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<h1><img src="../../../../boost.png" alt="boost.png (6897 bytes)" align=
"middle" width="277" height="86">Boost.MultiIndex Ordered indices reference</h1>

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Index reference
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Boost.MultiIndex reference
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<h2>Contents</h2>

<ul>
  <li><a href="#ord_index_fwd_synopsis">Header
    <code>"boost/multi_index/ordered_index_fwd.hpp"</code> synopsis</a></li>
  <li><a href="#synopsis">Header
    <code>"boost/multi_index/ordered_index.hpp"</code> synopsis</a>
    <ul>
      <li><a href="#unique_non_unique">
        Index specifiers <code>ordered_unique</code> and <code>ordered_non_unique</code>
        </a></li>
      <li><a href="#ord_indices">Ordered indices</a>
        <ul>
          <li><a href="#complexity_signature">Complexity signature</a></li>
          <li><a href="#instantiation_types">Instantiation types</a></li>
          <li><a href="#constructors">Constructors, copy and assignment</a></li>
          <li><a href="#iterators">Iterators</a></li>
          <li><a href="#modifiers">Modifiers</a></li>
          <li><a href="#observers">Observers</a></li>
          <li><a href="#set_operations">Set operations</a></li>
          <li><a href="#range_operations">Range operations</a></li>
          <li><a href="#serialization">Serialization</a></li>
        </ul>
      </li>
    </ul>
  </li>
</ul>

<h2>
<a name="ord_index_fwd_synopsis">Header
<a href="../../../../boost/multi_index/ordered_index_fwd.hpp">
<code>"boost/multi_index/ordered_index_fwd.hpp"</code></a> synopsis</a></h2>

<blockquote><pre>
<span class=keyword>namespace</span> <span class=identifier>boost</span><span class=special>{</span>

<span class=keyword>namespace</span> <span class=identifier>multi_index</span><span class=special>{</span>

<span class=comment>// index specifiers ordered_unique and ordered_non_unique</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>consult ordered_unique reference for arguments</b><span class=special>&gt;</span>
<span class=keyword>struct</span> <span class=identifier>ordered_unique</span><span class=special>;</span>
<span class=keyword>template</span><span class=special>&lt;</span><b>consult ordered_non_unique reference for arguments</b><span class=special>&gt;</span>
<span class=keyword>struct</span> <span class=identifier>ordered_non_unique</span><span class=special>;</span>

<span class=comment>// indices</span>

<span class=keyword>namespace</span> <span class=identifier>detail</span><span class=special>{</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>implementation defined</b><span class=special>&gt;</span> <span class=keyword>class</span> <b>index name is implementation defined</b><span class=special>;</span>

<span class=special>}</span> <span class=comment>// namespace boost::multi_index::detail</span>

<span class=special>}</span> <span class=comment>// namespace boost::multi_index</span> 

<span class=special>}</span> <span class=comment>// namespace boost</span>
</pre></blockquote>

<p>
<code>ordered_index_fwd.hpp</code> provides forward declarations for index specifiers 
<a href="#unique_non_unique"><code>ordered_unique</code> and <code>ordered_non_unique</code></a> and
their associated <a href="#ord_indices">ordered index</a> classes.
</p>

<h2>
<a name="synopsis">Header
<a href="../../../../boost/multi_index/ordered_index.hpp">
<code>"boost/multi_index/ordered_index.hpp"</code></a> synopsis</a></h2>

<blockquote><pre>
<span class=preprocessor>#include</span> <span class=special>&lt;</span><span class=identifier>initializer_list</span><span class=special>&gt;</span>

<span class=keyword>namespace</span> <span class=identifier>boost</span><span class=special>{</span>

<span class=keyword>namespace</span> <span class=identifier>multi_index</span><span class=special>{</span>

<span class=comment>// index specifiers ordered_unique and ordered_non_unique</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>consult ordered_unique reference for arguments</b><span class=special>&gt;</span>
<span class=keyword>struct</span> <span class=identifier>ordered_unique</span><span class=special>;</span>
<span class=keyword>template</span><span class=special>&lt;</span><b>consult ordered_non_unique reference for arguments</b><span class=special>&gt;</span>
<span class=keyword>struct</span> <span class=identifier>ordered_non_unique</span><span class=special>;</span>

<span class=comment>// indices</span>

<span class=keyword>namespace</span> <span class=identifier>detail</span><span class=special>{</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>implementation defined</b><span class=special>&gt;</span> <span class=keyword>class</span> <b>index class name implementation defined</b><span class=special>;</span>

<span class=comment>// index comparison:</span>

<span class=comment>// <b>OP</b> is any of ==,&lt;,!=,&gt;,&gt;=,&lt;=</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>arg set 1</b><span class=special>,</span><b>arg set 2</b><span class=special>&gt;</span>
<span class=keyword>bool</span> <span class=keyword>operator</span> <b><i>OP</i></b><span class=special>(</span>
  <span class=keyword>const</span> <b>index class name</b><span class=special>&lt;</span><b>arg set 1</b><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span><span class=keyword>const</span> <b>index class name</b><span class=special>&lt;</span><b>arg set 2</b><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>);</span>

<span class=comment>// index specialized algorithms:</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>implementation defined</b><span class=special>&gt;</span>
<span class=keyword>void</span> <span class=identifier>swap</span><span class=special>(</span><b>index class name</b><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span><b>index class name</b><span class=special>&amp;</span> <span class=identifier>y</span><span class=special>);</span>

<span class=special>}</span> <span class=comment>// namespace boost::multi_index::detail</span>

<span class=special>}</span> <span class=comment>// namespace boost::multi_index</span> 

<span class=special>}</span> <span class=comment>// namespace boost</span>
</pre></blockquote>

<h3><a name="unique_non_unique">
Index specifiers <code>ordered_unique</code> and <code>ordered_non_unique</code>
</a></h3>

<p>
These <a href="indices.html#index_specification">index specifiers</a> allow
for insertion of <a href="#ord_indices">ordered indices</a> without and with
allowance of duplicate elements, respectively. The syntax of <code>ordered_unique</code>
and <code>ordered_non_unique</code> coincide, thus we describe them in a grouped manner.
<code>ordered_unique</code> and <code>ordered_non_unique</code> can be instantiated in
two different forms, according to whether a tag list for the index is provided or not:
</p>

<blockquote><pre>
<span class=keyword>template</span><span class=special>&lt;</span>
  <span class=keyword>typename</span> <span class=identifier>KeyFromValue</span><span class=special>,</span>
  <span class=keyword>typename</span> <span class=identifier>Compare</span><span class=special>=</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>less</span><span class=special>&lt;</span><span class=identifier>KeyFromValue</span><span class=special>::</span><span class=identifier>result_type</span><span class=special>&gt;</span>
<span class=special>&gt;</span>
<span class=keyword>struct</span> <span class=special>(</span><span class=identifier>ordered_unique</span> <span class=special>|</span> <span class=identifier>ordered_non_unique</span><span class=special>)</span><span class=special>;</span>

<span class=keyword>template</span><span class=special>&lt;</span>
  <span class=keyword>typename</span> <span class=identifier>TagList</span><span class=special>,</span>
  <span class=keyword>typename</span> <span class=identifier>KeyFromValue</span><span class=special>,</span>
  <span class=keyword>typename</span> <span class=identifier>Compare</span><span class=special>=</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>less</span><span class=special>&lt;</span><span class=identifier>KeyFromValue</span><span class=special>::</span><span class=identifier>result_type</span><span class=special>&gt;</span>
<span class=special>&gt;</span>
<span class=keyword>struct</span> <span class=special>(</span><span class=identifier>ordered_unique</span> <span class=special>|</span> <span class=identifier>ordered_non_unique</span><span class=special>)</span><span class=special>;</span>
</pre></blockquote>

<p>
If provided, <code>TagList</code> must be an instantiation of the class template
<a href="indices.html#tag"><code>tag</code></a>.
The template arguments are used by the corresponding index implementation,
refer to the <a href="#ord_indices">ordered indices</a> reference section for further
explanations on their acceptable type values.
</p>

<h3><a name="ord_indices">Ordered indices</a></h3>

<p>
An ordered index provides a set-like interface to the underlying heap of
elements contained in a <code>multi_index_container</code>. An ordered index is
particularized according to a given
<a href="key_extraction.html#key_extractors"><code>Key Extractor</code></a>
that retrieves keys from elements of <code>multi_index_container</code> and a comparison
predicate.
</p>

<p>
There are two variants of ordered indices: <i>unique</i>, which do
not allow duplicate elements (with respect to its associated comparison
predicate) and <i>non-unique</i>, 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.
</p>

<p>
Except where noted or if the corresponding interface does not exist,
ordered indices (both unique and non-unique) satisfy the C++ requirements
for associative containers at <b>[associative.reqmts]</b>
(supporting unique and equivalent keys, respectively.)
Accordingly, validity of iterators and references to elements is
preserved. We only provide descriptions of those types and operations that 
do not exactly conform to or are not mandated by the standard requirements.
</p>

<blockquote><pre>
<span class=keyword>namespace</span> <span class=identifier>boost</span><span class=special>{</span>

<span class=keyword>namespace</span> <span class=identifier>multi_index</span><span class=special>{</span>

<b>implementation defined </b><span class=identifier>unbounded</span><span class=special>;</span> <span class=comment>// see range()</span>

<span class=keyword>namespace</span> <span class=identifier>detail</span><span class=special>{</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>implementation defined: dependent on types Value, Allocator,
  TagList, KeyFromValue, Compare</b><span class=special>&gt;</span>
<span class=keyword>class</span> <b>name is implementation defined</b>
<span class=special>{</span> 
<span class=keyword>public</span><span class=special>:</span>
  <span class=comment>// types:</span>

  <span class=keyword>typedef</span> <span class=keyword>typename</span> <span class=identifier>KeyFromValue</span><span class=special>::</span><span class=identifier>result_type</span>         <span class=identifier>key_type</span><span class=special>;</span>
  <span class=keyword>typedef</span> <span class=identifier>Value</span>                                      <span class=identifier>value_type</span><span class=special>;</span>
  <span class=keyword>typedef</span> <span class=identifier>KeyFromValue</span>                               <span class=identifier>key_from_value</span><span class=special>;</span>
  <span class=keyword>typedef</span> <span class=identifier>Compare</span>                                    <span class=identifier>key_compare</span><span class=special>;</span>
  <span class=keyword>typedef</span> <b>implementation defined                     </b><span class=identifier>value_compare</span><span class=special>;</span>
  <span class=keyword>typedef</span> <span class=identifier>boost</span><span class=special>::</span><span class=identifier>tuple</span><span class=special>&lt;</span><span class=identifier>key_from_value</span><span class=special>,</span><span class=identifier>key_compare</span><span class=special>&gt;</span>   <span class=identifier>ctor_args</span><span class=special>;</span>
  <span class=keyword>typedef</span> <span class=identifier>TagList</span>                                    <span class=identifier>tag_list</span><span class=special>;</span>
  <span class=keyword>typedef</span> <span class=identifier>Allocator</span>                                  <span class=identifier>allocator_type</span><span class=special>;</span>
  <span class=keyword>typedef</span> <span class=keyword>typename</span> <span class=identifier>Allocator</span><span class=special>::</span><span class=identifier>reference</span>              <span class=identifier>reference</span><span class=special>;</span>
  <span class=keyword>typedef</span> <span class=keyword>typename</span> <span class=identifier>Allocator</span><span class=special>::</span><span class=identifier>const_reference</span>        <span class=identifier>const_reference</span><span class=special>;</span>
  <span class=keyword>typedef</span> <b>implementation defined                     </b><span class=identifier>iterator</span><span class=special>;</span>
  <span class=keyword>typedef</span> <b>implementation defined                     </b><span class=identifier>const_iterator</span><span class=special>;</span>
  <span class=keyword>typedef</span> <b>implementation defined                     </b><span class=identifier>size_type</span><span class=special>;</span>      
  <span class=keyword>typedef</span> <b>implementation defined                     </b><span class=identifier>difference_type</span><span class=special>;</span>
  <span class=keyword>typedef</span> <span class=keyword>typename</span> <span class=identifier>Allocator</span><span class=special>::</span><span class=identifier>pointer</span>                <span class=identifier>pointer</span><span class=special>;</span>
  <span class=keyword>typedef</span> <span class=keyword>typename</span> <span class=identifier>Allocator</span><span class=special>::</span><span class=identifier>const_pointer</span>          <span class=identifier>const_pointer</span><span class=special>;</span>
  <span class=keyword>typedef</span> <b>equivalent to
    std::reverse_iterator&lt;iterator&gt;</b>                  <span class=identifier>reverse_iterator</span><span class=special>;</span>
  <span class=keyword>typedef</span> <b>equivalent to
    std::reverse_iterator&lt;const_iterator&gt;</b>            <span class=identifier>const_reverse_iterator</span><span class=special>;</span>

  <span class=comment>// construct/copy/destroy:</span>

  <b>index class name</b><span class=special>&amp;</span> <span class=keyword>operator</span><span class=special>=(</span><span class=keyword>const</span> <b>index class name</b><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>);</span>
  <b>index class name</b><span class=special>&amp;</span> <span class=keyword>operator</span><span class=special>=(</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>initializer_list</span><span class=special>&lt;</span><span class=identifier>value_type</span><span class=special>&gt;</span> <span class=identifier>list</span><span class=special>);</span>

  <span class=identifier>allocator_type</span> <span class=identifier>get_allocator</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>

  <span class=comment>// iterators:</span>

  <span class=identifier>iterator</span>               <span class=identifier>begin</span><span class=special>()</span><span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>const_iterator</span>         <span class=identifier>begin</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>iterator</span>               <span class=identifier>end</span><span class=special>()</span><span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>const_iterator</span>         <span class=identifier>end</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>reverse_iterator</span>       <span class=identifier>rbegin</span><span class=special>()</span><span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>const_reverse_iterator</span> <span class=identifier>rbegin</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>reverse_iterator</span>       <span class=identifier>rend</span><span class=special>()</span><span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>const_reverse_iterator</span> <span class=identifier>rend</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>const_iterator</span>         <span class=identifier>cbegin</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>const_iterator</span>         <span class=identifier>cend</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>const_reverse_iterator</span> <span class=identifier>crbegin</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>const_reverse_iterator</span> <span class=identifier>crend</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>
 
  <span class=identifier>iterator</span>       <span class=identifier>iterator_to</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>value_type</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>);</span>
  <span class=identifier>const_iterator</span> <span class=identifier>iterator_to</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>value_type</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

  <span class=comment>// capacity:</span>

  <span class=keyword>bool</span>      <span class=identifier>empty</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>size_type</span> <span class=identifier>size</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>size_type</span> <span class=identifier>max_size</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>

  <span class=comment>// modifiers:</span>

  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span><span class=special>...</span> <span class=identifier>Args</span><span class=special>&gt;</span>
  <span class=identifier>std</span><span class=special>::</span><span class=identifier>pair</span><span class=special>&lt;</span><span class=identifier>iterator</span><span class=special>,</span><span class=keyword>bool</span><span class=special>&gt;</span> <span class=identifier>emplace</span><span class=special>(</span><span class=identifier>Args</span><span class=special>&amp;&amp;...</span> <span class=identifier>args</span><span class=special>);</span>
  <span class=keyword>template</span> <span class=special>&lt;</span><span class=keyword>typename</span><span class=special>...</span> <span class=identifier>Args</span><span class=special>&gt;</span>
  <span class=identifier>iterator</span> <span class=identifier>emplace_hint</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>position</span><span class=special>,</span><span class=identifier>Args</span><span class=special>&amp;&amp;...</span> <span class=identifier>args</span><span class=special>);</span>
  <span class=identifier>std</span><span class=special>::</span><span class=identifier>pair</span><span class=special>&lt;</span><span class=identifier>iterator</span><span class=special>,</span><span class=keyword>bool</span><span class=special>&gt;</span> <span class=identifier>insert</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>value_type</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>);</span>
  <span class=identifier>std</span><span class=special>::</span><span class=identifier>pair</span><span class=special>&lt;</span><span class=identifier>iterator</span><span class=special>,</span><span class=keyword>bool</span><span class=special>&gt;</span> <span class=identifier>insert</span><span class=special>(</span><span class=identifier>value_type</span><span class=special>&amp;&amp;</span> <span class=identifier>x</span><span class=special>);</span>
  <span class=identifier>iterator</span> <span class=identifier>insert</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>position</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>value_type</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>);</span>
  <span class=identifier>iterator</span> <span class=identifier>insert</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>position</span><span class=special>,</span><span class=identifier>value_type</span><span class=special>&amp;&amp;</span> <span class=identifier>x</span><span class=special>);</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>InputIterator</span><span class=special>&gt;</span>
  <span class=keyword>void</span> <span class=identifier>insert</span><span class=special>(</span><span class=identifier>InputIterator</span> <span class=identifier>first</span><span class=special>,</span><span class=identifier>InputIterator</span> <span class=identifier>last</span><span class=special>);</span>
  <span class=keyword>void</span> <span class=identifier>insert</span><span class=special>(</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>initializer_list</span><span class=special>&lt;</span><span class=identifier>value_type</span><span class=special>&gt;</span> <span class=identifier>list</span><span class=special>);</span>

  <span class=identifier>iterator</span>  <span class=identifier>erase</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>position</span><span class=special>);</span>
  <span class=identifier>size_type</span> <span class=identifier>erase</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>key_type</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>);</span>
  <span class=identifier>iterator</span>  <span class=identifier>erase</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>first</span><span class=special>,</span><span class=identifier>iterator</span> <span class=identifier>last</span><span class=special>);</span>

  <span class=keyword>bool</span> <span class=identifier>replace</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>position</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>value_type</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>);</span>
  <span class=keyword>bool</span> <span class=identifier>replace</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>position</span><span class=special>,</span><span class=identifier>value_type</span><span class=special>&amp;&amp;</span> <span class=identifier>x</span><span class=special>);</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Modifier</span><span class=special>&gt;</span> <span class=keyword>bool</span> <span class=identifier>modify</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>position</span><span class=special>,</span><span class=identifier>Modifier</span> <span class=identifier>mod</span><span class=special>);</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Modifier</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Rollback</span><span class=special>&gt;</span>
  <span class=keyword>bool</span> <span class=identifier>modify</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>position</span><span class=special>,</span><span class=identifier>Modifier</span> <span class=identifier>mod</span><span class=special>,</span><span class=identifier>Rollback</span> <span class=identifier>back</span><span class=special>);</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Modifier</span><span class=special>&gt;</span> <span class=keyword>bool</span> <span class=identifier>modify_key</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>position</span><span class=special>,</span><span class=identifier>Modifier</span> <span class=identifier>mod</span><span class=special>);</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Modifier</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Rollback</span><span class=special>&gt;</span>
  <span class=keyword>bool</span> <span class=identifier>modify_key</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>position</span><span class=special>,</span><span class=identifier>Modifier</span> <span class=identifier>mod</span><span class=special>,</span><span class=identifier>Rollback</span> <span class=identifier>back</span><span class=special>);</span>
  
  <span class=keyword>void</span> <span class=identifier>swap</span><span class=special>(</span><b>index class name</b><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>);</span>
  <span class=keyword>void</span> <span class=identifier>clear</span><span class=special>()</span><span class=keyword>noexcept</span><span class=special>;</span>

  <span class=comment>// observers:</span>

  <span class=identifier>key_from_value</span> <span class=identifier>key_extractor</span><span class=special>()</span><span class=keyword>const</span><span class=special>;</span>
  <span class=identifier>key_compare</span>    <span class=identifier>key_comp</span><span class=special>()</span><span class=keyword>const</span><span class=special>;</span>
  <span class=identifier>value_compare</span>  <span class=identifier>value_comp</span><span class=special>()</span><span class=keyword>const</span><span class=special>;</span>

  <span class=comment>// set operations:</span>

  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>&gt;</span>
  <span class=identifier>iterator</span> <span class=identifier>find</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompatibleCompare</span><span class=special>&gt;</span>
  <span class=identifier>iterator</span> <span class=identifier>find</span><span class=special>(</span>
    <span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>CompatibleCompare</span><span class=special>&amp;</span> <span class=identifier>comp</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>&gt;</span>
  <span class=identifier>size_type</span> <span class=identifier>count</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompatibleCompare</span><span class=special>&gt;</span>
  <span class=identifier>size_type</span> <span class=identifier>count</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>CompatibleCompare</span><span class=special>&amp;</span> <span class=identifier>comp</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>&gt;</span>
  <span class=identifier>iterator</span> <span class=identifier>lower_bound</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompatibleCompare</span><span class=special>&gt;</span>
  <span class=identifier>iterator</span> <span class=identifier>lower_bound</span><span class=special>(</span>
    <span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>CompatibleCompare</span><span class=special>&amp;</span> <span class=identifier>comp</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>&gt;</span>
  <span class=identifier>iterator</span> <span class=identifier>upper_bound</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompatibleCompare</span><span class=special>&gt;</span>
  <span class=identifier>iterator</span> <span class=identifier>upper_bound</span><span class=special>(</span>
    <span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>CompatibleCompare</span><span class=special>&amp;</span> <span class=identifier>comp</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>&gt;</span>
  <span class=identifier>std</span><span class=special>::</span><span class=identifier>pair</span><span class=special>&lt;</span><span class=identifier>iterator</span><span class=special>,</span><span class=identifier>iterator</span><span class=special>&gt;</span> <span class=identifier>equal_range</span><span class=special>(</span>
    <span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompatibleCompare</span><span class=special>&gt;</span>
  <span class=identifier>std</span><span class=special>::</span><span class=identifier>pair</span><span class=special>&lt;</span><span class=identifier>iterator</span><span class=special>,</span><span class=identifier>iterator</span><span class=special>&gt;</span> <span class=identifier>equal_range</span><span class=special>(</span>
    <span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>CompatibleCompare</span><span class=special>&amp;</span> <span class=identifier>comp</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

  <span class=comment>// range:</span>

  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>LowerBounder</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>UpperBounder</span><span class=special>&gt;</span>
  <span class=identifier>std</span><span class=special>::</span><span class=identifier>pair</span><span class=special>&lt;</span><span class=identifier>iterator</span><span class=special>,</span><span class=identifier>iterator</span><span class=special>&gt;</span> <span class=identifier>range</span><span class=special>(</span>
    <span class=identifier>LowerBounder</span> <span class=identifier>lower</span><span class=special>,</span><span class=identifier>UpperBounder</span> <span class=identifier>upper</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
<span class=special>};</span>

<span class=comment>// index comparison:</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>arg set 1</b><span class=special>,</span><b>arg set 2</b><span class=special>&gt;</span>
<span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>==(</span>
  <span class=keyword>const</span> <b>index class name</b><span class=special>&lt;</span><b>arg set 1</b><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
  <span class=keyword>const</span> <b>index class name</b><span class=special>&lt;</span><b>arg set 2</b><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span>
<span class=special>{</span>
  <span class=keyword>return</span> <span class=identifier>x</span><span class=special>.</span><span class=identifier>size</span><span class=special>()==</span><span class=identifier>y</span><span class=special>.</span><span class=identifier>size</span><span class=special>()&amp;&amp;</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>equal</span><span class=special>(</span><span class=identifier>x</span><span class=special>.</span><span class=identifier>begin</span><span class=special>(),</span><span class=identifier>x</span><span class=special>.</span><span class=identifier>end</span><span class=special>(),</span><span class=identifier>y</span><span class=special>.</span><span class=identifier>begin</span><span class=special>());</span>
<span class=special>}</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>arg set 1</b><span class=special>,</span><b>arg set 2</b><span class=special>&gt;</span>
<span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>&lt;(</span>
  <span class=keyword>const</span> <b>index class name</b><span class=special>&lt;</span><b>arg set 1</b><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
  <span class=keyword>const</span> <b>index class name</b><span class=special>&lt;</span><b>arg set 2</b><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span>
<span class=special>{</span>
  <span class=keyword>return</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>lexicographical_compare</span><span class=special>(</span><span class=identifier>x</span><span class=special>.</span><span class=identifier>begin</span><span class=special>(),</span><span class=identifier>x</span><span class=special>.</span><span class=identifier>end</span><span class=special>(),</span><span class=identifier>y</span><span class=special>.</span><span class=identifier>begin</span><span class=special>(),</span><span class=identifier>y</span><span class=special>.</span><span class=identifier>end</span><span class=special>());</span>
<span class=special>}</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>arg set 1</b><span class=special>,</span><b>arg set 2</b><span class=special>&gt;</span>
<span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>!=(</span>
  <span class=keyword>const</span> <b>index class name</b><span class=special>&lt;</span><b>arg set 1</b><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
  <span class=keyword>const</span> <b>index class name</b><span class=special>&lt;</span><b>arg set 2</b><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span>
<span class=special>{</span>
  <span class=keyword>return</span> <span class=special>!(</span><span class=identifier>x</span><span class=special>==</span><span class=identifier>y</span><span class=special>);</span>
<span class=special>}</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>arg set 1</b><span class=special>,</span><b>arg set 2</b><span class=special>&gt;</span>
<span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>&gt;(</span>
  <span class=keyword>const</span> <b>index class name</b><span class=special>&lt;</span><b>arg set 1</b><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
  <span class=keyword>const</span> <b>index class name</b><span class=special>&lt;</span><b>arg set 2</b><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span>
<span class=special>{</span>
  <span class=keyword>return</span> <span class=identifier>y</span><span class=special>&lt;</span><span class=identifier>x</span><span class=special>;</span>
<span class=special>}</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>arg set 1</b><span class=special>,</span><b>arg set 2</b><span class=special>&gt;</span>
<span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>&gt;=(</span>
  <span class=keyword>const</span> <b>index class name</b><span class=special>&lt;</span><b>arg set 1</b><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
  <span class=keyword>const</span> <b>index class name</b><span class=special>&lt;</span><b>arg set 2</b><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span>
<span class=special>{</span>
  <span class=keyword>return</span> <span class=special>!(</span><span class=identifier>x</span><span class=special>&lt;</span><span class=identifier>y</span><span class=special>);</span>
<span class=special>}</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>arg set 1</b><span class=special>,</span><b>arg set 2</b><span class=special>&gt;</span>
<span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>&lt;=(</span>
  <span class=keyword>const</span> <b>index class name</b><span class=special>&lt;</span><b>arg set 1</b><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
  <span class=keyword>const</span> <b>index class name</b><span class=special>&lt;</span><b>arg set 2</b><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span>
<span class=special>{</span>
  <span class=keyword>return</span> <span class=special>!(</span><span class=identifier>x</span><span class=special>&gt;</span><span class=identifier>y</span><span class=special>);</span>
<span class=special>}</span>

<span class=comment>// index specialized algorithms:</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>implementation defined</b><span class=special>&gt;</span>
<span class=keyword>void</span> <span class=identifier>swap</span><span class=special>(</span><b>index class name</b><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span><b>index class name</b><span class=special>&amp;</span> <span class=identifier>y</span><span class=special>);</span>

<span class=special>}</span> <span class=comment>// namespace boost::multi_index::detail</span>

<span class=special>}</span> <span class=comment>// namespace boost::multi_index</span> 

<span class=special>}</span> <span class=comment>// namespace boost</span>
</pre></blockquote>

<h4><a name="complexity_signature">Complexity signature</a></h4>

<p>
Here and in the descriptions of operations of ordered indices, we adopt the
scheme outlined in the 
<a href="indices.html#complexity_signature">complexity signature
section</a>. The complexity signature of ordered indices is:
<ul>
  <li>copying: <code>c(n)=n*log(n)</code>,</li>
  <li>insertion: <code>i(n)=log(n)</code>,</li>
  <li>hinted insertion: <code>h(n)=1</code> (constant) if the hint element
    is immediately after the point of insertion, <code>h(n)=log(n)</code> otherwise,</li>
  <li>deletion: <code>d(n)=1</code> (amortized constant),</li>
  <li>replacement: <code>r(n)=1</code> (constant) if the element position does not
    change, <code>r(n)=log(n)</code> otherwise,</li>
  <li>modifying: <code>m(n)=1</code> (constant) if the element position does not
    change, <code>m(n)=log(n)</code> otherwise.</li>
</ul>
</p>

<h4><a name="instantiation_types">Instantiation types</a></h4>

<p>Ordered indices are instantiated internally to <code>multi_index_container</code> and
specified by means of <a href="indices.html#indexed_by"><code>indexed_by</code></a>
with <a href="#unique_non_unique"> index specifiers <code>ordered_unique</code>
and <code>ordered_non_unique</code></a>. Instantiations are dependent on the
following types:
<ul>
  <li><code>Value</code> from <code>multi_index_container</code>,</li>
  <li><code>Allocator</code> from <code>multi_index_container</code>,</li>
  <li><code>TagList</code> from the index specifier (if provided, otherwise <code>tag&lt;&gt;</code> is assumed),</li>
  <li><code>KeyFromValue</code> from the index specifier,</li>
  <li><code>Compare</code> from the index specifier.</li>
</ul>
<code>TagList</code> must be an instantiation of
<a href="indices.html#tag"><code>tag</code></a>. The type <code>KeyFromValue</code>,
which determines the mechanism for extracting a key from <code>Value</code>,
must be a model of <a href="key_extraction.html#key_extractors">
<code>Key Extractor</code></a> from <code>Value</code>. <code>Compare</code> is a
<code>CopyConstructible</code> binary predicate inducing a strict weak order
on elements of <code>KeyFromValue::result_type</code>.
</p>

<h4><a name="constructors">Constructors, copy and assignment</a></h4>

<p>
As explained in the <a href="indices.html#index_concepts">index
concepts section</a>, indices do not have public constructors or destructors.
Assignment, on the other hand, is provided.
</p>

<code><b>index class name</b>&amp; operator=(const <b>index class name</b>&amp; x);</code>

<blockquote>
<b>Effects:</b>
<blockquote><pre>
<span class=identifier>a</span><span class=special>=</span><span class=identifier>b</span><span class=special>;</span>
</pre></blockquote>
where <code>a</code> and <code>b</code> are the <code>multi_index_container</code>
objects to which <code>*this</code> and <code>x</code> belong, respectively.<br>
<b>Returns:</b> <code>*this</code>.<br>
</blockquote>

<code><b>index class name</b>&amp; operator=(std::initializer_list&lt;value_type&gt; list);</code>

<blockquote>
<b>Effects:</b>
<blockquote><pre>
<span class=identifier>a</span><span class=special>=</span><span class=identifier>list</span><span class=special>;</span>
</pre></blockquote>
where <code>a</code> is the <code>multi_index_container</code>
object to which <code>*this</code> belongs.<br>
<b>Returns:</b> <code>*this</code>.<br>
</blockquote>

<h4><a name="iterators">Iterators</a></h4>

<code>iterator&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;iterator_to(const value_type&amp; x);<br>
const_iterator iterator_to(const value_type&amp; x)const;</code>
  
<blockquote>
<b>Requires:</b> <code>x</code> is a reference to an element of the container.<br>
<b>Returns:</b> An iterator to <code>x</code>.<br>
<b>Complexity:</b> Constant.<br>
<b>Exception safety:</b> <code>nothrow</code>.<br>
</blockquote>

<h4><a name="modifiers">Modifiers</a></h4>

<code>template&lt;typename... Args&gt;<br>
std::pair&lt;iterator,bool&gt; emplace(Args&amp;&amp;... args);</code>

<blockquote>
<b>Requires:</b> <code>value_type</code> is <code>EmplaceConstructible</code>
into <code>multi_index_container</code> from <code>args</code>.<br>
<b>Effects:</b> Inserts a <code>value_type</code> object constructed with
<code>std::forward&lt;Args&gt;(args)...</code> into the <code>multi_index_container</code> to which
the index belongs if
<ul>
  <li>the index is non-unique OR no other element exists with
    equivalent key,</li>
  <li>AND insertion is allowed by all other indices of the
    <code>multi_index_container</code>.</li>
</ul>
<b>Returns:</b> The return value is a pair <code>p</code>. <code>p.second</code>
is <code>true</code> if and only if insertion took place. On successful insertion,
<code>p.first</code> points to the element inserted; otherwise, <code>p.first</code>
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.<br>
<b>Complexity:</b> <code>O(I(n))</code>.<br>
<b>Exception safety:</b> Strong.<br>
</blockquote>

<code>template&lt;typename... Args&gt;<br>
iterator emplace_hint(iterator position, Args&amp;&amp;... args);</code>

<blockquote>
<b>Requires:</b> <code>value_type</code> is <code>EmplaceConstructible</code>
into <code>multi_index_container</code> from <code>args</code>.
<code>position</code> is a valid iterator of the index.<br>
<b>Effects:</b> Inserts a <code>value_type</code> object constructed with
<code>std::forward&lt;Args&gt;(args)...</code> into the <code>multi_index_container</code> to which
the index belongs if
<ul>
  <li>the index is non-unique OR no other element exists with
    equivalent key,</li>
  <li>AND insertion is allowed by all other indices of the
    <code>multi_index_container</code>.</li>
</ul>
<code>position</code> is used as a hint to improve the efficiency of the
operation. If successful, insertion happens as close as possible to the
location just prior to <code>position</code>.<br>
<b>Returns:</b> 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.<br>
<b>Complexity:</b> <code>O(H(n))</code>.<br>
<b>Exception safety:</b> Strong.<br>
</blockquote>

<code>std::pair&lt;iterator,bool> insert(const value_type&amp; x);</code><br>
<code>std::pair&lt;iterator,bool> insert(value_type&amp;&amp; x);</code>

<blockquote>
<b>Requires (first version):</b> <code>value_type</code> is <code>CopyInsertable</code>
into <code>multi_index_container</code>.<br>
<b>Requires (second version):</b> <code>value_type</code> is <code>MoveInsertable</code>
into <code>multi_index_container</code>.<br>
<b>Effects:</b> Inserts <code>x</code> into the <code>multi_index_container</code> to which
the index belongs if
<ul>
  <li>the index is non-unique OR no other element exists with
    equivalent key,</li>
  <li>AND insertion is allowed by all other indices of the
    <code>multi_index_container</code>.</li>
</ul>
<b>Returns:</b> The return value is a pair <code>p</code>. <code>p.second</code>
is <code>true</code> if and only if insertion took place. On successful insertion,
<code>p.first</code> points to the element inserted; otherwise, <code>p.first</code>
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.<br>
<b>Complexity:</b> <code>O(I(n))</code>.<br>
<b>Exception safety:</b> Strong.<br>
</blockquote>

<code>iterator insert(iterator position,const value_type&amp; x);</code><br>
<code>iterator insert(iterator position,value_type&amp;&amp; x);</code>

<blockquote>
<b>Requires (first version):</b> <code>value_type</code> is <code>CopyInsertable</code>
into <code>multi_index_container</code>.
<code>position</code> is a valid iterator of the index.<br>
<b>Requires (second version):</b> <code>value_type</code> is <code>MoveInsertable</code>
into <code>multi_index_container</code>.
<code>position</code> is a valid iterator of the index.<br>
<b>Effects:</b> Inserts <code>x</code> into the <code>multi_index_container</code> to which
the index belongs if
<ul>
  <li>the index is non-unique OR no other element exists with
    equivalent key,</li>
  <li>AND insertion is allowed by all other indices of the
    <code>multi_index_container</code>.</li>
</ul>
<code>position</code> is used as a hint to improve the efficiency of the
operation. If successful, insertion happens as close as possible to the
location just prior to <code>position</code>.<br>
<b>Returns:</b> 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.<br>
<b>Complexity:</b> <code>O(H(n))</code>.<br>
<b>Exception safety:</b> Strong.<br>
</blockquote>

<code>template&lt;typename InputIterator><br>
void insert(InputIterator first,InputIterator last);</code>

<blockquote>
<b>Requires:</b> <code>InputIterator</code> is an input iterator.
<code>value_type</code> is <code>EmplaceConstructible</code> into
<code>multi_index_container</code> from <code>*first</code>.
<code>first</code> and <code>last</code> are not iterators into any
index of the <code>multi_index_container</code> to which this index belongs.
<code>last</code> is reachable from <code>first</code>.<br>
<b>Effects:</b>
For each element of [<code>first</code>, <code>last</code>), in this
order, inserts it into the <code>multi_index_container</code>
to which this index belongs if
<ul>
  <li>the index is non-unique OR no other element exists with
    equivalent key,</li>
  <li>AND insertion is allowed by all other indices of the
    <code>multi_index_container</code>.</li>
</ul>
<b>Complexity:</b> <code>O(m*H(n+m))</code>, where
<code>m</code> is the number of elements in [<code>first</code>,
<code>last</code>).<br>
<b>Exception safety:</b> Basic.<br>
</blockquote>

<code>void insert(std::initializer_list&lt;value_type&gt; list);</code>

<blockquote>
<b>Effects:</b>
<blockquote><pre>
<span class=identifier>insert</span><span class=special>(</span><span class=identifier>list</span><span class=special>.</span><span class=identifier>begin</span><span class=special>(),</span><span class=identifier>list</span><span class=special>.</span><span class=identifier>end</span><span class=special>())</span><span class=special>;</span>
</pre></blockquote>
</blockquote>

<code>iterator erase(iterator position);</code>

<blockquote>
<b>Requires:</b> <code>position</code> is a valid dereferenceable  iterator
of the index.<br>
<b>Effects:</b> Deletes the element pointed to by <code>position</code>.<br>
<b>Returns:</b> An iterator pointing to the element immediately following
the one that was deleted, or <code>end()</code>
if no such element exists.<br>
<b>Complexity:</b> <code>O(D(n))</code>.<br>
<b>Exception safety:</b> <code>nothrow</code>.<br>
</blockquote>

<code>size_type erase(const key_type&amp; x);</code>

<blockquote>
<b>Effects:</b> Deletes the elements with key equivalent to <code>x</code>.<br>
<b>Returns:</b> Number of elements deleted.<br>
<b>Complexity:</b> <code>O(log(n) + m*D(n))</code>, where <code>m</code> is
the number of elements deleted.<br>
<b>Exception safety:</b> Basic.<br>
</blockquote>

<code>iterator erase(iterator first,iterator last);</code>

<blockquote>
<b>Requires:</b> [<code>first</code>,<code>last</code>) is a valid
range of the index.<br>
<b>Effects:</b> Deletes the elements in [<code>first</code>,<code>last</code>).<br>
<b>Returns:</b> <code>last</code>.<br>
<b>Complexity:</b> <code>O(log(n) + m*D(n))</code>, where <code>m</code> is
the number of elements in [<code>first</code>,<code>last</code>).<br>
<b>Exception safety:</b> <code>nothrow</code>.<br>
</blockquote>

<a name="replace"><code>bool replace(iterator position,const value_type&amp; x);</code></a><br>
<code>bool replace(iterator position,value_type&amp;&amp; x);</code>

<blockquote>
<b>Requires (first version):</b> <code>value_type</code> is <code>CopyAssignable</code>.
<code>position</code> is a valid dereferenceable iterator of the index.<br>
<b>Requires (second version):</b> <code>value_type</code> is <code>MoveAssignable</code>.
<code>position</code> is a valid dereferenceable iterator of the index.<br>
<b>Effects:</b> Assigns the value <code>x</code> to the element pointed
to by <code>position</code> into the <code>multi_index_container</code> to which
the index belongs if, for the value <code>x</code>
<ul>
  <li>the index is non-unique OR no other element exists
    (except possibly <code>*position</code>) with equivalent key,</li>
  <li>AND replacing is allowed by all other indices of the
    <code>multi_index_container</code>.</li>
</ul>
<b>Postconditions:</b> Validity of <code>position</code> 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.<br>
<b>Returns:</b> <code>true</code> if the replacement took place,
<code>false</code> otherwise.<br>
<b>Complexity:</b> <code>O(R(n))</code>.<br>
<b>Exception safety:</b> Strong. If an exception is thrown by some
user-provided operation the <code>multi_index_container</code> to which the index
belongs remains in its original state.
</blockquote>
  
<a name="modify">
<code>template&lt;typename Modifier> bool modify(iterator position,Modifier mod);</code></a>

<blockquote>
<b>Requires:</b> <code>mod</code> is a unary function object
accepting arguments of type
<code>value_type&amp;</code>. <code>position</code> is a valid dereferenceable
iterator of the index.
The execution of <code>mod(e)</code>, where <code>e</code> is the element
pointed to by <code>position</code>, does not invoke any operation of the
<code>multi_index_container</code> after <code>e</code> is directly modified
or, before modification, if the operation would invalidate <code>position</code>.<br>
<b>Effects:</b> Calls <code>mod(e)</code> where <code>e</code> is the element
pointed to by <code>position</code> and rearranges <code>*position</code> into
all the indices of the <code>multi_index_container</code>. Rearrangement is successful if
<ul>
  <li>the index is non-unique OR no other element exists
    with  equivalent key,</li>
  <li>AND rearrangement is allowed by all other indices of the
    <code>multi_index_container</code>.</li>
</ul>
If the rearrangement fails, the element is erased.<br>
<b>Postconditions:</b> Validity of <code>position</code> 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.<br>
<b>Returns:</b> <code>true</code> if the operation succeeded, <code>false</code>
otherwise.<br>
<b>Complexity:</b> <code>O(M(n))</code>.<br>
<b>Exception safety:</b> Basic. If an exception is thrown by some
user-provided operation (including <code>mod</code>), then
the element pointed to by <code>position</code> is erased.
</blockquote>

<code>template&lt;typename Modifier,typename Rollback><br>
bool modify(iterator position,Modifier mod,Rollback back);</code>

<blockquote>
<b>Requires:</b> <code>mod</code> and <code>back</code> are unary function
objects accepting arguments of type
<code>value_type&amp;</code>. <code>position</code> is a valid dereferenceable
iterator of the index.
The execution of <code>mod(e)</code>, where <code>e</code> is the element
pointed to by <code>position</code>, does not invoke any operation of the
<code>multi_index_container</code> after <code>e</code> is directly modified
or, before modification, if the operation would invalidate <code>position</code>.
<code>back(e)</code> does not invoke any operation of the
<code>multi_index_container</code>.<br>
<b>Effects:</b> Calls <code>mod(e)</code> where <code>e</code> is the element
pointed to by <code>position</code> and tries to rearrange <code>*position</code> into
all the indices of the <code>multi_index_container</code>. Rearrangement is successful if
<ul>
  <li>the index is non-unique OR no other element exists
    with  equivalent key,</li>
  <li>AND rearrangement is allowed by all other indices of the
    <code>multi_index_container</code>.</li>
</ul>
If the rearrangement fails, <code>back(e)</code> is invoked: if the resulting value
of <code>e</code> is consistent with its original position and constraints in all
indices, the element is kept, otherwise it is erased.<br>
<b>Postconditions:</b> Validity of <code>position</code> 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.<br>
<b>Returns:</b> <code>true</code> if the operation succeeded, <code>false</code>
otherwise.<br>
<b>Complexity:</b> <code>O(M(n))</code>.<br>
<b>Exception safety:</b> Strong, except if <code>mod</code> or <code>back</code> throw an
exception or <code>back(e)</code> fails to properly restore the element or there is
a throwing user-provided operation after invoking <code>back(e)</code>, in which cases
the modified element is erased. If <code>back</code>
throws inside the handling code executing after some other user-provided
operation has thrown, it is the exception generated by <code>back</code> that
is rethrown.
</blockquote>

<a name="modify_key">    
<code>template&lt;typename Modifier> bool modify_key(iterator position,Modifier mod);</code></a>

<blockquote>
<b>Requires:</b> <code>key_from_value</code> is a read/write
<a href="key_extraction.html#key_extractors"><code>Key Extractor</code></a>
from <code>value_type</code>. <code>mod</code> is a
unary function object accepting arguments of type
<code>key_type&amp;</code>. <code>position</code> is a valid dereferenceable
iterator of the index.
The execution of <code>mod(k)</code>, where <code>k</code> is the key of the element
pointed to by <code>position</code>, does not invoke any operation of the
<code>multi_index_container</code> after <code>k</code> is directly modified
or, before modification, if the operation would invalidate <code>position</code>.<br>
<b>Effects:</b> Equivalent to <code>modify(position,mod')</code>,
with <code>mod'</code> defined in such a way that
<code>mod'(x)</code> is the same as <code>mod(key(x))</code>, where
<code>key</code> is the internal <code>KeyFromValue</code> object of the index.
</blockquote>

<code>template&lt;typename Modifier,typename Rollback><br>
bool modify_key(iterator position,Modifier mod,Rollback back);</code>

<blockquote>
<b>Requires:</b> <code>key_from_value</code> is a read/write
<a href="key_extraction.html#key_extractors"><code>Key Extractor</code></a>
from <code>value_type</code>. <code>mod</code> and <code>back</code>
are unary function objects accepting arguments of type
<code>key_type&amp;</code>. <code>position</code> is a valid dereferenceable
iterator of the index.
The execution of <code>mod(k)</code>, where <code>k</code> is the key of the element
pointed to by <code>position</code>, does not invoke any operation of the
<code>multi_index_container</code> after <code>k</code> is directly modified
or, before modification, if the operation would invalidate <code>position</code>.
<code>back(k)</code> does not invoke any operation of the
<code>multi_index_container</code>.<br>
<b>Effects:</b> Equivalent to <code>modify(position,mod',back')</code>,
with <code>mod'</code> and <code>back</code> defined in such a way that
<code>mod'(x)</code> is the same as <code>mod(key(x))</code> and
<code>back'(x)</code> is the same as <code>back(key(x))</code>, where
<code>key</code> is the internal <code>KeyFromValue</code> object of the index.
</blockquote>

<h4><a name="observers">Observers</a></h4>

<p>Apart from standard <code>key_comp</code> and <code>value_comp</code>,
ordered indices have a member function for retrieving the internal key extractor
used.
</p>

<code>key_from_value key_extractor()const;</code>

<blockquote>
Returns a copy of the <code>key_from_value</code> object used to construct
the index.<br>
<b>Complexity:</b> Constant.
</blockquote>

<h4><a name="set_operations">Set operations</a></h4>

<p>
Ordered indices provide the full lookup functionality required by
<b>[associative.reqmts]</b>, namely <code>find</code>,
<code>count</code>, <code>lower_bound</code>, <code>upper_bound</code>
and <code>equal_range</code>. 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.
</p>

<p>
Consider a binary predicate <code>Compare</code> inducing a strict
weak order over values of type <code>Key</code>. A pair of types (<code>CompatibleKey</code>, 
<code>CompatibleCompare</code>) is said to be a <i>compatible extension</i>
of <code>Compare</code> if
<ol>
  <li><code>CompatibleCompare</code> is a binary predicate over (<code>Key</code>,
    <code>CompatibleKey</code>),</li>
  <li><code>CompatibleCompare</code> is a binary predicate over (<code>CompatibleKey</code>,
    <code>Key</code>),</li>
  <li>if <code>c_comp(ck,k1)</code> then <code>!c_comp(k1,ck)</code>,</li>
  <li>if <code>!c_comp(ck,k1)</code> and <code>!comp(k1,k2)</code> then
    <code>!c_comp(ck,k2)</code>,</li>
  <li>if <code>!c_comp(k1,ck)</code> and <code>!comp(k2,k1)</code> then
    <code>!c_comp(k2,ck)</code>,</li>
</ol>
for every <code>c_comp</code> of type <code>CompatibleCompare</code>,
<code>comp</code> of type <code>Compare</code>, <code>ck</code> of type
<code>CompatibleKey</code> and <code>k1</code>, <code>k2</code> of type
<code>Key</code>.
</p>


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

<p>
In the context of a compatible extension or a compatible key, the expressions
"equivalent", "less than" and "greater than" take on their obvious
interpretations.
</p>

<code>template&lt;typename CompatibleKey> iterator find(const CompatibleKey&amp; x)const;
</code>

<blockquote>
<b>Requires:</b> <code>CompatibleKey</code> is a compatible key of
<code>key_compare</code>.<br>
<b>Effects:</b> Returns a pointer to an element whose key is equivalent to
<code>x</code>, or <code>end()</code> if such an element does not exist.<br>
<b>Complexity:</b> <code>O(log(n))</code>.<br>
</blockquote>

<code>template&lt;typename CompatibleKey,typename CompatibleCompare><br>
iterator find(const CompatibleKey&amp; x,const CompatibleCompare&amp; comp)const;
</code>

<blockquote>
<b>Requires:</b> (<code>CompatibleKey</code>, <code>CompatibleCompare</code>)
is a compatible extension of <code>key_compare</code>.<br>
<b>Effects:</b> Returns a pointer to an element whose key is equivalent to
<code>x</code>, or <code>end()</code> if such an element does not exist.<br>
<b>Complexity:</b> <code>O(log(n))</code>.<br>
</blockquote>

<code>template&lt;typename CompatibleKey> size_type<br>
count(const CompatibleKey&amp; x)const;
</code>

<blockquote>
<b>Requires:</b> <code>CompatibleKey</code> is a compatible key of
<code>key_compare</code>.<br>
<b>Effects:</b> Returns the number of elements with key equivalent to <code>x</code>.<br>
<b>Complexity:</b> <code>O(log(n) + count(x))</code>.<br>
</blockquote>

<code>template&lt;typename CompatibleKey,typename CompatibleCompare><br>
size_type count(const CompatibleKey&amp; x,const CompatibleCompare&amp; comp)const;
</code>

<blockquote>
<b>Requires:</b> (<code>CompatibleKey</code>, <code>CompatibleCompare</code>)
is a compatible extension of <code>key_compare</code>.<br>
<b>Effects:</b> Returns the number of elements with key equivalent to <code>x</code>.<br>
<b>Complexity:</b> <code>O(log(n) + count(x,comp))</code>.<br>
</blockquote>

<code>template&lt;typename CompatibleKey><br>
iterator lower_bound(const CompatibleKey&amp; x)const;
</code>

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

<code>template&lt;typename CompatibleKey,typename CompatibleCompare><br>
iterator lower_bound(const CompatibleKey&amp; x,const CompatibleCompare&amp; comp)const;
</code>

<blockquote>
<b>Requires:</b> (<code>CompatibleKey</code>, <code>CompatibleCompare</code>)
is a compatible extension of <code>key_compare</code>.<br>
<b>Effects:</b> Returns an iterator pointing to the first element with
key not less than <code>x</code>, or <code>end()</code> if such an element does
not exist.<br>
<b>Complexity:</b> <code>O(log(n))</code>.<br>
</blockquote>

<code>template&lt;typename CompatibleKey><br>
iterator upper_bound(const CompatibleKey&amp; x)const;
</code>

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

<code>template&lt;typename CompatibleKey,typename CompatibleCompare><br>
iterator upper_bound(const CompatibleKey&amp; x,const CompatibleCompare&amp; comp)const;
</code>

<blockquote>
<b>Requires:</b> (<code>CompatibleKey</code>, <code>CompatibleCompare</code>)
is a compatible extension of <code>key_compare</code>.<br>
<b>Effects:</b> Returns an iterator pointing to the first element with
key greater than <code>x</code>, or <code>end()</code> if such an element does
not exist.<br>
<b>Complexity:</b> <code>O(log(n))</code>.<br>
</blockquote>

<code>template&lt;typename CompatibleKey><br>
std::pair&lt;iterator,iterator> equal_range(<br>
&nbsp;&nbsp;const CompatibleKey&amp; x)const;
</code>

<blockquote>
<b>Requires:</b> <code>CompatibleKey</code> is a compatible key of
<code>key_compare</code>.<br>
<b>Effects:</b> Equivalent to <code>make_pair(lower_bound(x),upper_bound(x))</code>.<br>
<b>Complexity:</b> <code>O(log(n))</code>.<br>
</blockquote>

<code>template&lt;typename CompatibleKey,typename CompatibleCompare><br>
std::pair&lt;iterator,iterator> equal_range(<br>
&nbsp;&nbsp;const CompatibleKey&amp; x,const CompatibleCompare&amp; comp)const;
</code>

<blockquote>
<b>Requires:</b> (<code>CompatibleKey</code>, <code>CompatibleCompare</code>)
is a compatible extension of <code>key_compare</code>.<br>
<b>Effects:</b> Equivalent to
<code>make_pair(lower_bound(x,comp),upper_bound(x,comp))</code>.<br>
<b>Complexity:</b> <code>O(log(n))</code>.<br>
</blockquote>


<h4><a name="range_operations">Range operations</a></h4>

<p>
The member function <code>range</code> is not defined for sorted associative
containers, but ordered indices provide it as a convenient utility. A range
or interval is defined by two conditions for the lower and upper bounds, which
are modeled after the following concepts.
</p>

<p>
Consider a binary predicate <code>Compare</code> inducing a strict
weak order over values of type <code>Key</code>. A type <code>LowerBounder</code> is said to be
a <i>lower bounder</i> of <code>Compare</code> if
<ol>
  <li><code>LowerBounder</code> is a predicate over <code>Key</code>,</li>
  <li>if <code>lower(k1)</code> and <code>!comp(k2,k1)</code> then
    <code>lower(k2)</code>,</li>
</ol>
for every <code>lower</code> of type <code>LowerBounder</code>,
<code>comp</code> of type <code>Compare</code>, and <code>k1</code>,
<code>k2</code> of type <code>Key</code>. Similarly, an <i>upper bounder</i>
is a type <code>UpperBounder</code> such that
<ol>
  <li><code>UpperBounder</code> is a predcate over <code>Key</code>,</li>
  <li>if <code>upper(k1)</code> and <code>!comp(k1,k2)</code> then
    <code>upper(k2)</code>,</li>
</ol>
for every <code>upper</code> of type <code>UpperBounder</code>,
<code>comp</code> of type <code>Compare</code>, and <code>k1</code>,
<code>k2</code> of type <code>Key</code>.
</p>

<code>template&lt;typename LowerBounder,typename UpperBounder><br>
std::pair&lt;iterator,iterator> range(<br>
&nbsp;&nbsp;LowerBounder lower,UpperBounder upper)const;
</code>

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

<h4><a name="serialization">Serialization</a></h4>

<p>
Indices cannot be serialized on their own, but only as part of the
<code>multi_index_container</code> into which they are embedded. In describing
the additional preconditions and guarantees associated to ordered indices
with respect to serialization of their embedding containers, we
use the concepts defined in the <code>multi_index_container</code>
<a href="multi_index_container.html#serialization">serialization section</a>.
</p>

Operation: saving of a <code>multi_index_container</code> <code>m</code> to an
output archive (XML archive) <code>ar</code>.

<blockquote>
<b>Requires:</b> No additional requirements to those imposed by the container.
</blockquote>

Operation: loading of a <code>multi_index_container</code> <code>m'</code> from an
input archive (XML archive) <code>ar</code>.

<blockquote>
<b>Requires:</b> Additionally to the general requirements, <code>value_comp()</code>
must be serialization-compatible with <code>m.get&lt;i&gt;().value_comp()</code>,
where <code>i</code> is the position of the ordered index in the container.<br>
<b>Postconditions:</b> On successful loading, each of the elements of
[<code>begin()</code>, <code>end()</code>) is a restored copy of the corresponding
element in [<code>m.get&lt;i&gt;().begin()</code>, <code>m.get&lt;i&gt;().end()</code>).
</blockquote>

Operation: saving of an <code>iterator</code> or <code>const_iterator</code>
<code>it</code> to an output archive (XML archive) <code>ar</code>.

<blockquote>
<b>Requires:</b> <code>it</code> is a valid iterator of the index. The associated
<code>multi_index_container</code> has been previously saved.
</blockquote>

Operation: loading of an <code>iterator</code> or <code>const_iterator</code>
<code>it'</code> from an input archive (XML archive) <code>ar</code>.

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

<hr>

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<p>Revised August 24th 2017</p>

<p>&copy; Copyright 2003-2017 Joaqu&iacute;n M L&oacute;pez Mu&ntilde;oz.
Distributed under the Boost Software 
License, Version 1.0. (See accompanying file <a href="../../../../LICENSE_1_0.txt">
LICENSE_1_0.txt</a> or copy at <a href="http://www.boost.org/LICENSE_1_0.txt">
http://www.boost.org/LICENSE_1_0.txt</a>)
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