(),y.begin());
>     }

>     template<arg set 1,arg set 2>
>     bool operator<(
>       const index class name<arg set 1>& x,
>       const index class name<arg set 2>& y)
>     {
>       return std::lexicographical_compare(x.begin(),x.end(),y.begin(),y.end());
>     }

>     template<arg set 1,arg set 2>
>     bool operator!=(
>       const index class name<arg set 1>& x,
>       const index class name<arg set 2>& y)
>     {
>       return !(x==y);
>     }

>     template<arg set 1,arg set 2>
>     bool operator>(
>       const index class name<arg set 1>& x
>       ,const index class name<arg set 2>& y)
>     {
>       return y<x;
>     }

>     template<arg set 1,arg set 2>
>     bool operator>=(
>       const index class name<arg set 1>& x,
>       const index class name<arg set 2>& y)
>     {
>       return !(x<y);
>     }

>     template<arg set 1,arg set 2>
>     bool operator<=(
>       const index class name<arg set 1>& x,
>       const index class name<arg set 2>& 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

#### Complexity signature

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

- copying: `c(n)=n*log(n)`,
- insertion: `i(n)=1` (constant),
- hinted insertion: `h(n)=1` (constant),
- deletion: `d(n)=1` (constant),
- replacement: `r(n)=1` (constant),
- modifying: `m(n)=1` (constant).

#### Instantiation types

Sequenced indices are instantiated internally to `multi_index_container` and specified by means of `indexed_by` with the `sequenced` index specifier. 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).

`TagList` must be an instantiation of `tag`.

#### 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.

`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`.

`template <class InputIterator>
void assign(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:

> >     clear();
> >     insert(end(),first,last);

`void assign(size_type n,const value_type& value);`

> Effects:

> >     clear();
> >     for(size_type i=0;i<n;++n)push_back(v);

#### Iterators

`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`.

#### Capacity operations

`void resize(size_type n,const value_type& x=value_type());`

> Effects:

> >     if(n>size())insert(end(),n-size(),x);
> >     else if(n<size()){
> >       iterator it=begin();
> >       std::advance(it,n);
> >       erase(it,end());
> >     }

> Note: If an expansion is requested, the size of the index is not guaranteed to be `n` after this operation (other indices may ban insertions.)

#### Modifiers

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

> Effects: Inserts `x` at the beginning of the sequence if no other index of the `multi_index_container` bans the insertion.
> 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.

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

> Effects: Inserts `x` at the end of the sequence if no other index of the `multi_index_container` bans the insertion.
> 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.

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

> Requires: `position` is a valid iterator of the index.
> Effects: Inserts `x` before `position` if 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.

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

> Requires: `position` is a valid iterator of the index.
> Effects:

> >     for(size_type i=0;i<n;++i)insert(position,x);

`template<typename InputIterator>
void insert(iterator position,InputIterator first,InputIterator last);`

> Requires: `position` is a valid iterator of the index. `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:

> >     while(first!=last)insert(position,*first++);

> Complexity: `O(m*I(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`.

`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 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 on sequenced indices does not change the position of the element with respect to the index; rearrangement on other indices may or might not succeed. 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,typename Rollback>
bool modify(iterator position,Modifier mod,Rollback back);`

> Requires: `Modifier` and `Rollback` are models of `Unary Function` accepting arguments of type `value_type&`. `position` is a valid dereferenceable iterator of the index. The sequence of operations `mod(e)`, `back(e)`, where `e` is the element pointed to by `position`, restores all keys of the element to their original state.
> 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 on sequenced indices does not change the position of the element with respect to the index; rearrangement on other indices may or might not succeed. If the rearrangement fails, `back(e)` is invoked and the element is kept at its original position in all indices.
> Postconditions: Validity of `position` is preserved except if the element is erased under the conditions described below.
> Returns: `true` if the operation succeeded, `false` otherwise.
> Complexity: `O(M(n))`.
> Exception safety: Strong, except if `back` throws an exception, in which case 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.

#### List operations

Sequenced indices provide the full set of list operations found in `std::list`; the semantics of these member functions, however, differ from that of `std::list` in some cases as insertions might not succeed due to banning by other indices. Similarly, the complexity of the operations may depend on the other indices belonging to the same `multi_index_container`.

`void splice(iterator position,index class name& x);`

> Requires: `position` is a valid iterator of the index. `&x!=this`.
> Effects: Inserts the contents of `x` before `position`, in the same order as they were in `x`. Those elements succesfully inserted are erased from `x`.
> Complexity: `O(x.size()*I(n+x.size()) + x.size()*D(x.size()))`.
> Exception safety: Basic.

`void splice(iterator position,index class name& x,iterator i);`

> Requires: `position` is a valid iterator of the index. `i` is a valid dereferenceable iterator `x`.
> Effects: Inserts the element pointed to by `i` before `position`: if insertion is succesful, the element is erased from `x`. In the special case `&x==this`, no copy or deletion is performed, and the operation is always succesful. If `position==i`, no operation is performed.
> Postconditions: If `&x==this`, no iterator or reference is invalidated.
> Complexity: If `&x==this`, constant; otherwise `O(I(n) + D(n))`.
> Exception safety: If `&x==this`, `nothrow`; otherwise, strong.

`void splice(iterator position,index class name& x,iterator first,iterator last);`

> Requires: `position` is a valid iterator of the index. `first` and `last` are valid iterators of `x`. `last` is reachable from `first`. `position` is not in the range [`first`,`last`).
> Effects: For each element in the range [`first`,`last`), insertion is tried before `position`; if the operation is succesful, the element is erased from `x`. In the special case `&x==this`, no copy or deletion is performed, and insertions are always succesful.
> Postconditions: If `&x==this`, no iterator or reference is invalidated.
> Complexity: If `&x==this`, constant; otherwise `O(m*I(n+m) + m*D(x.size()))` where `m` is the number of elements in [`first`,`last`).
> Exception safety: If `&x==this`, `nothrow`; otherwise, basic.

`void remove(const value_type& value);`

> Effects: Erases all elements of the index which compare equal to `value`.
> Complexity: `O(n + m*D(n))`, where `m` is the number of elements erased.
> Exception safety: Basic.

`template<typename Predicate> void remove_if(Predicate pred);`

> Effects: Erases all elements `x` of the index for which `pred(x)` holds.
> Complexity: `O(n + m*D(n))`, where `m` is the number of elements erased.
> Exception safety: Basic.

`void unique();`

> Effects: Eliminates all but the first element from every consecutive group of equal elements referred to by the iterator `i` in the range [`first+1`,`last`) for which `*i==*(i-1)`.
> Complexity: `O(n + m*D(n))`, where `m` is the number of elements erased.
> Exception safety: Basic.

`template <class BinaryPredicate> void unique(BinaryPredicate binary_pred);`

> Effects: Eliminates all but the first element from every consecutive group of elements referred to by the iterator `i` in the range [`first+1`,`last`) for which `binary_pred(*i,*(i-1))` holds.
> Complexity: `O(n + m*D(n))`, where `m` is the number of elements erased.
> Exception safety: Basic.

`void merge(index class name& x);`

> Requires: `std::less<value_type>` is a `Strict Weak Ordering` over `value_type`. Both the index and `x` are sorted according to `std::less<value_type>`.
> Effects: Attempts to insert every element of `x` into the corresponding position of the index (according to the order). Elements successfully inserted are erased from `x`. The resulting sequence is stable, i.e. equivalent elements of either container preserve their relative position. In the special case `&x==this`, no operation is performed.
> Postconditions: Elements in the index and remaining elements in `x` are sorted. Validity of iterators to the index and of non-erased elements of `x` references is preserved.
> Complexity: If `&x==this`, constant; otherwise `O(n + x.size()*I(n+x.size()) + x.size()*D(x.size()))`.
> Exception safety: If `&x==this`, `nothrow`; otherwise, basic.

`template <typename Compare> void merge(index class name& x,Compare comp);`

> Requires: `Compare` is a `Strict Weak Ordering` over `value_type`. Both the index and `x` are sorted according to `comp`.
> Effects: Attempts to insert every element of `x` into the corresponding position of the index (according to `comp`). Elements successfully inserted are erased from `x`. The resulting sequence is stable, i.e. equivalent elements of either container preserve their relative position. In the special case `&x==this`, no operation is performed.
> Postconditions: Elements in the index and remaining elements in `x` are sorted according to `comp`. Validity of iterators to the index and of non-erased elements of `x` references is preserved.
> Complexity: If `&x==this`, constant; otherwise `O(n + x.size()*I(n+x.size()) + x.size()*D(x.size()))`.
> Exception safety: If `&x==this`, `nothrow`; otherwise, basic.

`void sort();`

> Requires: `std::less<value_type>` is a `Strict Weak Ordering` over `value_type`.
> Effects: Sorts the index according to `std::less<value_type>`. The sorting is stable, i.e. equivalent elements preserve their relative position.
> Postconditions: Validity of iterators and references is preserved.
> Complexity: `O(n*log(n))`.
> Exception safety: `nothrow` if `std::less<value_type>` does not throw; otherwise, basic.

`template <typename Compare> void sort(Compare comp);`

> Requires: `Compare` is a `Strict Weak Ordering` over `value_type`.
> Effects: Sorts the index according to `comp`. The sorting is stable, i.e. equivalent elements preserve their relative position.
> Postconditions: Validity of iterators and references is preserved.
> Complexity: `O(n*log(n))`.
> Exception safety: `nothrow` if `comp` does not throw; otherwise, basic.

`void reverse();`

> Effects: Reverses the order of the elements in the index.
> Postconditions: Validity of iterators and references is preserved.
> Complexity: `O(n)`.
> Exception safety: `nothrow`.

#### Rearrange operations

These operations, without counterpart in `std::list` (although `splice` provides partially overlapping functionality), perform individual and global repositioning of elements inside the index.

`void relocate(iterator position,iterator i);`

> Requires: `position` is a valid iterator of the index. `i` is a valid dereferenceable iterator of the index.
> Effects: Inserts the element pointed to by `i` before `position`. If `position==i`, no operation is performed.
> Postconditions: No iterator or reference is invalidated.
> Complexity: Constant.
> Exception safety: `nothrow`.

`void relocate(iterator position,iterator first,iterator last);`

> Requires: `position` is a valid iterator of the index. `first` and `last` are valid iterators of the index. `last` is reachable from `first`. `position` is not in the range [`first`,`last`).
> Effects: The range of elements [`first`,`last`) is repositioned just before `position`.
> Postconditions: No iterator or reference is invalidated.
> Complexity: Constant.
> Exception safety: `nothrow`.

`template<typename InputIterator> void rearrange(InputIterator first);`

> Requires: The range [`first`, `std::advance(first,n)`), where `n` is the size of the index, is a free view of the index.
> Effects: The elements are rearranged so as to match the order of the previously described view.
> Postconditions: No iterator or reference is invalidated.
> Complexity: `O(n)`.
> Exception safety: Basic.

#### 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 sequenced 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: No additional requirements to those imposed by the container.
> Postconditions: On succesful 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()`), where `i` is the position of the sequenced index in the container.

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.

Hashed indices
Boost.MultiIndex reference
Random access indices

Revised July 21st 2009

© Copyright 2003-2009 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)