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

 <div class="prev_link"><a href="ord_indices.html"><img src="../prev.gif" alt="ordered indices" border="0"><br>
 Ordered indices
 </a></div>
 <div class="up_link"><a href="index.html"><img src="../up.gif" alt="Boost.MultiIndex reference" border="0"><br>
 Boost.MultiIndex reference
 </a></div>
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 Sequenced indices
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 <hr>

 <h2>Contents</h2>

 <ul>
   <li><a href="#hash_index_fwd_synopsis">Header
     <code>"boost/multi_index/hashed_index_fwd.hpp"</code> synopsis</a></li>
   <li><a href="#synopsis">Header
     <code>"boost/multi_index/hashed_index.hpp"</code> synopsis</a>
     <ul>
       <li><a href="#unique_non_unique">
         Index specifiers <code>hashed_unique</code> and <code>hashed_non_unique</code>
         </a></li>
       <li><a href="#hash_indices">Hashed indices</a>
         <ul>
           <li><a href="#complexity_signature">Complexity signature</a></li>
           <li><a href="#instantiation_types">Instantiation types</a></li>
           <li><a href="#types">Nested 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="#lookup">Lookup</a></li>
           <li><a href="#bucket_interface">Bucket interface</a></li>
           <li><a href="#hash_policy">Hash policy</a></li>
           <li><a href="#serialization">Serialization</a></li>
         </ul>
       </li>
     </ul>
   </li>
 </ul>

 <h2>
 <a name="hash_index_fwd_synopsis">Header
 <a href="../../../../boost/multi_index/hashed_index_fwd.hpp">
 <code>"boost/multi_index/hashed_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 hashed_unique and hashed_non_unique</span>

 <span class=keyword>template</span><span class=special>&lt;</span><b>consult hashed_unique reference for arguments</b><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>hashed_unique</span><span class=special>;</span>
 <span class=keyword>template</span><span class=special>&lt;</span><b>consult hashed_non_unique reference for arguments</b><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>hashed_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>hashed_index_fwd.hpp</code> provides forward declarations for index specifiers
 <a href="#unique_non_unique"><code>hashed_unique</code> and <code>hashed_non_unique</code></a> and
 their associated <a href="#hash_indices">hashed index</a> classes.
 </p>

 <h2>
 <a name="synopsis">Header
 <a href="../../../../boost/multi_index/hashed_index.hpp">
 <code>"boost/multi_index/hashed_index.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 hashed_unique and hashed_non_unique</span>

 <span class=keyword>template</span><span class=special>&lt;</span><b>consult hashed_unique reference for arguments</b><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>hashed_unique</span><span class=special>;</span>
 <span class=keyword>template</span><span class=special>&lt;</span><b>consult hashed_non_unique reference for arguments</b><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>hashed_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 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>hashed_unique</code> and <code>hashed_non_unique</code>
 </a></h3>

 <p>
 These <a href="indices.html#index_specification">index specifiers</a> allow
 for insertion of <a href="#hash_indices">hashed indices</a> without and with
 allowance of duplicate elements, respectively. The syntax of <code>hashed_unique</code>
 and <code>hashed_non_unique</code> coincide, thus we describe them in a grouped manner.
 <code>hashed_unique</code> and <code>hashed_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>Hash</span><span class=special>=</span><span class=identifier>boost</span><span class=special>::</span><span class=identifier>hash</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=keyword>typename</span> <span class=identifier>Pred</span><span class=special>=</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>equal_to</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>hashed_unique</span> <span class=special>|</span> <span class=identifier>hashed_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>Hash</span><span class=special>=</span><span class=identifier>boost</span><span class=special>::</span><span class=identifier>hash</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=keyword>typename</span> <span class=identifier>Pred</span><span class=special>=</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>equal_to</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>hashed_unique</span> <span class=special>|</span> <span class=identifier>hashed_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="#hash_indices">hashed indices</a> reference section for further
 explanations on their acceptable type values.
 </p>

 <h3><a name="hash_indices">Hashed indices</a></h3>

 <p>
 A hashed index provides fast retrieval of elements of a <code>multi_index_container</code>
 through hashing tecnhiques. The interface and semantics of hashed indices are modeled according
 to the proposal for unordered associative containers given in the C++
 <a href="http://www.open-std.org/JTC1/SC22/WG21/docs/papers/2005/n1836.pdf">Proposed
 Draft Tecnhical Report on Standard Library Extensions</a>, also known as TR1. A hashed
 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>, a <code>Hash</code>
 function object which returns hash values for the keys and a binary predicate <code>Pred</code>
 acting as an equivalence relation on values of <code>Key</code>.
 </p>

 <p>
 There are two variants of hashed indices: <i>unique</i>, which do
 not allow duplicate elements (with respect to its associated equality
 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, hashed indices (both unique and non-unique) are models of
 <code>Unordered Associative Container</code>, in the spirit of
 <code>std::tr1::unordered_set</code>s. Validity of iterators and references to
 elements is preserved in all cases. Occasionally, the exception safety guarantees provided
 are actually stronger than required by the extension draft. We only provide descriptions
 of those types and operations that are either not present in the concepts modeled or
 do not exactly conform to the requirements for unordered associative containers.
 </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>

 <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, Hash, Pred</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>Hash</span>                                       <span class=identifier>hasher</span><span class=special>;</span>
   <span class=keyword>typedef</span> <span class=identifier>Pred</span>                                       <span class=identifier>key_equal</span><span class=special>;</span>
   <span class=keyword>typedef</span> <span class=identifier>tuple</span><span class=special>&lt;</span>
     <span class=identifier>size_type</span><span class=special>,</span><span class=identifier>key_from_value</span><span class=special>,</span><span class=identifier>hasher</span><span class=special>,</span><span class=identifier>key_equal</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>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> <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>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> <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>local_iterator</span><span class=special>;</span>
   <span class=keyword>typedef</span> <b>implementation defined                     </b><span class=identifier>const_local_iterator</span><span class=special>;</span>

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

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

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

   <span class=keyword>bool</span>      <span class=identifier>empty</span><span class=special>()</span><span class=keyword>const</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=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=special>;</span>

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

   <span class=identifier>iterator</span>       <span class=identifier>begin</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=special>;</span>
   <span class=identifier>iterator</span>       <span class=identifier>end</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=special>;</span>
   <span class=identifier>const_iterator</span> <span class=identifier>cbegin</span><span class=special>()</span><span class=keyword>const</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=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>// modifiers:</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>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=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=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>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>clear</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=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>hasher</span>         <span class=identifier>hash_function</span><span class=special>()</span><span class=keyword>const</span><span class=special>;</span>
   <span class=identifier>key_equal</span>      <span class=identifier>key_eq</span><span class=special>()</span><span class=keyword>const</span><span class=special>;</span>

   <span class=comment>// lookup:</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>CompatibleHash</span><span class=special>,</span> <span class=keyword>typename</span> <span class=identifier>CompatiblePred</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>CompatibleHash</span><span class=special>&amp;</span> <span class=identifier>hash</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>CompatiblePred</span><span class=special>&amp;</span> <span class=identifier>eq</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>CompatibleHash</span><span class=special>,</span> <span class=keyword>typename</span> <span class=identifier>CompatiblePred</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>CompatibleHash</span><span class=special>&amp;</span> <span class=identifier>hash</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>CompatiblePred</span><span class=special>&amp;</span> <span class=identifier>eq</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>CompatibleHash</span><span class=special>,</span> <span class=keyword>typename</span> <span class=identifier>CompatiblePred</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>CompatibleHash</span><span class=special>&amp;</span> <span class=identifier>hash</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>CompatiblePred</span><span class=special>&amp;</span> <span class=identifier>eq</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=comment>// bucket interface:</span>

   <span class=identifier>size_type</span> <span class=identifier>bucket_count</span><span class=special>()</span><span class=keyword>const</span><span class=special>;</span>
   <span class=identifier>size_type</span> <span class=identifier>max_bucket_count</span><span class=special>()</span><span class=keyword>const</span><span class=special>;</span>
   <span class=identifier>size_type</span> <span class=identifier>bucket_size</span><span class=special>(</span><span class=identifier>size_type</span> <span class=identifier>n</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
   <span class=identifier>size_type</span> <span class=identifier>bucket</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>key_type</span><span class=special>&amp;</span> <span class=identifier>k</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=identifier>local_iterator</span>       <span class=identifier>begin</span><span class=special>(</span><span class=identifier>size_type</span> <span class=identifier>n</span><span class=special>);</span>
   <span class=identifier>const_local_iterator</span> <span class=identifier>begin</span><span class=special>(</span><span class=identifier>size_type</span> <span class=identifier>n</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
   <span class=identifier>local_iterator</span>       <span class=identifier>end</span><span class=special>(</span><span class=identifier>size_type</span> <span class=identifier>n</span><span class=special>);</span>
   <span class=identifier>const_local_iterator</span> <span class=identifier>end</span><span class=special>(</span><span class=identifier>size_type</span> <span class=identifier>n</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
   <span class=identifier>const_local_iterator</span> <span class=identifier>cbegin</span><span class=special>(</span><span class=identifier>size_type</span> <span class=identifier>n</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
   <span class=identifier>const_local_iterator</span> <span class=identifier>cend</span><span class=special>(</span><span class=identifier>size_type</span> <span class=identifier>n</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=identifier>local_iterator</span>       <span class=identifier>local_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_local_iterator</span> <span class=identifier>local_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>// hash policy:</span>

   <span class=keyword>float</span> <span class=identifier>load_factor</span><span class=special>()</span><span class=keyword>const</span><span class=special>;</span>
   <span class=keyword>float</span> <span class=identifier>max_load_factor</span><span class=special>()</span><span class=keyword>const</span><span class=special>;</span>
   <span class=keyword>void</span>  <span class=identifier>max_load_factor</span><span class=special>(</span><span class=keyword>float</span> <span class=identifier>z</span><span class=special>);</span>
   <span class=keyword>void</span>  <span class=identifier>rehash</span><span class=special>(</span><span class=identifier>size_type</span> <span class=identifier>n</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 hashed indices, we adopt the
 scheme outlined in the
 <a href="indices.html#complexity_signature">complexity signature
 section</a>. The complexity signature of hashed indices is:
 <ul>
   <li>copying: <code>c(n)=n*log(n)</code>,</li>
   <li>insertion: average case <code>i(n)=1</code> (constant),
     worst case <code>i(n)=n</code>,</li>
   <li>hinted insertion: average case <code>h(n)=1</code> (constant),
     worst case <code>h(n)=n</code>,</li>
   <li>deletion: average case <code>d(n)=1</code> (constant),
     worst case <code>d(n)=n</code>,</li>
   <li>replacement:
     <ul>
       <li>if the new element key is equivalent to the original, <code>r(n)=1</code> (constant),</li>
       <li>otherwise, average case <code>r(n)=1</code> (constant),
         worst case <code>r(n)=n</code>,</li>
     </ul></li>
   <li>modifying: average case <code>m(n)=1</code> (constant),
     worst case <code>m(n)=n</code>.</li>
 </ul>
 </p>

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

 <p>Hashed 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>hashed_unique</code>
 and <code>hashed_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>Hash</code> from the index specifier,</li>
   <li><code>Pred</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>Hash</code> is a
 <a href="http://www.sgi.com/tech/stl/UnaryFunction.html"><code>Unary Function</code></a>
 taking a single argument of type <code>KeyFromValue::result_type</code> and returning a
 value of type <code>std::size_t</code> in the range
 <code>[0, std::numeric_limits&lt;std::size_t&gt;::max())</code>.
 <code>Pred</code> is a
 <a href="http://www.sgi.com/tech/stl/BinaryPredicate.html">
 <code>Binary Predicate</code></a> inducing an equivalence relation
 on elements of <code>KeyFromValue::result_type</code>. It is required that
 the <code>Hash</code> object return the same value for keys
 equivalent under <code>Pred</code>.
 </p>

 <h4><a name="types">Nested types</a></h4>

 <code>ctor_args</code>

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

 <code>iterator<br>
 const_iterator<br>
 local_iterator<br>
 const_local_iterator</code>

 <blockquote>
 These types are models of
 <a href="http://www.sgi.com/tech/stl/ForwardIterator.html"><code>Forward
 Iterator</code></a>.
 </blockquote>

 <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. Upon construction,
 <code>max_load_factor()</code> is 1.0.
 </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>

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

 <blockquote>
 <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>

 <blockquote>
 <b>Requires:</b> <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.<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 a model of
 <a href="http://www.sgi.com/tech/stl/InputIterator.html">
 <code>Input Iterator</code></a> over elements of type
 <code>value_type</code> or a type convertible to <code>value_type</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>
 <blockquote><pre>
 <span class=identifier>iterator</span> <span class=identifier>hint</span><span class=special>=</span><span class=identifier>end</span><span class=special>();</span>
 <span class=keyword>while</span><span class=special>(</span><span class=identifier>first</span><span class=special>!=</span><span class=identifier>last</span><span class=special>)</span><span class=identifier>hint</span><span class=special>=</span><span class=identifier>insert</span><span class=special>(</span><span class=identifier>hint</span><span class=special>,*</span><span class=identifier>first</span><span class=special>++);</span>
 </pre></blockquote>
 <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>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> Average case, <code>O(1 + m*D(n))</code>, worst case
 <code>O(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(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>

 <blockquote>
 <b>Requires:</b> <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>Modifier</code> is a model of
 <a href="http://www.sgi.com/tech/stl/UnaryFunction.html">
 <code>Unary Function</code></a> accepting arguments of type
 <code>value_type&amp;</code>. <code>position</code> is a valid dereferenceable
 iterator of the index.<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 (except possibly <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>Modifier</code> and <code>Rollback</code> are models of
 <a href="http://www.sgi.com/tech/stl/UnaryFunction.html">
 <code>Unary Function</code></a> accepting arguments of type
 <code>value_type&amp;</code>. <code>position</code> is a valid dereferenceable
 iterator of the index. The sequence of operations <code>mod(e)</code>,
 <code>back(e)</code>, where <code>e</code> is the element
 pointed to by <code>position</code>, restores all keys of the element
 to their original state.<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 and the
 element is kept at its original position in all indices.<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>back</code> throws an
 exception, in which case 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>Modifier</code> is a model of
 <a href="http://www.sgi.com/tech/stl/UnaryFunction.html">
 <code>Unary Function</code></a> accepting arguments of type
 <code>key_type&amp;</code>. <code>position</code> is a valid dereferenceable
 iterator of the index.<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>Modifier</code> and <code>Rollback</code>
 are models of <a href="http://www.sgi.com/tech/stl/UnaryFunction.html">
 <code>Unary Function</code></a> accepting arguments of type
 <code>key_type&amp;</code>. <code>position</code> is a valid dereferenceable
 iterator of the index.
 The sequence of operations <code>mod(k)</code>,
 <code>back(k)</code>, where <code>k</code> is the key of the element
 pointed to by <code>position</code>, restores k to its original state.<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>hash_function</code> and <code>key_eq</code>,
 hashed 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="lookup">Lookup</a></h4>

 <p>
 Hashed indices provide the full lookup functionality required by
 unordered associative containers, namely <code>find</code>,
 <code>count</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 pair (<code>Hash</code>, <code>Pred</code>) where
 <code>Hash</code> is a hash functor over values of type <code>Key</code>
 and <code>Pred</code> is a
 <a href="http://www.sgi.com/tech/stl/BinaryPredicate.html">
 <code>Binary Predicate</code></a> inducing an equivalence relation
 on <code>Key</code>, with the additional constraint that equivalent
 keys have the same hash value.
 A triplet of types (<code>CompatibleKey</code>, <code>CompatibleHash</code>,
 <code>CompatiblePred</code>) is said to be a <i>compatible extension</i>
 of (<code>Hash</code>, <code>Pred</code>) if
 <ol>
   <li><code>CompatibleHash</code> is a hash functor on values of
     type <code>CompatibleKey</code>,</li>
   <li><code>CompatiblePred</code> is a
     <a href="http://www.sgi.com/tech/stl/BinaryPredicate.html">
     <code>Binary Predicate</code></a> over (<code>Key</code>,
     <code>CompatibleKey</code>),</li>
   <li><code>CompatiblePred</code> is a
     <a href="http://www.sgi.com/tech/stl/BinaryPredicate.html">
     <code>Binary Predicate</code></a> over (<code>CompatibleKey</code>,
     <code>Key</code>),</li>
   <li>if <code>c_eq(ck,k1)</code> then <code>c_eq(k1,ck)</code>,</li>
   <li>if <code>c_eq(ck,k1)</code> and <code>eq(k1,k2)</code> then
     <code>c_eq(ck,k2)</code>,</li>
   <li>if <code>c_eq(ck,k1)</code> and <code>c_eq(ck,k2)</code> then
     <code>eq(k1,k2)</code>,</li>
   <li>if <code>c_eq(ck,k1)</code> then <code>c_hash(ck)==hash(k1)</code>,</li>
 </ol>
 for every <code>c_hash</code> of type <code>CompatibleHash</code>,
 <code>c_eq</code> of type <code>CompatiblePred</code>,
 <code>hash</code> of type <code>Hash</code>,
 <code>eq</code> of type <code>Pred</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>Hash</code>, <code>Pred</code>) if
 (<code>CompatibleKey</code>, <code>Hash</code>, <code>Pred</code>)
 is a compatible extension of (<code>Hash</code>, <code>Pred</code>).
 This implies that <code>Hash</code> and <code>Pred</code> accept arguments
 of type <code>CompatibleKey</code>, which usually means they have
 several overloads of therir corresponding <code>operator()</code>
 member functions.
 </p>

 <p>
 In the context of a compatible extension or a compatible key, the expression
 "equivalent key" takes on its obvious interpretation.
 </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>hasher</code>, <code>key_equal</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> Average case <code>O(1)</code> (constant), worst case
 <code>O(n)</code>.<br>
 </blockquote>

 <code>template&lt;<br>
 &nbsp;&nbsp;typename CompatibleKey,typename CompatibleHash, typename CompatiblePred<br>
 &gt;<br>
 iterator find(<br>
 &nbsp;&nbsp;const CompatibleKey&amp; x,<br>
 &nbsp;&nbsp;const CompatibleHash&amp; hash,const CompatiblePred&amp; eq)const;
 </code>

 <blockquote>
 <b>Requires:</b> (<code>CompatibleKey</code>, <code>CompatibleHash</code>,
 <code>CompatiblePred</code>) is a compatible extension of
 (<code>hasher</code>, <code>key_equal</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> Average case <code>O(1)</code> (constant), worst case
 <code>O(n)</code>.<br>
 </blockquote>

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

 <blockquote>
 <b>Requires:</b> <code>CompatibleKey</code> is a compatible key of
 (<code>hasher</code>, <code>key_equal</code>).<br>
 <b>Effects:</b> Returns the number of elements with key equivalent to <code>x</code>.<br>
 <b>Complexity:</b> Average case <code>O(count(x))</code>, worst case
 <code>O(n)</code>.<br>
 </blockquote>

 <code>template&lt;<br>
 &nbsp;&nbsp;typename CompatibleKey,typename CompatibleHash, typename CompatiblePred<br>
 &gt;<br>
 size_type count(<br>
 &nbsp;&nbsp;const CompatibleKey&amp; x,<br>
 &nbsp;&nbsp;const CompatibleHash&amp; hash,const CompatiblePred&amp; eq)const;
 </code>

 <blockquote>
 <b>Requires:</b> (<code>CompatibleKey</code>, <code>CompatibleHash</code>,
 <code>CompatiblePred</code>) is a compatible extension of
 (<code>hasher</code>, <code>key_equal</code>).<br>
 <b>Effects:</b> Returns the number of elements with key equivalent to <code>x</code>.<br>
 <b>Complexity:</b> Average case <code>O(count(x,hash,eq))</code>, worst case
 <code>O(n)</code>.<br>
 </blockquote>

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

 <blockquote>
 <b>Requires:</b> <code>CompatibleKey</code> is a compatible key of
 (<code>hasher</code>, <code>key_equal</code>).<br>
 <b>Effects:</b> Returns a range containing all elements with keys equivalent
 to <code>x</code> (and only those), or (<code>end()</code>,<code>end()</code>)
 if no such elements exist.<br>
 <b>Complexity:</b> Average case <code>O(count(x))</code>, worst case
 <code>O(n)</code>.<br>
 </blockquote>

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

 <blockquote>
 <b>Requires:</b> (<code>CompatibleKey</code>, <code>CompatibleHash</code>,
 <code>CompatiblePred</code>) is a compatible extension of
 (<code>hasher</code>, <code>key_equal</code>).<br>
 <b>Effects:</b> Returns a range containing all elements with keys equivalent
 to <code>x</code> (and only those), or (<code>end()</code>,<code>end()</code>)
 if no such elements exist.<br>
 <b>Complexity:</b> Average case <code>O(count(x,hash,eq))</code>, worst case
 <code>O(n)</code>.<br>
 </blockquote>

 <h4><a name="bucket_interface">Bucket interface</a></h4>

 <code>local_iterator&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;local_iterator_to(const value_type&amp; x);<br>
 const_local_iterator local_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="hash_policy">Hash policy</a></h4>

 <code>void rehash(size_type n);</code>

 <blockquote>
 <b>Effects:</b> Increases if necessary the number of internal buckets
 so that <code>size()/bucket_count()</code> does not exceed the maximum
 load factor, and <code>bucket_count()>=n</code>.<br>
 <b>Postconditions:</b> Validity of iterators and references to the
 elements contained is preserved.<br>
 <b>Complexity:</b> Average case <code>O(size())</code>, worst case
 <code>O(size(n)<sup>2</sup>)</code>.<br>
 <b>Exception safety:</b> Strong.
 </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 hashed 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>key_eq()</code>
 must be serialization-compatible with <code>m.get&lt;i&gt;().key_eq()</code>,
 where <code>i</code> is the position of the hashed index in the container.<br>
 <b>Postconditions:</b> On succesful loading, the range
 [<code>begin()</code>, <code>end()</code>) contains restored copies of every
 element in [<code>m.get&lt;i&gt;().begin()</code>, <code>m.get&lt;i&gt;().end()</code>),
 though not necessarily in the same order.
 </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 succesful 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>

 Operation: saving of a <code>local_iterator</code> or
 <code>const_local_iterator</code>
 <code>it</code> to an output archive (XML archive) <code>ar</code>.

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

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

 <blockquote>
 <b>Postconditions:</b> On succesful loading, if <code>it</code> was dereferenceable
 then <code>*it'</code> is the restored copy of <code>*it</code>; if <code>it</code>
 was <code>m.get&lt;i&gt;().end(n)</code> for some <code>n</code>, then
 <code>it'==m'.get&lt;i&gt;().end(n)</code> (where <code>m</code> is the original
 <code>multi_index_container</code>, <code>m'</code> its restored copy
 and <code>i</code> is the ordinal of the index.)<br>
 <b>Note:</b> It is allowed that <code>it</code> be a <code>const_local_iterator</code>
 and the restored <code>it'</code> a <code>local_iterator</code>, or viceversa.
 </blockquote>

 <hr>

 <div class="prev_link"><a href="ord_indices.html"><img src="../prev.gif" alt="ordered indices" border="0"><br>
 Ordered indices
 </a></div>
 <div class="up_link"><a href="index.html"><img src="../up.gif" alt="Boost.MultiIndex reference" border="0"><br>
 Boost.MultiIndex reference
 </a></div>
 <div class="next_link"><a href="seq_indices.html"><img src="../next.gif" alt="sequenced indices" border="0"><br>
 Sequenced indices
 </a></div><br clear="all" style="clear: all;">

 <br>

 <p>Revised July 21st 2009</p>

 <p>&copy; Copyright 2003-2009 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>)
 </p>

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