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

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 <h2>Contents</h2>

 <ul>
   <li><a href="#intro">Introduction</a>
     <ul>
       <li><a href="#multiple_sort">Multiple sorts on a single set</a></li>
       <li><a href="#list_fast_lookup">A bidirectional list with fast lookup</a></li>
     </ul>
   </li>
   <li><a href="#index_spec">Index specification</a></li>
   <li><a href="#tagging">Tagging</a></li>
   <li><a href="#iterator_access">Iterator access</a></li>
   <li><a href="#index_types">Index types</a>
     <ul>
       <li><a href="#ord_indices">Ordered indices</a>
         <ul>
           <li><a href="#unique_non_unique">Unique and non-unique variants</a></li>
           <li><a href="#ord_spec">Specification</a></li>
           <li><a href="#key_extraction">Key extraction</a></li>
           <li><a href="#comparison_predicates">Comparison predicates</a></li>
           <li><a href="#special_lookup">Special lookup operations</a></li>
           <li><a href="#range">Retrieval of ranges</a></li>
           <li><a href="#ord_updating">Updating</a></li>
         </ul>
       </li>
       <li><a href="#seq_indices">Sequenced indices</a>
         <ul>
           <li><a href="#seq_spec">Specification</a></li>
           <li><a href="#list_ops">List operations</a></li>
           <li><a href="#seq_updating">Updating</a></li>
         </ul>
       </li>
     </ul>
   </li>
   <li><a href="#projection">Projection of iterators</a></li>
   <li><a href="#complexity">Complexity and exception safety</a></li>
 </ul>

 <h2><a name="intro">Introduction</a></h2>

 <p>
 We introduce the main concepts of Boost.MultiIndex through the study of
 two typical use cases.
 </p>

 <h3><a name="multiple_sort">Multiple sorts on a single set</a></h3>

 <p>
 STL sets and multisets are varying-length containers where elements are efficiently
 sorted according to a given comparison predicate. These container classes fall short
 of functionality when the programmer wishes to efficiently sort and look up the elements
 following a different sorting criterion. Consider for instance:
 </p>

 <blockquote><pre>
 <span class=keyword>struct</span> <span class=identifier>employee</span>
 <span class=special>{</span>
   <span class=keyword>int</span>         <span class=identifier>id</span><span class=special>;</span>
   <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span> <span class=identifier>name</span><span class=special>;</span>

   <span class=identifier>employee</span><span class=special>(</span><span class=keyword>int</span> <span class=identifier>id</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>&amp;</span> <span class=identifier>name</span><span class=special>):</span><span class=identifier>id</span><span class=special>(</span><span class=identifier>id</span><span class=special>),</span><span class=identifier>name</span><span class=special>(</span><span class=identifier>name</span><span class=special>){}</span>

   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>&lt;(</span><span class=keyword>const</span> <span class=identifier>employee</span><span class=special>&amp;</span> <span class=identifier>e</span><span class=special>)</span><span class=keyword>const</span><span class=special>{</span><span class=keyword>return</span> <span class=identifier>id</span><span class=special>&lt;</span><span class=identifier>e</span><span class=special>.</span><span class=identifier>id</span><span class=special>;}</span>
 <span class=special>};</span>
 </pre></blockquote>

 <p>The fact that IDs are unique to each employee is reflected by the way
 <code>operator&lt;</code> is defined, so a natural data structure for storing of
 <code>employee</code>s is just a <code>std::set&lt;employee></code>. Now,
 if one wishes to print out a listing of all employees in alphabetical order, available
 solutions may have disadvantages either in terms of storage space, complexity or ease
 of maintenance:
 <ul>
 <li>Copy the employee set into a vector or similar and sort this by a comparison
 functor dependent upon <code>employee::name</code>.
 <li>Keep a secondary data structure of pointers to the elements of the set, appropriately
 sorted by name.
 </ul>
 Of these, probably the second solution will be the one adopted by most programmers
 concerned about efficiency, but it imposes the annoying burden of keeping the two
 structures in sync. If the code is additionally required to be exception-safe, this
 construct easily becomes unmaintainable.
 </p>

 <p>
 Boost.MultiIndex features <a href="#ord_indices"><i>ordered indices</i></a>, which
 sort the elements according to a particular key, and are designed to help programmers
 in need of sequences of elements for which <i>more than one</i> sorting criteria are
 relevant. We do so by defining a <code>multi_index_container</code>
 instantiation composed of several ordered indices: each index, viewed in isolation,
 behaves much as an ordered <code>std::set</code> (or <code>std::multiset</code>), whilst
 the overall integrity of the entire data structure is preserved. Our example problem
 thus can be solved with Boost.MultiIndex as follows:
 </p>

 <blockquote><pre>
 <span class=preprocessor>#include</span> <span class=special>&lt;</span><span class=identifier>boost</span><span class=special>/</span><span class=identifier>multi_index_container</span><span class=special>.</span><span class=identifier>hpp</span><span class=special>&gt;</span>
 <span class=preprocessor>#include</span> <span class=special>&lt;</span><span class=identifier>boost</span><span class=special>/</span><span class=identifier>multi_index</span><span class=special>/</span><span class=identifier>ordered_index</span><span class=special>.</span><span class=identifier>hpp</span><span class=special>&gt;</span>
 <span class=preprocessor>#include</span> <span class=special>&lt;</span><span class=identifier>boost</span><span class=special>/</span><span class=identifier>multi_index</span><span class=special>/</span><span class=identifier>identity</span><span class=special>.</span><span class=identifier>hpp</span><span class=special>&gt;</span>
 <span class=preprocessor>#include</span> <span class=special>&lt;</span><span class=identifier>boost</span><span class=special>/</span><span class=identifier>multi_index</span><span class=special>/</span><span class=identifier>member</span><span class=special>.</span><span class=identifier>hpp</span><span class=special>&gt;</span>

 <span class=comment>// define a multiply indexed set with indices by id and name</span>
 <span class=keyword>typedef</span> <span class=identifier>multi_index_container</span><span class=special>&lt;</span>
   <span class=identifier>employee</span><span class=special>,</span>
   <span class=identifier>indexed_by</span><span class=special>&lt;</span>
     <span class=comment>// sort by employee::operator&lt;</span>
     <span class=identifier>ordered_unique</span><span class=special>&lt;</span><span class=identifier>identity</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>&gt;</span> <span class=special>&gt;,</span>

     <span class=comment>// sort by less&lt;string&gt; on name</span>
     <span class=identifier>ordered_non_unique</span><span class=special>&lt;</span><span class=identifier>member</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>,</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>,&amp;</span><span class=identifier>employee</span><span class=special>::</span><span class=identifier>name</span><span class=special>&gt;</span> <span class=special>&gt;</span>
   <span class=special>&gt;</span>
 <span class=special>&gt;</span> <span class=identifier>employee_set</span><span class=special>;</span>

 <span class=keyword>void</span> <span class=identifier>print_out_by_name</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>employee_set</span><span class=special>&amp;</span> <span class=identifier>es</span><span class=special>)</span>
 <span class=special>{</span>
   <span class=comment>// get a view to index #1 (name)</span>
   <span class=keyword>const</span> <span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>nth_index</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;::</span><span class=identifier>type</span><span class=special>&amp;</span> <span class=identifier>name_index</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;();</span>
   <span class=comment>// use name_index as a regular std::set</span>
   <span class=identifier>std</span><span class=special>::</span><span class=identifier>copy</span><span class=special>(</span>
     <span class=identifier>name_index</span><span class=special>.</span><span class=identifier>begin</span><span class=special>(),</span><span class=identifier>name_index</span><span class=special>.</span><span class=identifier>end</span><span class=special>(),</span>
     <span class=identifier>std</span><span class=special>::</span><span class=identifier>ostream_iterator</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>&gt;(</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>cout</span><span class=special>));</span>
 <span class=special>}</span>
 </pre></blockquote>

 <p>
 Instead of a single comparison predicate type, as it happens for STL associative
 containers, <code>multi_index_container</code> is passed a
 <a href="../reference/multi_index_container.html#multi_index_container">list</a> of index
 specifications (<code>indexed_by</code>), each one inducing the corresponding index.
 Indices are accessed via
 <a href="../reference/multi_index_container.html#index_retrieval"><code>get</code></a><code>&lt;N>()</code>
 where <i>N</i> ranges between 0 and the number of comparison
 predicates minus one. The functionality of index #0 can be accessed directly from a
 <code>multi_index_container</code> object without using <code>get&lt;0>()</code>: for instance,
 <code>es.begin()</code> is equivalent to <code>es.get&lt;0>().begin()</code>.
 </p>

 <p>
 Note that <code>get</code> returns a <i>reference</i> to the index, and not
 an index object. Indices cannot be constructed as separate objects from the
 container they belong to, so the following
 </p>

 <blockquote><pre>
 <span class=comment>// Wrong: we forgot the &amp; after employee_set::nth_index&lt;1&gt;::type</span>
 <span class=keyword>const</span> <span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>nth_index</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;::</span><span class=identifier>type</span> <span class=identifier>name_index</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;();</span>
 </pre></blockquote>

 <p>
 does not compile, since it is trying to construct the index object
 <code>name_index</code>. This is a common source of errors in user code.
 </p>

 <h3><a name="list_fast_lookup">A bidirectional list with fast lookup</a></h3>

 <p>
 This study case allows us to introduce so-called
 <a href="#seq_indices"><i>sequenced indices</i></a>, and how they
 interact with ordered indices to construct powerful containers. Suppose
 we have a text parsed into words and stored in a list like this:
 </p>

 <blockquote><pre>
 <span class=keyword>typedef</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>list</span><span class=special>&lt;</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>&gt;</span> <span class=identifier>text_container</span><span class=special>;</span>

 <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span> <span class=identifier>text</span><span class=special>=</span>
   <span class=string>&quot;Alice was beginning to get very tired of sitting by her sister on the &quot;</span>
   <span class=string>&quot;bank, and of having nothing to do: once or twice she had peeped into the &quot;</span>
   <span class=string>&quot;book her sister was reading, but it had no pictures or conversations in &quot;</span>
   <span class=string>&quot;it, 'and what is the use of a book,' thought Alice 'without pictures or &quot;</span>
   <span class=string>&quot;conversation?'&quot;</span><span class=special>;</span>

 <span class=comment>// feed the text into the list</span>
 <span class=identifier>text_container</span> <span class=identifier>tc</span><span class=special>;</span>
 <span class=identifier>boost</span><span class=special>::</span><span class=identifier>tokenizer</span><span class=special>&lt;</span><span class=identifier>boost</span><span class=special>::</span><span class=identifier>char_separator</span><span class=special>&lt;</span><span class=keyword>char</span><span class=special>&gt;</span> <span class=special>&gt;</span> <span class=identifier>tok</span>
   <span class=special>(</span><span class=identifier>text</span><span class=special>,</span><span class=identifier>boost</span><span class=special>::</span><span class=identifier>char_separator</span><span class=special>&lt;</span><span class=keyword>char</span><span class=special>&gt;(</span><span class=string>&quot; \t\n.,;:!?'\&quot;-&quot;</span><span class=special>));</span>
 <span class=identifier>std</span><span class=special>::</span><span class=identifier>copy</span><span class=special>(</span><span class=identifier>tok</span><span class=special>.</span><span class=identifier>begin</span><span class=special>(),</span><span class=identifier>tok</span><span class=special>.</span><span class=identifier>end</span><span class=special>(),</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>back_inserter</span><span class=special>(</span><span class=identifier>tc</span><span class=special>));</span>
 </pre></blockquote>

 <p>
 If we want to count the occurrences of a given word into the text we will resort
 to <code>std::count</code>:
 </p>

 <blockquote><pre>
 <span class=identifier>std</span><span class=special>::</span><span class=identifier>size_t</span> <span class=identifier>occurrences</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>&amp;</span> <span class=identifier>word</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>count</span><span class=special>(</span><span class=identifier>tc</span><span class=special>.</span><span class=identifier>begin</span><span class=special>(),</span><span class=identifier>tc</span><span class=special>.</span><span class=identifier>end</span><span class=special>(),</span><span class=identifier>word</span><span class=special>);</span>
 <span class=special>}</span>
 </pre></blockquote>

 <p>
 But this implementation of <code>occurrences</code> performs in linear time, which
 could be unacceptable for large quantities of text. Similarly, other operations like
 deletion of selected words are just too costly to carry out on a
 <code>std::list</code>:
 </p>

 <blockquote><pre>
 <span class=keyword>void</span> <span class=identifier>delete_word</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>&amp;</span> <span class=identifier>word</span><span class=special>)</span>
 <span class=special>{</span>
   <span class=identifier>tc</span><span class=special>.</span><span class=identifier>remove</span><span class=special>(</span><span class=identifier>word</span><span class=special>);</span> <span class=comment>// scans the entire list looking for word</span>
 <span class=special>}</span>
 </pre></blockquote>

 <p>
 When performance is a concern, we will need an additional data structure that indexes
 the elements in <code>tc</code>, presumably in alphabetical order. Boost.MultiIndex
 does precisely this through the combination of sequenced and ordered indices:
 </p>

 <blockquote><pre>
 <span class=preprocessor>#include</span> <span class=special>&lt;</span><span class=identifier>boost</span><span class=special>/</span><span class=identifier>multi_index_container</span><span class=special>.</span><span class=identifier>hpp</span><span class=special>&gt;</span>
 <span class=preprocessor>#include</span> <span class=special>&lt;</span><span class=identifier>boost</span><span class=special>/</span><span class=identifier>multi_index</span><span class=special>/</span><span class=identifier>sequenced_index</span><span class=special>.</span><span class=identifier>hpp</span><span class=special>&gt;</span>
 <span class=preprocessor>#include</span> <span class=special>&lt;</span><span class=identifier>boost</span><span class=special>/</span><span class=identifier>multi_index</span><span class=special>/</span><span class=identifier>ordered_index</span><span class=special>.</span><span class=identifier>hpp</span><span class=special>&gt;</span>
 <span class=preprocessor>#include</span> <span class=special>&lt;</span><span class=identifier>boost</span><span class=special>/</span><span class=identifier>multi_index</span><span class=special>/</span><span class=identifier>identity</span><span class=special>.</span><span class=identifier>hpp</span><span class=special>&gt;</span>

 <span class=comment>// define a multi_index_container with a list-like index and an ordered index</span>
 <span class=keyword>typedef</span> <span class=identifier>multi_index_container</span><span class=special>&lt;</span>
   <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>,</span>
   <span class=identifier>indexed_by</span><span class=special>&lt;</span>
     <span class=identifier>sequenced</span><span class=special>&lt;&gt;,</span> <span class=comment>// list-like index</span>
     <span class=identifier>ordered_non_unique</span><span class=special>&lt;</span><span class=identifier>identity</span><span class=special>&lt;</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>&gt;</span> <span class=special>&gt;</span> <span class=comment>// words by alphabetical order</span>
   <span class=special>&gt;</span>
 <span class=special>&gt;</span> <span class=identifier>text_container</span><span class=special>;</span>

 <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span> <span class=identifier>text</span><span class=special>=...</span>

 <span class=comment>// feed the text into the list</span>
 <span class=identifier>text_container</span> <span class=identifier>tc</span><span class=special>;</span>
 <span class=identifier>boost</span><span class=special>::</span><span class=identifier>tokenizer</span><span class=special>&lt;</span><span class=identifier>boost</span><span class=special>::</span><span class=identifier>char_separator</span><span class=special>&lt;</span><span class=keyword>char</span><span class=special>&gt;</span> <span class=special>&gt;</span> <span class=identifier>tok</span>
   <span class=special>(</span><span class=identifier>text</span><span class=special>,</span><span class=identifier>boost</span><span class=special>::</span><span class=identifier>char_separator</span><span class=special>&lt;</span><span class=keyword>char</span><span class=special>&gt;(</span><span class=string>&quot; \t\n.,;:!?'\&quot;-&quot;</span><span class=special>));</span>
 <span class=identifier>std</span><span class=special>::</span><span class=identifier>copy</span><span class=special>(</span><span class=identifier>tok</span><span class=special>.</span><span class=identifier>begin</span><span class=special>(),</span><span class=identifier>tok</span><span class=special>.</span><span class=identifier>end</span><span class=special>(),</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>back_inserter</span><span class=special>(</span><span class=identifier>tc</span><span class=special>));</span>
 </pre></blockquote>

 <p>
 So far, the substitution of <code>multi_index_container</code> for <code>std::list</code>
 does not show any advantage. The code for inserting the text into the container
 does not change as sequenced indices provide an interface similar to that of
 <code>std::list</code> (no explicit access to this index through
 <code>get&lt;0>()</code> is needed as <code>multi_index_container</code> inherits the
 functionality of index #0.) But the specification of an additional ordered index
 allows us to implement <code>occurrences</code> and <code>delete_word</code>
 in a much more efficient manner:
 </p>

 <blockquote><pre>
 <span class=identifier>std</span><span class=special>::</span><span class=identifier>size_t</span> <span class=identifier>occurrences</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>&amp;</span> <span class=identifier>word</span><span class=special>)</span>
 <span class=special>{</span>
   <span class=comment>// get a view to index #1</span>
   <span class=identifier>text_container</span><span class=special>::</span><span class=identifier>nth_index</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;::</span><span class=identifier>type</span><span class=special>&amp;</span> <span class=identifier>sorted_index</span><span class=special>=</span><span class=identifier>tc</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;();</span>

   <span class=comment>// use sorted_index as a regular std::set</span>
   <span class=keyword>return</span> <span class=identifier>sorted_index</span><span class=special>.</span><span class=identifier>count</span><span class=special>(</span><span class=identifier>word</span><span class=special>);</span>
 <span class=special>}</span>

 <span class=keyword>void</span> <span class=identifier>delete_word</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>&amp;</span> <span class=identifier>word</span><span class=special>)</span>
 <span class=special>{</span>
   <span class=comment>// get a view to index #1</span>
   <span class=identifier>text_container</span><span class=special>::</span><span class=identifier>nth_index</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;::</span><span class=identifier>type</span><span class=special>&amp;</span> <span class=identifier>sorted_index</span><span class=special>=</span><span class=identifier>tc</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;();</span>

   <span class=comment>// use sorted_index as a regular std::set</span>
   <span class=identifier>sorted_index</span><span class=special>.</span><span class=identifier>erase</span><span class=special>(</span><span class=identifier>word</span><span class=special>);</span>
 <span class=special>}</span>
 </pre></blockquote>

 <p>
 Now, <code>occurrences</code> and <code>delete_word</code> have logarithmic
 complexity. The programmer can use index #0 for accessing the text as with
 <code>std::list</code>, and use index #1 when logarithmic lookup is needed.
 </p>

 <h2>
 <a name="index_spec">Index specification</a>
 </h2>

 <p>
 The indices of a <code>multi_index_container</code> instantiation are specified by
 means of the <a href="../reference/indices.html#indexed_by">
 <code>indexed_by</code></a> construct. For instance, the instantiation
 </p>

 <blockquote><pre>
 <span class=keyword>typedef</span> <span class=identifier>multi_index_container</span><span class=special>&lt;</span>
   <span class=identifier>employee</span><span class=special>,</span>
   <span class=identifier>indexed_by</span><span class=special>&lt;</span>
     <span class=identifier>ordered_unique</span><span class=special>&lt;</span><span class=identifier>identity</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>&gt;</span> <span class=special>&gt;,</span>
     <span class=identifier>ordered_non_unique</span><span class=special>&lt;</span><span class=identifier>member</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>,</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>,&amp;</span><span class=identifier>employee</span><span class=special>::</span><span class=identifier>name</span><span class=special>&gt;</span> <span class=special>&gt;</span>
   <span class=special>&gt;</span>
 <span class=special>&gt;</span> <span class=identifier>employee_set</span><span class=special>;</span>
 </pre></blockquote>

 <p>
 is comprised of a <a href="#unique_non_unique">unique ordered index</a> and a
 <a href="#unique_non_unique">non-unique ordered index</a>, while in
 </p>

 <blockquote><pre>
 <span class=keyword>typedef</span> <span class=identifier>multi_index_container</span><span class=special>&lt;</span>
   <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>,</span>
   <span class=identifier>indexed_by</span><span class=special>&lt;</span>
     <span class=identifier>sequenced</span><span class=special>&lt;&gt;,</span>
     <span class=identifier>ordered_non_unique</span><span class=special>&lt;</span><span class=identifier>identity</span><span class=special>&lt;</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>&gt;</span> <span class=special>&gt;</span>
   <span class=special>&gt;</span>
 <span class=special>&gt;</span> <span class=identifier>text_container</span><span class=special>;</span>
 </pre></blockquote>

 <p>
 we specifiy two indices, the first of <a href="#seq_indices">sequenced type</a>,
 the second a non-unique <a href="#ord_indices">ordered index</a>. In general, we
 can specify an arbitrary number of indices: each of the arguments of
 <code>indexed_by</code> is called an
 <a href="../reference/indices.html#index_specification"><i>index specifier</i></a>.
 Depending on the type of index being specified, the corresponding specifier
 will need additional information: for instance, the specifiers <code>ordered_unique</code>
 and <code>ordered_non_unique</code> are provided with a
 <a href="#key_extraction">key extractor</a> and an optional
 <a href="#comparison_predicates">comparison predicate</a> which jointly indicate
 how the sorting of elements will be performed.
 </p>

 <p>
 A <code>multi_index_container</code> instantiation can be declared without supplying
 the <code>indexed_by</code> part: in this case, default index values are taken
 so that the resulting type is equivalent to a regular <code>std::set</code>.
 Concretely, the instantiation
 </p>

 <blockquote><pre>
 <span class=identifier>multi_index_container</span><span class=special>&lt;</span><i>(element)</i><span class=special>&gt;</span>
 </pre></blockquote>

 <p>
 is equivalent to
 </p>

 <blockquote><pre>
 <span class=identifier>multi_index_container</span><span class=special>&lt;</span>
   <i>(element)</i><span class=special>,</span>
   <span class=identifier>indexed_by</span><span class=special>&lt;</span>
     <span class=identifier>ordered_unique</span><span class=special>&lt;</span><span class=identifier>identity</span><span class=special>&lt;(</span><span class=identifier>element</span><span class=special>)&gt;</span> <span class=special>&gt;</span>
   <span class=special>&gt;</span>
 <span class=special>&gt;</span>
 </pre></blockquote>

 <h2><a name="tagging">Tagging</a></h2>

 <p>
 In order to retrieve (a reference to) an index of a given <code>multi_index_container</code>,
 the programmer must provide its order number, which is cumbersome and not very
 self-descriptive. Optionally, indices can be assigned <i>tags</i> (C++ types) that
 act as more convenient mnemonics. If provided, tags must be passed as the
 first parameter of the corresponding index specifier. The following is a revised version of
 <code>employee_set</code> with inclusion of tags:
 </p>

 <blockquote><pre>
 <span class=comment>// tags</span>
 <span class=keyword>struct</span> <span class=identifier>name</span><span class=special>{};</span>

 <span class=keyword>typedef</span> <span class=identifier>multi_index_container</span><span class=special>&lt;</span>
   <span class=identifier>employee</span><span class=special>,</span>
   <span class=identifier>indexed_by</span><span class=special>&lt;</span>
     <span class=identifier>ordered_unique</span><span class=special>&lt;</span><span class=identifier>identity</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>&gt;</span> <span class=special>&gt;,</span>
     <span class=identifier>ordered_non_unique</span><span class=special>&lt;</span><span class=identifier>tag</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;,</span><span class=identifier>member</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>,</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>,&amp;</span><span class=identifier>employee</span><span class=special>::</span><span class=identifier>name</span><span class=special>&gt;</span> <span class=special>&gt;</span>
   <span class=special>&gt;</span>
 <span class=special>&gt;</span> <span class=identifier>employee_set</span><span class=special>;</span>
 </pre></blockquote>

 <p>
 Tags have to be passed inside the <a href="../reference/indices.html#tag"><code>tag</code></a>
 construct. Any type can be used as a tag for an index, although in general one will choose
 names that are descriptive of the index they are associated with. The tagging mechanism allows
 us to write expressions like</p>

 <blockquote><pre>
 <span class=keyword>typedef</span> <span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>index</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;::</span><span class=identifier>type</span> <span class=identifier>employee_set_by_name</span><span class=special>;</span>
 <span class=identifier>employee_set_by_name</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;().</span><span class=identifier>begin</span><span class=special>();</span>
 </pre></blockquote>

 <p>
 If no tag is provided for an index (as is the case for index #0 of the previous
 example), access to that index can only be performed by number. Note the existence
 of two different <code>typedef</code>s <code>nth_index</code> and
 <code>index</code> for referring to an index by number and by tag, respectively;
 for instance,
 <ul>
   <li><code>employee_set::nth_index&lt;1>::type</code> is the type of
     index #1,</li>
   <li><code>employee_set::index&lt;name>::type</code> is the type of the index
     tagged with <code>name</code> (the same index #1 in this case.)</li>
 </ul>
 <code>get()</code>, on the other hand, is overloaded to serve both styles of access:
 </p>

 <blockquote><pre>
 <span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>index</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;::</span><span class=identifier>type</span><span class=special>&amp;</span> <span class=identifier>name_index</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;();</span>
 <span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>nth_index</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;::</span><span class=identifier>type</span><span class=special>&amp;</span> <span class=identifier>name_index2</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;();</span> <span class=comment>// same index</span>
 </pre></blockquote>

 <p>
 Additionally, the <code>tag</code> class template accepts several tags for one
 index, that we can use interchangeably: for instance, the specification of index #1
 in the previous example can be rewritten to hold two different tags
 <code>name</code> and <code>by_name</code>:
 </p>

 <blockquote><pre>
 <span class=comment>// tags</span>
 <span class=keyword>struct</span> <span class=identifier>name</span><span class=special>{};</span>
 <span class=keyword>struct</span> <span class=identifier>by_name</span><span class=special>{};</span>

 <span class=keyword>typedef</span> <span class=identifier>multi_index_container</span><span class=special>&lt;</span>
   <span class=special>...</span>
     <span class=identifier>ordered_non_unique</span><span class=special>&lt;</span>
       <span class=identifier>tag</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>,</span><span class=identifier>by_name</span><span class=special>&gt;,</span>
       <span class=identifier>member</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>,</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>,&amp;</span><span class=identifier>employee</span><span class=special>::</span><span class=identifier>name</span><span class=special>&gt;</span>
     <span class=special>&gt;</span>
   <span class=special>...</span>
 <span class=special>&gt;</span> <span class=identifier>employee_set</span><span class=special>;</span>
 </pre></blockquote>

 <h2><a name="iterator_access">Iterator access</a></h2>

 <p>
 Each index of a <code>multi_index_container</code> uses its own
 iterator types, which are different from those of another indices. As is
 the rule with STL containers, these iterators are defined as nested
 types of the index:
 </p>

 <blockquote><pre>
 <span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>nth_index</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;::</span><span class=identifier>type</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it</span><span class=special>=</span>
   <span class=identifier>es</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;().</span><span class=identifier>find</span><span class=special>(</span><span class=string>&quot;Judy Smith&quot;</span><span class=special>);</span>
 </pre></blockquote>

 <p>
 This kind of expressions can be rendered more readable by
 means of user-defined <code>typedef</code>s:
 </p>

 <blockquote><pre>
 <span class=keyword>typedef</span> <span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>nth_index</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;::</span><span class=identifier>type</span> <span class=identifier>employee_set_by_name</span><span class=special>;</span>
 <span class=identifier>employee_set_by_name</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it</span><span class=special>=</span>
   <span class=identifier>es</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;().</span><span class=identifier>find</span><span class=special>(</span><span class=string>&quot;Judy Smith&quot;</span><span class=special>);</span>
 </pre></blockquote>

 <h2>
 <a name="index_types">Index types</a>
 </h2>

 <p>
 Currently, Boost.MultiIndex provides the following index types:
 <ul>
   <li>Ordered indices sort the elements like <code>std::set</code>s do and
     provide a similar interface. There are <i>unique</i> and <i>non-unique</i>
     variants: the former do not allow for duplicates, while the latter permit
     them (like <code>std::multiset</code>.)</li>
   <li>Sequenced indices are modeled after the semantics and interface of
     <code>std::list</code>: they arrange the elements as if in a bidirectional
     list.</li>
   <li>Hashed indices provide fast access to the elements through hashing
     tecnhiques, in a similar way as non-standard <code>hash_set</code>s provided
     by some vendors. Recently, <i>unordered associative containers</i> have been
     proposed as part of an extension of the C++ standard library known
     in the standardization commitee as TR1. Hashed indices closely model this
     proposal.</li>
   <li>Random access indices provide an interface similar to that of
     sequenced indices, and additionally feature random access iterators
     and positional access to the elements.</li>
 </ul>
 The examples in the <a href="#intro">introduction</a> exercise ordered and sequenced
 indices, which are the most commonly used; the other kinds of indices are presented
 in the <a href="indices.html">index types</a> section of the tutorial.
 </p>

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

 <p>
 Ordered indices sort the elements in a <code>multi_index_container</code> according
 to a specified key and an associated comparison predicate. These indices can
 be viewed as analogues of the standard container <code>std::set</code>, and in fact
 they do replicate its interface, albeit with some minor differences dictated
 by the general constraints of Boost.MultiIndex.
 </p>

 <h4>
 <a name="unique_non_unique">Unique and non-unique variants</a>
 </h4>

 <p>
 Ordered indices are classified into <i>unique</i>, which prohibit two
 elements to have the same key value, and <i>non-unique</i> indices,
 which allow for duplicates. Consider again the definition
 </p>

 <blockquote><pre>
 <span class=keyword>typedef</span> <span class=identifier>multi_index_container</span><span class=special>&lt;</span>
   <span class=identifier>employee</span><span class=special>,</span>
   <span class=identifier>indexed_by</span><span class=special>&lt;</span>
     <span class=identifier>ordered_unique</span><span class=special>&lt;</span><span class=identifier>identity</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>&gt;</span> <span class=special>&gt;,</span>
     <span class=identifier>ordered_non_unique</span><span class=special>&lt;</span><span class=identifier>member</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>,</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>,&amp;</span><span class=identifier>employee</span><span class=special>::</span><span class=identifier>name</span><span class=special>&gt;</span> <span class=special>&gt;</span>
   <span class=special>&gt;</span>
 <span class=special>&gt;</span> <span class=identifier>employee_set</span><span class=special>;</span>
 </pre></blockquote>

 <p>
 In this instantiation of <code>multi_index_container</code>, the first index is to be
 treated as unique (since IDs are exclusive to each employee) and thus is declared using
 <code>ordered_unique</code>, whereas the second index is non-unique (as the possibility exists
 that say two John Smiths are hired in the same company), which is specified by the use
 of <code>ordered_non_unique</code>.
 </p>

 <p>
 The classification of ordered indices in unique and non-unique has an impact on which
 elements are allowed to be inserted into a given <code>multi_index_container</code>; briefly put,
 unique ordered indices mimic the behavior of <code>std::set</code>s while non-unique
 ordered indices are similar to <code>std::multiset</code>s. For instance, an
 <code>employee_set</code> can hold the objects <code>employee(0,"George Brown")</code>
 and <code>employee(1,"George Brown")</code>, but will not accept the insertion of an
 <code>employee</code> object whose ID coincides with that of some previously inserted
 employee.
 </p>

 <p>
 More than one unique index can be specified. For instance, if we augment
 <code>employee</code> to include an additional member for the Social Security number,
 which is reasonably treated as unique, the following captures this design:
 </p>

 <blockquote><pre>
 <span class=keyword>struct</span> <span class=identifier>employee</span>
 <span class=special>{</span>
   <span class=keyword>int</span>         <span class=identifier>id</span><span class=special>;</span>
   <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span> <span class=identifier>name</span><span class=special>;</span>
   <span class=keyword>int</span>         <span class=identifier>ssnumber</span><span class=special>;</span>

   <span class=identifier>employee</span><span class=special>(</span><span class=keyword>int</span> <span class=identifier>id</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>&amp;</span> <span class=identifier>name</span><span class=special>,</span><span class=keyword>int</span> <span class=identifier>ssnumber</span><span class=special>):</span>
     <span class=identifier>id</span><span class=special>(</span><span class=identifier>id</span><span class=special>),</span><span class=identifier>name</span><span class=special>(</span><span class=identifier>name</span><span class=special>),</span><span class=identifier>ssnumber</span><span class=special>(</span><span class=identifier>ssnumber</span><span class=special>){}</span>

   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>&lt;(</span><span class=keyword>const</span> <span class=identifier>employee</span><span class=special>&amp;</span> <span class=identifier>e</span><span class=special>)</span><span class=keyword>const</span><span class=special>{</span><span class=keyword>return</span> <span class=identifier>id</span><span class=special>&lt;</span><span class=identifier>e</span><span class=special>.</span><span class=identifier>id</span><span class=special>;}</span>
 <span class=special>};</span>

 <span class=keyword>typedef</span> <span class=identifier>multi_index_container</span><span class=special>&lt;</span>
   <span class=identifier>employee</span><span class=special>,</span>
   <span class=identifier>indexed_by</span><span class=special>&lt;</span>
     <span class=comment>// sort by employee::operator&lt;</span>
     <span class=identifier>ordered_unique</span><span class=special>&lt;</span><span class=identifier>identity</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>&gt;</span> <span class=special>&gt;,</span>

     <span class=comment>// sort by less&lt;string&gt; on name</span>
     <span class=identifier>ordered_non_unique</span><span class=special>&lt;</span><span class=identifier>member</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>,</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>,&amp;</span><span class=identifier>employee</span><span class=special>::</span><span class=identifier>name</span><span class=special>&gt;</span> <span class=special>&gt;,</span>

     <span class=comment>// sort by less&lt;int&gt; on ssnumber</span>
     <span class=identifier>ordered_unique</span><span class=special>&lt;</span><span class=identifier>member</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>,</span><span class=keyword>int</span><span class=special>,&amp;</span><span class=identifier>employee</span><span class=special>::</span><span class=identifier>ssnumber</span><span class=special>&gt;</span> <span class=special>&gt;</span>
   <span class=special>&gt;</span>
 <span class=special>&gt;</span> <span class=identifier>employee_set</span><span class=special>;</span>
 </pre></blockquote>

 <h4>
 <a name="ord_spec">Specification</a>
 </h4>

 <p>
 Ordered index specifiers in <code>indexed_by</code> must conform to one of the
 following syntaxes:
 </p>

 <blockquote><pre>
 <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>&lt;[</span><i>(tag)</i><span class=special>[,</span><i>(key extractor)</i><span class=special>[,</span><i>(comparison predicate)</i><span class=special>]]]&gt;</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>&lt;[</span><i>(key extractor)</i><span class=special>[,</span><i>(comparison predicate)</i><span class=special>]]&gt;</span>
 </pre></blockquote>

 <p>
 The first optional argument is used if <a href="#tagging">tags</a> are associated
 with the index. We now proceed to briefly discuss the remaining arguments
 of an ordered index specifier.
 </p>

 <h4>
 <a name="key_extraction">Key extraction</a>
 </h4>

 <p>
 The first template parameter (or the second, if tags are supplied)
 in the specification of an ordered index provides a <i>key extraction</i> predicate.
 This predicate takes a whole element (in our example, a reference to an
 <code>employee</code> object) and returns the piece of information by which
 the sorting is performed. In most cases, one of the following two situations arises:
 <ul>
 <li>The whole element serves as the key, as is the case of the first index
 in <code>employee_set</code>. The predefined
 <a href="key_extraction.html#identity"><code>identity</code></a> predicate
 can be used here as a key extractor; <code>identity</code> returns as the key the
 same object passed as argument.</li>
 <li>The comparison is performed on a particular data member of the element; this
 closely follows the specification of indices on a column of a table in relational
 databases. Boost.MultiIndex provides
 <a href="key_extraction.html#member"><code>member</code></a>, which returns
 as the key a member of the element specified by a given pointer.</li>
 </ul>
 As an example, consider again the definition of <code>employee_set</code>. The
 definition of the first index:
 </p>

 <blockquote><pre>
 <span class=identifier>ordered_unique</span><span class=special>&lt;</span><span class=identifier>identity</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>&gt;</span> <span class=special>&gt;</span>
 </pre></blockquote>

 <p>
 specifies by means of <code>identity</code> that <code>element</code>
 objects themselves serve as key for this index. On the other hand, in the second
 index:
 </p>

 <blockquote><pre>
 <span class=identifier>ordered_non_unique</span><span class=special>&lt;</span><span class=identifier>member</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>,</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>,&amp;</span><span class=identifier>employee</span><span class=special>::</span><span class=identifier>name</span><span class=special>&gt;</span> <span class=special>&gt;</span>
 </pre></blockquote>

 <p>
 we use <code>member</code> to extract the <code>name</code> part of the
 <code>employee</code> object. The key type of this index is then
 <code>std::string</code>.
 </p>

 <p>
 Apart from <code>identity</code> and <code>member</code>, Boost.MultiIndex provides
 several other predefined key extractors and powerful ways to combine them.
 Key extractors can also be defined by the user.
 Consult the <a href="key_extraction.html">key extraction section</a> of
 the tutorial for a more detailed exposition of this topic.
 </p>

 <h4><a name="comparison_predicates">Comparison predicates</a></h4>

 <p>
 The last part of the specification of an ordered index is the associated
 <i>comparison predicate</i>, which must order the keys in a less-than fashion.
 These comparison predicates are not different from those used by STL containers like
 <code>std::set</code>. By default (i.e. if no comparison predicate is provided),
 an index with keys of type <code>key_type</code> sorts the elements by
 <code>std::less&lt;key_type></code>. Should other comparison criteria be needed,
 they can be specified as an additional parameter in the index declaration:
 </p>

 <blockquote><pre>
 <span class=comment>// define a multiply indexed set with indices by id and by name
 // in reverse alphabetical order</span>
 <span class=keyword>typedef</span> <span class=identifier>multi_index_container</span><span class=special>&lt;</span>
   <span class=identifier>employee</span><span class=special>,</span>
   <span class=identifier>indexed_by</span><span class=special>&lt;</span>
     <span class=identifier>ordered_unique</span><span class=special>&lt;</span><span class=identifier>identity</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>&gt;</span> <span class=special>&gt;,</span> <span class=comment>// as usual</span>
     <span class=identifier>ordered_non_unique</span><span class=special>&lt;</span>
       <span class=identifier>member</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>,</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>,&amp;</span><span class=identifier>employee</span><span class=special>::</span><span class=identifier>name</span><span class=special>&gt;,</span>
       <span class=identifier>std</span><span class=special>::</span><span class=identifier>greater</span><span class=special>&lt;</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>&gt;</span>  <span class=comment>// default would be std::less&lt;std::string&gt;</span>
     <span class=special>&gt;</span>
   <span class=special>&gt;</span>
 <span class=special>&gt;</span> <span class=identifier>employee_set</span><span class=special>;</span>
 </pre></blockquote>

 <h4><a name="special_lookup">Special lookup operations</a></h4>

 <p>
 A given ordered index allows for lookup based on its key type, rather than the
 whole element. For instance, to find Veronica Cruz in an
 <code>employee_set</code> one would write:
 </p>

 <blockquote><pre>
 <span class=identifier>employee_set</span> <span class=identifier>es</span><span class=special>;</span>
 <span class=special>...</span>
 <span class=keyword>typedef</span> <span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>index</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;::</span><span class=identifier>type</span> <span class=identifier>employee_set_by_name</span><span class=special>;</span>
 <span class=identifier>employee_set_by_name</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;().</span><span class=identifier>find</span><span class=special>(</span><span class=string>&quot;Veronica Cruz&quot;</span><span class=special>);</span>
 </pre></blockquote>

 <p>As a plus, Boost.MultiIndex provides lookup operations accepting search keys
 different from the <code>key_type</code> of the index, which is a specially useful
 facility when <code>key_type</code> objects  are expensive to create. Ordered STL containers
 fail to provide this functionality, which often leads to inelegant workarounds: consider for
 instance the problem of determining the employees whose IDs fall in the range [0,100]. Given
 that the key of <code>employee_set</code> index #0
 is <code>employee</code> itself, on a first approach one would write the following:
 </p>

 <blockquote><pre>
 <span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>p0</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>lower_bound</span><span class=special>(</span><span class=identifier>employee</span><span class=special>(</span><span class=number>0</span><span class=special>,</span><span class=string>&quot;&quot;</span><span class=special>));</span>
 <span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>p1</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>upper_bound</span><span class=special>(</span><span class=identifier>employee</span><span class=special>(</span><span class=number>100</span><span class=special>,</span><span class=string>&quot;&quot;</span><span class=special>));</span>
 </pre></blockquote>

 <p>
 Note however that <code>std::less&lt;employee></code> actually only depends
 on the IDs of the employees, so it would be more convenient to avoid
 the creation of entire <code>employee</code> objects just for the sake of
 their IDs. Boost.MultiIndex allows for this: define an appropriate
 comparison predicate
 </p>

 <blockquote><pre>
 <span class=keyword>struct</span> <span class=identifier>comp_id</span>
 <span class=special>{</span>
   <span class=comment>// compare an ID and an employee</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>int</span> <span class=identifier>x</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>employee</span><span class=special>&amp;</span> <span class=identifier>e2</span><span class=special>)</span><span class=keyword>const</span><span class=special>{</span><span class=keyword>return</span> <span class=identifier>x</span><span class=special>&lt;</span><span class=identifier>e2</span><span class=special>.</span><span class=identifier>id</span><span class=special>;}</span>

   <span class=comment>// compare an employee and an ID</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>employee</span><span class=special>&amp;</span> <span class=identifier>e1</span><span class=special>,</span><span class=keyword>int</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>{</span><span class=keyword>return</span> <span class=identifier>e1</span><span class=special>.</span><span class=identifier>id</span><span class=special>&lt;</span><span class=identifier>x</span><span class=special>;}</span>
 <span class=special>};</span>
 </pre></blockquote>

 <p>and now write the search as</p>

 <blockquote><pre>
 <span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>p0</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>lower_bound</span><span class=special>(</span><span class=number>0</span><span class=special>,</span><span class=identifier>comp_id</span><span class=special>());</span>
 <span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>p1</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>upper_bound</span><span class=special>(</span><span class=number>100</span><span class=special>,</span><span class=identifier>comp_id</span><span class=special>());</span>
 </pre></blockquote>

 <p>
 Here we are not only passing IDs instead of <code>employee</code> objects:
 an alternative comparison predicate is passed as well. In general, lookup operations
 of ordered indices are overloaded to accept
 <a href="../reference/ord_indices.html#set_operations"><i>compatible sorting
 criteria</i></a>. The somewhat cumbersone definition of compatibility in this context
 is given in the reference, but roughly speaking we say that a comparison predicate
 <code>C1</code> is compatible with <code>C2</code> if any sequence sorted by
 <code>C2</code> is also sorted with respect to <code>C1</code>.
 The following shows a more interesting use of compatible predicates:
 </p>

 <blockquote><pre>
 <span class=comment>// sorting by name's initial</span>
 <span class=keyword>struct</span> <span class=identifier>comp_initial</span>
 <span class=special>{</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>char</span> <span class=identifier>ch</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>&amp;</span> <span class=identifier>s</span><span class=special>)</span><span class=keyword>const</span><span class=special>{</span>
     <span class=keyword>if</span><span class=special>(</span><span class=identifier>s</span><span class=special>.</span><span class=identifier>empty</span><span class=special>())</span><span class=keyword>return</span> <span class=keyword>false</span><span class=special>;</span>
     <span class=keyword>return</span> <span class=identifier>ch</span><span class=special>&lt;</span><span class=identifier>s</span><span class=special>[</span><span class=number>0</span><span class=special>];</span>
   <span class=special>}</span>

   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>&amp;</span> <span class=identifier>s</span><span class=special>,</span><span class=keyword>char</span> <span class=identifier>ch</span><span class=special>)</span><span class=keyword>const</span><span class=special>{</span>
     <span class=keyword>if</span><span class=special>(</span><span class=identifier>s</span><span class=special>.</span><span class=identifier>empty</span><span class=special>())</span><span class=keyword>return</span> <span class=keyword>true</span><span class=special>;</span>
     <span class=keyword>return</span> <span class=identifier>s</span><span class=special>[</span><span class=number>0</span><span class=special>]&lt;</span><span class=identifier>ch</span><span class=special>;</span>
   <span class=special>}</span>
 <span class=special>};</span>

 <span class=comment>// obtain first employee whose name begins with 'J' (ordered by name)</span>
 <span class=keyword>typedef</span> <span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>index</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;::</span><span class=identifier>type</span> <span class=identifier>employee_set_by_name</span><span class=special>;</span>
 <span class=identifier>employee_set_by_name</span><span class=special>&amp;</span> <span class=identifier>name_index</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;();</span>
 <span class=identifier>employee_set_by_name</span><span class=special>::</span><span class=identifier>const_iterator</span> <span class=identifier>it</span><span class=special>=</span>
   <span class=identifier>name_index</span><span class=special>.</span><span class=identifier>lower_bound</span><span class=special>(</span><span class=literal>'J'</span><span class=special>,</span><span class=identifier>comp_initial</span><span class=special>());</span>
 </pre></blockquote>

 <h4><a name="range">Retrieval of ranges</a></h4>

 <p>
 Range searching, i.e. the lookup of all elements in a given interval, is a very
 frequent operation for which standard <code>lower_bound</code> and
 <code>upper_bound</code> can be resorted to, though in a cumbersome manner.
 For instance, the following code retrieves the elements of an
 <code>multi_index_container&lt;double></code> in the interval [100,200]:
 </p>

 <blockquote><pre>
 <span class=keyword>typedef</span> <span class=identifier>multi_index_container</span><span class=special>&lt;</span><span class=keyword>double</span><span class=special>&gt;</span> <span class=identifier>double_set</span><span class=special>;</span>
 <span class=comment>// note: default template parameters resolve to
 // multi_index_container&lt;double,indexed_by&lt;unique&lt;identity&lt;double&gt; &gt; &gt; &gt;.</span>

 <span class=identifier>double_set</span> <span class=identifier>s</span><span class=special>;</span>
 <span class=special>...</span>
 <span class=identifier>double_set</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it0</span><span class=special>=</span><span class=identifier>s</span><span class=special>.</span><span class=identifier>lower_bound</span><span class=special>(</span><span class=number>100.0</span><span class=special>);</span>
 <span class=identifier>double_set</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it1</span><span class=special>=</span><span class=identifier>s</span><span class=special>.</span><span class=identifier>upper_bound</span><span class=special>(</span><span class=number>200.0</span><span class=special>);</span>
 <span class=comment>// range [it0,it1) contains the elements in [100,200]</span>
 </pre></blockquote>

 <p>
 Subtle changes to the code are required when strict inequalities are considered.
 To retrieve the elements <i>greater</i> than 100 and <i>less</i> than 200, the
 code has to be rewritten as
 </p>

 <blockquote><pre>
 <span class=identifier>double_set</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it0</span><span class=special>=</span><span class=identifier>s</span><span class=special>.</span><span class=identifier>upper_bound</span><span class=special>(</span><span class=number>100.0</span><span class=special>);</span>
 <span class=identifier>double_set</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it1</span><span class=special>=</span><span class=identifier>s</span><span class=special>.</span><span class=identifier>lower_bound</span><span class=special>(</span><span class=number>200.0</span><span class=special>);</span>
 <span class=comment>// range [it0,it1) contains the elements in (100,200)</span>
 </pre></blockquote>

 <p>
 To add to this complexity, the careful programmer has to take into account
 that the lower and upper bounds of the interval searched be compatible: for
 instance, if the lower bound is 200 and the upper bound is 100, the iterators
 <code>it0</code> and <code>it1</code> produced by the code above will be in reverse
 order, with possibly catastrophic results if a traversal from <code>it0</code>
 to <code>it1</code> is tried. All these details make range searching a tedious
 and error prone task.
 </p>

 <p>
 The <a href="../reference/ord_indices.html#range_operations"><code>range</code></a>
 member function, often in combination with
 <a href="../../../../libs/lambda/index.html">Boost.Lambda</a> expressions, can
 greatly help alleviate this situation:
 </p>

 <blockquote><pre>
 <span class=keyword>using</span> <span class=keyword>namespace</span> <span class=identifier>boost</span><span class=special>::</span><span class=identifier>lambda</span><span class=special>;</span>

 <span class=keyword>typedef</span> <span class=identifier>multi_index_container</span><span class=special>&lt;</span><span class=keyword>double</span><span class=special>&gt;</span> <span class=identifier>double_set</span><span class=special>;</span>
 <span class=identifier>double_set</span> <span class=identifier>s</span><span class=special>;</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>double_set</span><span class=special>::</span><span class=identifier>iterator</span><span class=special>,</span><span class=identifier>double_set</span><span class=special>::</span><span class=identifier>iterator</span><span class=special>&gt;</span> <span class=identifier>p</span><span class=special>=</span>
   <span class=identifier>s</span><span class=special>.</span><span class=identifier>range</span><span class=special>(</span><span class=number>100.0</span><span class=special>&lt;=</span><span class=identifier>_1</span><span class=special>,</span><span class=identifier>_1</span><span class=special>&lt;=</span><span class=number>200</span><span class=special>);</span> <span class=comment>// 100&lt;= x &lt;=200</span>
 <span class=special>...</span>
 <span class=identifier>p</span><span class=special>=</span><span class=identifier>s</span><span class=special>.</span><span class=identifier>range</span><span class=special>(</span><span class=number>100.0</span><span class=special>&lt;</span><span class=identifier>_1</span><span class=special>,</span><span class=identifier>_1</span><span class=special>&lt;</span><span class=number>200</span><span class=special>);</span>   <span class=comment>// 100&lt;  x &lt; 200</span>
 <span class=special>...</span>
 <span class=identifier>p</span><span class=special>=</span><span class=identifier>s</span><span class=special>.</span><span class=identifier>range</span><span class=special>(</span><span class=number>100.0</span><span class=special>&lt;=</span><span class=identifier>_1</span><span class=special>,</span><span class=identifier>_1</span><span class=special>&lt;</span><span class=number>200</span><span class=special>);</span>  <span class=comment>// 100&lt;= x &lt; 200</span>
 </pre></blockquote>

 <p>
 <code>range</code> simply accepts predicates specifying the lower and upper bounds
 of the interval searched. Please consult the reference for a detailed explanation
 of the permissible predicates passed to <code>range</code>.</p>

 <p>
 One or both bounds can be omitted with the special <code>unbounded</code> marker:
 </p>

 <blockquote><pre>
 <span class=identifier>p</span><span class=special>=</span><span class=identifier>s</span><span class=special>.</span><span class=identifier>range</span><span class=special>(</span><span class=number>100.0</span><span class=special>&lt;=</span><span class=identifier>_1</span><span class=special>,</span><span class=identifier>unbounded</span><span class=special>);</span> <span class=comment>// 100 &lt;= x</span>
 <span class=identifier>p</span><span class=special>=</span><span class=identifier>s</span><span class=special>.</span><span class=identifier>range</span><span class=special>(</span><span class=identifier>unbounded</span><span class=special>,</span><span class=identifier>_1</span><span class=special>&lt;</span><span class=number>200.0</span><span class=special>);</span>  <span class=comment>//   x &lt;  200</span>
 <span class=identifier>p</span><span class=special>=</span><span class=identifier>s</span><span class=special>.</span><span class=identifier>range</span><span class=special>(</span><span class=identifier>unbounded</span><span class=special>,</span><span class=identifier>unbounded</span><span class=special>);</span> <span class=comment>// equiv. to std::make_pair(s.begin(),s.end())</span>
 </pre></blockquote>

 <h4><a name="ord_updating">Updating</a></h4>

 <p>
 The <a href="../reference/ord_indices.html#replace"><code>replace</code></a> member function
 performs in-place replacement of a given element as the following example shows:
 </p>

 <blockquote><pre>
 <span class=keyword>typedef</span> <span class=identifier>index</span><span class=special>&lt;</span><span class=identifier>employee_set</span><span class=special>,</span><span class=identifier>name</span><span class=special>&gt;::</span><span class=identifier>type</span> <span class=identifier>employee_set_by_name</span><span class=special>;</span>
 <span class=identifier>employee_set_by_name</span><span class=special>&amp;</span> <span class=identifier>name_index</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;();</span>

 <span class=identifier>employee_set_by_name</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it</span><span class=special>=</span><span class=identifier>name_index</span><span class=special>.</span><span class=identifier>find</span><span class=special>(</span><span class=string>&quot;Anna Jones&quot;</span><span class=special>);</span>
 <span class=identifier>employee</span> <span class=identifier>anna</span><span class=special>=*</span><span class=identifier>it</span><span class=special>;</span>
 <span class=identifier>anna</span><span class=special>.</span><span class=identifier>name</span><span class=special>=</span><span class=string>&quot;Anna Smith&quot;</span><span class=special>;</span>      <span class=comment>// she just got married to Calvin Smith</span>
 <span class=identifier>name_index</span><span class=special>.</span><span class=identifier>replace</span><span class=special>(</span><span class=identifier>it</span><span class=special>,</span><span class=identifier>anna</span><span class=special>);</span> <span class=comment>// update her record</span>
 </pre></blockquote>

 <p>
 <code>replace</code> performs this substitution in such a manner that:
 <ul>
 <li>The complexity is constant time if the changed element retains its original
 order with respect to all indices; it is logarithmic otherwise.
 <li>Iterator and reference validity are preserved.
 <li>The operation is strongly exception-safe, i.e. the <code>multi_index_container</code>
 remains unchanged if some exception (originated by the system or the user's data
 types) is thrown.
 </ul>
 <code>replace</code> is a powerful operation not provided by standard STL
 containers, and one that is specially handy when strong exception-safety is
 required.
 </p>

 <p>
 The observant reader might have noticed that the convenience of <code>replace</code>
 comes at a cost: namely the whole element has to be copied <i>twice</i> to do
 the updating (when retrieving it and inside <code>replace</code>). If elements
 are expensive to copy, this may be quite a computational cost for the modification
 of just a tiny part of the object. To cope with this situation, Boost.MultiIndex
 provides an alternative updating mechanism called
 <a href="../reference/ord_indices.html#modify"><code>modify</code></a>:
 </p>

 <blockquote><pre>
 <span class=keyword>struct</span> <span class=identifier>change_name</span>
 <span class=special>{</span>
   <span class=identifier>change_name</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>&amp;</span> <span class=identifier>new_name</span><span class=special>):</span><span class=identifier>new_name</span><span class=special>(</span><span class=identifier>new_name</span><span class=special>){}</span>

   <span class=keyword>void</span> <span class=keyword>operator</span><span class=special>()(</span><span class=identifier>employee</span><span class=special>&amp;</span> <span class=identifier>e</span><span class=special>)</span>
   <span class=special>{</span>
     <span class=identifier>e</span><span class=special>.</span><span class=identifier>name</span><span class=special>=</span><span class=identifier>new_name</span><span class=special>;</span>
   <span class=special>}</span>

 <span class=keyword>private</span><span class=special>:</span>
   <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span> <span class=identifier>new_name</span><span class=special>;</span>
 <span class=special>};</span>
 <span class=special>...</span>
 <span class=keyword>typedef</span> <span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>index</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;::</span><span class=identifier>type</span> <span class=identifier>employee_set_by_name</span><span class=special>;</span>
 <span class=identifier>employee_set_by_name</span><span class=special>&amp;</span> <span class=identifier>name_index</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;();</span>

 <span class=identifier>employee_set_by_name</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it</span><span class=special>=</span><span class=identifier>name_index</span><span class=special>.</span><span class=identifier>find</span><span class=special>(</span><span class=string>&quot;Anna Jones&quot;</span><span class=special>);</span>
 <span class=identifier>name_index</span><span class=special>.</span><span class=identifier>modify</span><span class=special>(</span><span class=identifier>it</span><span class=special>,</span><span class=identifier>change_name</span><span class=special>(</span><span class=string>&quot;Anna Smith&quot;</span><span class=special>));</span>
 </pre></blockquote>

 <p><code>modify</code> accepts a functor (or pointer to function) that is
 passed a reference to the element to be changed, thus eliminating the need
 for spurious copies. Like <code>replace</code>, <code>modify</code> does preserve
 the internal orderings of all the indices of the <code>multi_index_container</code>.
 However, the semantics of <code>modify</code> is not entirely equivalent to
 <code>replace</code>. Consider what happens if a collision occurs as a result
 of modifying the element, i.e. the modified element clashes with another with
 respect to some unique ordered index. In the case of <code>replace</code>, the
 original value is kept and the method returns without altering the container, but
 <code>modify</code> cannot afford such an approach, since the modifying functor
 leaves no trace of the previous value of the element. Integrity constraints
 thus lead to the following policy: when a collision happens in the
 process of calling <code>modify</code>, the element is erased and the method returns
 <code>false</code>. There is a further version of <code>modify</code> which
 accepts a <i>rollback</i> functor to undo the changes in case of collision:
 </p>

 <blockquote><pre>
 <span class=keyword>struct</span> <span class=identifier>change_id</span>
 <span class=special>{</span>
   <span class=identifier>change_id</span><span class=special>(</span><span class=keyword>int</span> <span class=identifier>new_id</span><span class=special>):</span><span class=identifier>new_id</span><span class=special>(</span><span class=identifier>new_id</span><span class=special>){}</span>

   <span class=keyword>void</span> <span class=keyword>operator</span><span class=special>()(</span><span class=identifier>employee</span><span class=special>&amp;</span> <span class=identifier>e</span><span class=special>)</span>
   <span class=special>{</span>
     <span class=identifier>e</span><span class=special>.</span><span class=identifier>id</span><span class=special>=</span><span class=identifier>new_id</span><span class=special>;</span>
   <span class=special>}</span>

 <span class=keyword>private</span><span class=special>:</span>
   <span class=keyword>int</span> <span class=identifier>new_id</span><span class=special>;</span>
 <span class=special>};</span>
 <span class=special>...</span>
 <span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it</span><span class=special>=...</span>

 <span class=keyword>int</span> <span class=identifier>old_id</span><span class=special>=</span><span class=identifier>it</span><span class=special>-&gt;</span><span class=identifier>id</span><span class=special>;</span> <span class=comment>// keep the original id

 // try to modify the id, restore it in case of collisions</span>
 <span class=identifier>es</span><span class=special>.</span><span class=identifier>modify</span><span class=special>(</span><span class=identifier>it</span><span class=special>,</span><span class=identifier>change_id</span><span class=special>(</span><span class=number>321</span><span class=special>),</span><span class=identifier>change_id</span><span class=special>(</span><span class=identifier>old_id</span><span class=special>));</span>
 </pre></blockquote>

 <p>In the example, <code>change_id(old_id)</code> is invoked to restore the original
 conditions when the modification results in collisions with some other element.
 The differences in behavior between <code>replace</code>, <code>modify</code> and
 <code>modify</code> with rollback have to be considered by the programmer on a
 case-by-case basis to determine the best updating mechanism.
 </p>

 <p align="center">
 <table cellspacing="0">
   <caption><b>Behavior of the different updating mechanisms.</b></caption>
 <tr>
   <th align="center">updating function</th>
   <th>If there is a collision...</th>
 </tr>
 <tr>
   <td align="center"><code>replace(it,x)</code></td>
   <td>replacement does not take place.</td>
 </tr>
 <tr class="odd_tr">
   <td align="center"><code>modify(it,mod)</code></td>
   <td>the element is erased.</td>
 </tr>
 <tr>
   <td align="center"><code>modify(it,mod,back)</code></td>
   <td><code>back</code> is used to restore the original conditions.
     (If <code>back</code> throws, the element is erased.)
   </td>
 </tr>
 </table>
 </p>


 <p>
 Key-based versions of <code>modify</code>, named
 <a href="../reference/ord_indices.html#modify_key"><code>modify_key</code></a>, are
 provided as well. In this case, the modifying functors are passed a reference to
 the <code>key_type</code> part of the element instead of the whole object.
 </p>

 <blockquote><pre>
 <span class=keyword>struct</span> <span class=identifier>change_str</span>
 <span class=special>{</span>
   <span class=identifier>change_str</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>&amp;</span> <span class=identifier>new_str</span><span class=special>):</span><span class=identifier>new_str</span><span class=special>(</span><span class=identifier>new_str</span><span class=special>){}</span>

   <span class=comment>// note this is passed a string, not an employee</span>
   <span class=keyword>void</span> <span class=keyword>operator</span><span class=special>()(</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>&amp;</span> <span class=identifier>str</span><span class=special>)</span>
   <span class=special>{</span>
     <span class=identifier>str</span><span class=special>=</span><span class=identifier>new_str</span><span class=special>;</span>
   <span class=special>}</span>

 <span class=keyword>private</span><span class=special>:</span>
   <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span> <span class=identifier>new_str</span><span class=special>;</span>
 <span class=special>};</span>
 <span class=special>...</span>
 <span class=keyword>typedef</span> <span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>index</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;::</span><span class=identifier>type</span> <span class=identifier>employee_set_by_name</span><span class=special>;</span>
 <span class=identifier>employee_set_by_name</span><span class=special>&amp;</span> <span class=identifier>name_index</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;();</span>

 <span class=identifier>employee_set_by_name</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it</span><span class=special>=</span><span class=identifier>name_index</span><span class=special>.</span><span class=identifier>find</span><span class=special>(</span><span class=string>&quot;Anna Jones&quot;</span><span class=special>);</span>
 <span class=identifier>name_index</span><span class=special>.</span><span class=identifier>modify_key</span><span class=special>(</span><span class=identifier>it</span><span class=special>,</span><span class=identifier>change_str</span><span class=special>(</span><span class=string>&quot;Anna Smith&quot;</span><span class=special>));</span>
 </pre></blockquote>

 <p>
 Like <code>modify</code>, there are versions of <code>modify_key</code> with and
 without rollback. <code>modify</code> and
 <code>modify_key</code> are particularly well suited to use in conjunction to
 <a href="../../../../libs/lambda/index.html">Boost.Lambda</a>
 for defining the modifying functors:
 </p>

 <blockquote><pre>
 <span class=keyword>using</span> <span class=keyword>namespace</span> <span class=identifier>boost</span><span class=special>::</span><span class=identifier>lambda</span><span class=special>;</span>

 <span class=keyword>typedef</span> <span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>index</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;::</span><span class=identifier>type</span> <span class=identifier>employee_set_by_name</span><span class=special>;</span>
 <span class=identifier>employee_set_by_name</span><span class=special>&amp;</span> <span class=identifier>name_index</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;();</span>

 <span class=identifier>employee_set_by_name</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it</span><span class=special>=</span><span class=identifier>name_index</span><span class=special>.</span><span class=identifier>find</span><span class=special>(</span><span class=string>&quot;Anna Jones&quot;</span><span class=special>);</span>
 <span class=identifier>name_index</span><span class=special>.</span><span class=identifier>modify_key</span><span class=special>(</span><span class=identifier>it</span><span class=special>,</span><span class=identifier>_1</span><span class=special>=</span><span class=string>&quot;Anna Smith&quot;</span><span class=special>);</span>
 </pre></blockquote>

 <p>
 <code>modify_key</code> requires that the key extractor be of
 a special type called
 <a href="key_extraction.html#read_write_key_extractors">read/write</a>:
 this is usually, but not always, the case.
 </p>

 <h3>
 <a name="seq_indices">Sequenced indices</a>
 </h3>

 <p>
 Unlike ordered indices, sequenced indices do not impose a fixed order on the
 elements: instead, these can be arranged in any position on the sequence, in the
 same way as <code>std::list</code> permits. The interface of sequenced indices
 is thus designed upon that of <code>std::list</code>; nearly every operation
 provided in the standard container is replicated here, occasionally with changes
 in the syntax and/or semantics to cope with the constraints imposed by
 Boost.MultiIndex. In particular, there is an important limitation of sequenced
 indices with respect to <code>std::list</code>s, namely that elements of an
 <code>multi_index_container</code> are not mutable through an iterator:
 </p>

 <blockquote><pre>
 <span class=identifier>multi_index_container</span><span class=special>&lt;</span>
   <span class=keyword>int</span><span class=special>,</span>
   <span class=identifier>indexed_by</span><span class=special>&lt;</span><span class=identifier>sequenced</span><span class=special>&lt;&gt;</span> <span class=special>&gt;</span>
 <span class=special>&gt;</span> <span class=identifier>s</span><span class=special>;</span>            <span class=comment>// list-like container</span>

 <span class=identifier>s</span><span class=special>.</span><span class=identifier>push_front</span><span class=special>(</span><span class=number>0</span><span class=special>);</span>
 <span class=special>*(</span><span class=identifier>s</span><span class=special>.</span><span class=identifier>begin</span><span class=special>())=</span><span class=number>1</span><span class=special>;</span> <span class=comment>// ERROR: the element cannot be changed</span>
 </pre></blockquote>

 <p>
 That is, iterators of a sequenced index (of all types of indices, actually)
 point to constant elements. This limitation might come as a surprise, but
 it is imposed by the way <code>multi_index_container</code>s work; if elements were
 allowed to be changed in this manner, we could introduce inconsistencies
 in other ordered indices of the <code>multi_index_container</code>. Element modification
 can nevertheless be done by means of
 <a href="#seq_updating">update operations</a>.
 </p>

 <p>
 Consider a <code>multi_index_container</code> with two or more indices, one of them
 of sequenced type. If an element is inserted through another index,
 then it will be automatically appended to the end of the sequenced index.
 An example will help to clarify this:
 </p>

 <blockquote><pre>
 <span class=identifier>multi_index_container</span><span class=special>&lt;</span>
   <span class=keyword>int</span><span class=special>,</span>
   <span class=identifier>indexed_by</span><span class=special>&lt;</span>
     <span class=identifier>sequenced</span><span class=special>&lt;&gt;,</span>           <span class=comment>// sequenced type</span>
     <span class=identifier>ordered_unique</span><span class=special>&lt;</span><span class=identifier>identity</span><span class=special>&lt;</span><span class=keyword>int</span><span class=special>&gt;</span> <span class=special>&gt;</span> <span class=comment>// another index</span>
   <span class=special>&gt;</span>
 <span class=special>&gt;</span> <span class=identifier>s</span><span class=special>;</span>

 <span class=identifier>s</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;().</span><span class=identifier>insert</span><span class=special>(</span><span class=number>1</span><span class=special>);</span> <span class=comment>// insert 1 through index #1</span>
 <span class=identifier>s</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;().</span><span class=identifier>insert</span><span class=special>(</span><span class=number>0</span><span class=special>);</span> <span class=comment>// insert 0 through index #1

 // list elements through sequenced index #0</span>
 <span class=identifier>std</span><span class=special>::</span><span class=identifier>copy</span><span class=special>(</span><span class=identifier>s</span><span class=special>.</span><span class=identifier>begin</span><span class=special>(),</span><span class=identifier>s</span><span class=special>.</span><span class=identifier>end</span><span class=special>(),</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>ostream_iterator</span><span class=special>&lt;</span><span class=keyword>int</span><span class=special>&gt;(</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>cout</span><span class=special>));</span>

 <span class=comment>// result: 1 0</span>
 </pre></blockquote>

 <p>
 Thus the behavior of sequenced indices when insertions are not made through
 them is to preserve insertion order.
 </p>

 <h4><a name="seq_spec">Specification</a></h4>

 <p>
 Sequenced indices are specified with the <code>sequenced</code> construct:
 </p>

 <blockquote><pre>
 <span class=identifier>sequenced</span><span class=special>&lt;[</span><i>(tag)</i><span class=special>]&gt;</span>
 </pre></blockquote>

 <p>
 The <a href="#tagging">tag</a> parameter is optional.
 </p>

 <h4><a name="list_ops">List operations</a></h4>

 <p>
 As mentioned before, sequenced indices mimic the interface of
 <code>std::list</code>, and most of the original operations therein are
 provided as well. The semantics and complexity of these operations, however,
 do not always coincide with those of the standard container. Differences
 result mainly from the fact that insertions into a sequenced index are not
 guaranteed to succeed, due to the possible banning by other indices
 of the <code>multi_index_container</code>. Consult the
 <a href="../reference/seq_indices.html">reference</a> for further details.
 </p>

 <h4><a name="seq_updating">Updating</a></h4>

 <p>
 Like ordered indices, sequenced indices provide
 <a href="../reference/seq_indices.html#replace"><code>replace</code></a> and
 <a href="../reference/seq_indices.html#modify"><code>modify</code></a>
 operations, with identical functionality. There is however no analogous
 <code>modify_key</code>, since sequenced indices are not key-based.
 </p>

 <h2><a name="projection">Projection of iterators</a></h2>

 <p>
 Given indices <code>i1</code> and <code>i2</code> on the same <code>multi_index_container</code>,
 <a href="../reference/multi_index_container.html#projection"><code>project</code></a> can be used to
 retrieve an <code>i2</code>-iterator from an <code>i1</code>-iterator, both of them
 pointing to the same element of the container. This functionality allows the programmer to
 move between different indices of the same <code>multi_index_container</code> when performing
 elaborate operations:
 </p>

 <blockquote><pre>
 <span class=keyword>typedef</span> <span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>index</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;::</span><span class=identifier>type</span> <span class=identifier>employee_set_by_name</span><span class=special>;</span>
 <span class=identifier>employee_set_by_name</span><span class=special>&amp;</span> <span class=identifier>name_index</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;();</span>

 <span class=comment>// list employees by ID starting from Robert Brown's ID</span>

 <span class=identifier>employee_set_by_name</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it1</span><span class=special>=</span><span class=identifier>name_index</span><span class=special>.</span><span class=identifier>find</span><span class=special>(</span><span class=string>&quot;Robert Brown&quot;</span><span class=special>);</span>

 <span class=comment>// obtain an iterator of index #0 from it1</span>
 <span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it2</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>project</span><span class=special>&lt;</span><span class=number>0</span><span class=special>&gt;(</span><span class=identifier>it1</span><span class=special>);</span>

 <span class=identifier>std</span><span class=special>::</span><span class=identifier>copy</span><span class=special>(</span><span class=identifier>it2</span><span class=special>,</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>end</span><span class=special>(),</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>ostream_iterator</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>&gt;(</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>cout</span><span class=special>));</span>
 </pre></blockquote>

 <p>
 A slightly more interesting example:
 </p>

 <blockquote><pre>
 <span class=identifier>text_container</span> <span class=identifier>tc</span><span class=special>;</span>

 <span class=comment>// get a view to index #1 (ordered index on the words)</span>
 <span class=identifier>text_container</span><span class=special>::</span><span class=identifier>nth_index</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;::</span><span class=identifier>type</span><span class=special>&amp;</span> <span class=identifier>sorted_index</span><span class=special>=</span><span class=identifier>tc</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;();</span>

 <span class=comment>// prepend &quot;older&quot; to all occurrences of &quot;sister&quot;</span>

 <span class=identifier>text_container</span><span class=special>::</span><span class=identifier>nth_index</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;::</span><span class=identifier>type</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it1</span><span class=special>=</span>
   <span class=identifier>sorted_index</span><span class=special>.</span><span class=identifier>lower_bound</span><span class=special>(</span><span class=string>&quot;sister&quot;</span><span class=special>);</span>

 <span class=keyword>while</span><span class=special>(</span><span class=identifier>it1</span><span class=special>!=</span><span class=identifier>sorted_index</span><span class=special>.</span><span class=identifier>end</span><span class=special>()&amp;&amp;*</span><span class=identifier>it1</span><span class=special>==</span><span class=string>&quot;sister&quot;</span><span class=special>){</span>
   <span class=comment>// convert to an iterator to the sequenced index</span>
   <span class=identifier>text_container</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it2</span><span class=special>=</span><span class=identifier>tc</span><span class=special>.</span><span class=identifier>project</span><span class=special>&lt;</span><span class=number>0</span><span class=special>&gt;(</span><span class=identifier>it1</span><span class=special>);</span>

   <span class=identifier>tc</span><span class=special>.</span><span class=identifier>insert</span><span class=special>(</span><span class=identifier>it2</span><span class=special>,</span><span class=string>&quot;older&quot;</span><span class=special>);</span>
   <span class=special>++</span><span class=identifier>it1</span><span class=special>;</span>
 <span class=special>}</span>
 </pre></blockquote>

 <p>
 When provided, <code>project</code> can also be used with
 <a href="#tagging">tags</a>.
 </p>

 <h2><a name="complexity">Complexity and exception safety</a></h2>

 <p>
 <code>multi_index_container</code> provides the same complexity and exception safety
 guarantees as the equivalent STL containers do. Iterator and reference validity
 is preserved in the face of insertions, even for replace and modify operations.
 </p>

 <p>
 Appropriate instantiations of <code>multi_index_container</code> can in fact simulate
 <code>std::set</code>, <code>std::multiset</code> and (with more limitations)
 <code>std::list</code>, as shown in the
 <a href="techniques.html#emulate_std_containers">techniques</a>
 section. These simulations are as nearly as efficient as the original STL
 containers; consult the <a href="../reference/index.html">reference</a> for further
 information on complexity guarantees and the
 <a href="../performance.html">performance section</a> for practical measurements of
 efficiency.
 </p>

 <hr>

 <div class="prev_link"><a href="index.html"><img src="../prev.gif" alt="tutorial" border="0"><br>
 Boost.MultiIndex Tutorial
 </a></div>
 <div class="up_link"><a href="index.html"><img src="../up.gif" alt="Boost.MultiIndex tutorial" border="0"><br>
 Boost.MultiIndex tutorial
 </a></div>
 <div class="next_link"><a href="indices.html"><img src="../next.gif" alt="index types" border="0"><br>
 Index types
 </a></div><br clear="all" style="clear: all;">

 <br>

 <p>Revised November 7th 2008</p>

 <p>&copy; Copyright 2003-2008 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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