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+<title>Concept BidirectionalIterator</title>
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+</div>
+<div class="refentry">
+<a name="BidirectionalIterator"></a><div class="titlepage"></div>
+<div class="refnamediv">
+<h2><span class="refentrytitle">Concept BidirectionalIterator</span></h2>
+<p>BidirectionalIterator</p>
+</div>
+<div class="refsect1">
+<a name="idp720898176"></a><h2>Description</h2>
+<p>A bidirectional iterator is an iterator that can read through a sequence
+ of values. It can move in either direction through the sequence, and can
+ be either mutable (data pointed to by it can be changed) or not mutable.</p>
+<p>An iterator represents a position in a sequence. Therefore, the
+ iterator can point into the sequence (returning a value when dereferenced
+ and being incrementable), or be off-the-end (and not dereferenceable or
+ incrementable).</p>
+</div>
+<div class="refsect1">
+<a name="idp720899984"></a><h2>Refinement of</h2>
+<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem"><p><a class="link" href="ForwardIterator.html" title="Concept ForwardIterator">ForwardIterator</a></p></li></ul></div>
+</div>
+<div class="refsect1">
+<a name="idp720901456"></a><h2>Associated types</h2>
+<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
+<li class="listitem">
+<p><span class="bold"><strong>value_type</strong></span></p>
+<pre class="literallayout">std::iterator_traits&lt;Iter&gt;::value_type</pre>
+<p>The value type of the iterator</p>
+</li>
+<li class="listitem">
+<p><span class="bold"><strong>category</strong></span></p>
+<pre class="literallayout">std::iterator_traits&lt;Iter&gt;::iterator_category</pre>
+<p>The category of the iterator</p>
+</li>
+</ul></div>
+</div>
+<div class="refsect1">
+<a name="idp720906048"></a><h2>Notation</h2>
+<div class="variablelist"><dl class="variablelist">
+<dt><span class="term">Iter</span></dt>
+<dd>A type playing the role of iterator-type in the <a class="link" href="BidirectionalIterator.html" title="Concept BidirectionalIterator">BidirectionalIterator</a> concept.</dd>
+<dt>
+<span class="term"><code class="varname">i</code>, </span><span class="term"><code class="varname">j</code></span>
+</dt>
+<dd>Objects of type Iter</dd>
+<dt><span class="term"><code class="varname">x</code></span></dt>
+<dd>Object of type value_type</dd>
+</dl></div>
+</div>
+<div class="refsect1">
+<a name="idp720910544"></a><h2>Type expressions</h2>
+<div class="variablelist"><dl class="variablelist">
+<dt><span class="term">Category tag</span></dt>
+<dd><p><span class="type">category</span> must be
+ derived from <span class="type">std::bidirectional_iterator_tag</span>.
+ </p></dd>
+</dl></div>
+</div>
+<div class="refsect1">
+<a name="idp720912704"></a><h2>Valid expressions</h2>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>Name</th>
+<th>Expression</th>
+<th>Type</th>
+<th>Precondition</th>
+<th>Semantics</th>
+<th>Postcondition</th>
+</tr></thead>
+<tbody>
+<tr>
+<td><p>Predecrement</p></td>
+<td><p>--i</p></td>
+<td><p><span class="type">Iter &amp;</span></p></td>
+<td><p><code class="computeroutput">i</code> is incrementable (not
+ off-the-end) and some dereferenceable iterator <code class="computeroutput">j</code> exists
+ such that <code class="computeroutput">i == ++j</code></p></td>
+<td>&#160;</td>
+<td>&#160;</td>
+</tr>
+<tr>
+<td><p>Postdecrement</p></td>
+<td><p>i--</p></td>
+<td><p><span class="type">Iter</span></p></td>
+<td><p>Same as for predecrement</p></td>
+<td><p>Equivalent to <code class="computeroutput">{Iter j = i; --i; return j;}</code></p></td>
+<td><p><code class="computeroutput">i</code> is dereferenceable or
+ off-the-end</p></td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<div class="refsect1">
+<a name="idp720923664"></a><h2>Complexity</h2>
+<p>
+ All iterator operations must take amortized constant time.
+ </p>
+</div>
+<div class="refsect1">
+<a name="idp720924416"></a><h2>Invariants</h2>
+<div class="variablelist"><dl class="variablelist">
+<dt><span class="term">Predecrement must return object</span></dt>
+<dd><p>
+ <code class="computeroutput">&amp;i = &amp;(--i)</code>
+ </p></dd>
+<dt><span class="term">Unique path through sequence</span></dt>
+<dd><p>
+ <code class="computeroutput">i == j</code> implies <code class="computeroutput">--i == --j</code>
+ </p></dd>
+<dt><span class="term">Increment and decrement are inverses</span></dt>
+<dd><p>
+ <code class="computeroutput">++i; --i;</code> and <code class="computeroutput">--i; ++i;</code> must end up with the
+ value of <code class="computeroutput">i</code> unmodified, if <code class="computeroutput">i</code> both of the
+ operations in the pair are valid.
+ </p></dd>
+</dl></div>
+</div>
+<div class="refsect1">
+<a name="idp720932368"></a><h2>Models</h2>
+<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
+<li class="listitem"><span class="simplelist"><span class="type">T *</span></span></li>
+<li class="listitem"><span class="simplelist"><span class="type">std::list&lt;T&gt;::iterator</span></span></li>
+</ul></div>
+</div>
+<div class="refsect1">
+<a name="idp720934816"></a><h2>See also</h2>
+<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem"><p><a class="link" href="RandomAccessIterator.html" title="Concept RandomAccessIterator">RandomAccessIterator</a></p></li></ul></div>
+</div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright &#169; 2001, 2002 Indiana University<br>Copyright &#169; 2000, 2001 University of Notre Dame du Lac<br>Copyright &#169; 2000 Jeremy Siek, Lie-Quan Lee, Andrew Lumsdaine<br>Copyright &#169; 1996-1999 Silicon Graphics Computer Systems, Inc.<br>Copyright &#169; 1994 Hewlett-Packard Company<p>Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file <code class="filename">LICENSE_1_0.txt</code> or copy at
+ <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
+ </p>
+<p>This product includes software developed at the University
+ of Notre Dame and the Pervasive Technology Labs at Indiana
+ University. For technical information contact Andrew Lumsdaine
+ at the Pervasive Technology Labs at Indiana University. For
+ administrative and license questions contact the Advanced
+ Research and Technology Institute at 351 West 10th Street.
+ Indianapolis, Indiana 46202, phone 317-278-4100, fax
+ 317-274-5902.</p>
+<p>Some concepts based on versions from the MTL draft manual
+ and Boost Graph and Property Map documentation, the SGI Standard
+ Template Library documentation and the Hewlett-Packard STL,
+ under the following license:
+ </p>
+<div class="blockquote"><blockquote class="blockquote"><p>Permission to use, copy, modify, distribute and
+ sell this software and its documentation for any purpose is
+ hereby granted without fee, provided that the above copyright
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