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<td class="header-group page-location"><a href="../refmanual.html" class="navigation-link">Front Page</a> / <a href="./algorithms.html" class="navigation-link">Algorithms</a> / <a href="./algorithms-concepts.html" class="navigation-link">Concepts</a> / <a href="./reversible-algorithm.html" class="navigation-link">Reversible Algorithm</a></td>
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<div class="section" id="reversible-algorithm">
<h1><a class="toc-backref" href="./algorithms-concepts.html#id1463">Reversible Algorithm</a></h1>
<div class="section" id="id459">
<h3><a class="subsection-title" href="#description" name="description">Description</a></h3>
<p>A <a class="reference internal" href="./reversible-algorithm.html">Reversible Algorithm</a> is a member of a pair of
transformation algorithms that iterate over their input sequence(s)
in opposite directions. For each reversible
algorithm <tt class="literal"><span class="pre">x</span></tt> there exists a <em>counterpart</em> algorithm <tt class="literal"><span class="pre">reverse_x</span></tt>,
that exhibits the exact semantics of <tt class="literal"><span class="pre">x</span></tt> except that the elements
of its input sequence argument(s) are processed in the reverse
order.</p>
</div>
<div class="section" id="id460">
<h3><a class="subsection-title" href="#expression-requirements" name="expression-requirements">Expression requirements</a></h3>
<p>In the following table and subsequent specifications, <tt class="literal"><span class="pre">x</span></tt> is a placeholder token for the actual
<a class="reference internal" href="./reversible-algorithm.html">Reversible Algorithm</a>'s name, <em>s</em><sub>1</sub>,<em>s</em><sub>2</sub>,...<em>s</em><sub>n</sub> are
<a class="reference internal" href="./forward-sequence.html">Forward Sequence</a>s, and <tt class="literal"><span class="pre">in</span></tt> is an <a class="reference internal" href="./inserter.html">Inserter</a>.</p>
<table border="1" class="docutils table">
<colgroup>
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<col width="28%" />
<col width="23%" />
</colgroup>
<thead valign="bottom">
<tr><th class="head">Expression</th>
<th class="head">Type</th>
<th class="head">Complexity</th>
</tr>
</thead>
<tbody valign="top">
<tr><td><tt class="literal"><span class="pre">x&lt;</span></tt><em>s</em><sub>1</sub>,<em>s</em><sub>2</sub>,...<em>s</em><sub>n</sub>, ...<tt class="literal"><span class="pre">&gt;::type</span></tt></td>
<td><a class="reference internal" href="./forward-sequence.html">Forward Sequence</a></td>
<td>Unspecified.</td>
</tr>
<tr><td><tt class="literal"><span class="pre">x&lt;</span></tt><em>s</em><sub>1</sub>,<em>s</em><sub>2</sub>,...<em>s</em><sub>n</sub>, ... <tt class="literal"><span class="pre">in&gt;::type</span></tt></td>
<td>Any type</td>
<td>Unspecified.</td>
</tr>
<tr><td><tt class="literal"><span class="pre">reverse_x&lt;</span></tt><em>s</em><sub>1</sub>,<em>s</em><sub>2</sub>,...<em>s</em><sub>n</sub>, ...<tt class="literal"><span class="pre">&gt;::type</span></tt></td>
<td><a class="reference internal" href="./forward-sequence.html">Forward Sequence</a></td>
<td>Unspecified.</td>
</tr>
<tr><td><tt class="literal"><span class="pre">reverse_x&lt;</span></tt><em>s</em><sub>1</sub>,<em>s</em><sub>2</sub>,...<em>s</em><sub>n</sub>, ... <tt class="literal"><span class="pre">in&gt;::type</span></tt></td>
<td>Any type</td>
<td>Unspecified.</td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="id461">
<h3><a class="subsection-title" href="#expression-semantics" name="expression-semantics">Expression semantics</a></h3>
<pre class="literal-block">
typedef x&lt;<em>s</em><sub>1</sub>,<em>s</em><sub>2</sub>,...<em>s</em><sub>n</sub>,...&gt;::type t;
</pre>
<table class="docutils field-list" frame="void" rules="none">
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<tbody valign="top">
<tr class="field"><th class="field-name">Precondition:</th><td class="field-body"><p class="first"><em>s</em><sub>1</sub> is an <a class="reference internal" href="./extensible-sequence.html">Extensible Sequence</a>.</p>
</td>
</tr>
<tr class="field"><th class="field-name">Semantics:</th><td class="field-body"><p class="first"><tt class="literal"><span class="pre">t</span></tt> is equivalent to</p>
<pre class="literal-block">
x&lt;
      <em>s</em><sub>1</sub>,<em>s</em><sub>2</sub>,...<em>s</em><sub>n</sub>,...
    , <a href="./back-inserter.html" class="identifier">back_inserter</a>&lt; <a href="./clear.html" class="identifier">clear</a>&lt;<em>s</em><sub>1</sub>&gt;::type &gt;
    &gt;::type
</pre>
<p>if <tt class="literal"><span class="pre">has_push_back&lt;</span></tt><em>s</em><sub>1</sub><tt class="literal"><span class="pre">&gt;::value</span> <span class="pre">==</span> <span class="pre">true</span></tt> and</p>
<pre class="literal-block">
reverse_x&lt;
      <em>s</em><sub>1</sub>,<em>s</em><sub>2</sub>,...<em>s</em><sub>n</sub>,...
    , <a href="./front-inserter.html" class="identifier">front_inserter</a>&lt; <a href="./clear.html" class="identifier">clear</a>&lt;<em>s</em><sub>1</sub>&gt;::type &gt;
    &gt;::type
</pre>
<p class="last">otherwise.</p>
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<pre class="literal-block">
typedef x&lt;<em>s</em><sub>1</sub>,<em>s</em><sub>2</sub>,...<em>s</em><sub>n</sub>,...in&gt;::type t;
</pre>
<table class="docutils field-list" frame="void" rules="none">
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<tbody valign="top">
<tr class="field"><th class="field-name">Semantics:</th><td class="field-body"><tt class="literal"><span class="pre">t</span></tt> is the result of an <tt class="literal"><span class="pre">x</span></tt> invocation with arguments
<em>s</em><sub>1</sub>,<em>s</em><sub>2</sub>,... <em>s</em><sub>n</sub>,...<tt class="literal"><span class="pre">in</span></tt>.</td>
</tr>
</tbody>
</table>
<!-- .......................................................................... -->
<pre class="literal-block">
typedef reverse_x&lt;<em>s</em><sub>1</sub>,<em>s</em><sub>2</sub>,... <em>s</em><sub>n</sub>,... &gt;::type t;
</pre>
<table class="docutils field-list" frame="void" rules="none">
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<tbody valign="top">
<tr class="field"><th class="field-name">Precondition:</th><td class="field-body"><p class="first"><em>s</em><sub>1</sub> is an <a class="reference internal" href="./extensible-sequence.html">Extensible Sequence</a>.</p>
</td>
</tr>
<tr class="field"><th class="field-name">Semantics:</th><td class="field-body"><p class="first"><tt class="literal"><span class="pre">t</span></tt> is equivalent to</p>
<pre class="literal-block">
x&lt;
      <em>s</em><sub>1</sub>,<em>s</em><sub>2</sub>,...<em>s</em><sub>n</sub>,...
    , <a href="./front-inserter.html" class="identifier">front_inserter</a>&lt; <a href="./clear.html" class="identifier">clear</a>&lt;<em>s</em><sub>1</sub>&gt;::type &gt;
    &gt;::type
</pre>
<p>if <tt class="literal"><span class="pre">has_push_front&lt;</span></tt><em>s</em><sub>1</sub><tt class="literal"><span class="pre">&gt;::value</span> <span class="pre">==</span> <span class="pre">true</span></tt> and</p>
<pre class="literal-block">
reverse_x&lt;
      <em>s</em><sub>1</sub>,<em>s</em><sub>2</sub>,...<em>s</em><sub>n</sub>,...
    , <a href="./back-inserter.html" class="identifier">back_inserter</a>&lt; <a href="./clear.html" class="identifier">clear</a>&lt;<em>s</em><sub>1</sub>&gt;::type &gt;
    &gt;::type
</pre>
<p class="last">otherwise.</p>
</td>
</tr>
</tbody>
</table>
<!-- .......................................................................... -->
<pre class="literal-block">
typedef reverse_x&lt;<em>s</em><sub>1</sub>,<em>s</em><sub>2</sub>,...<em>s</em><sub>n</sub>,... in&gt;::type t;
</pre>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field"><th class="field-name">Semantics:</th><td class="field-body"><tt class="literal"><span class="pre">t</span></tt> is the result of a <tt class="literal"><span class="pre">reverse_x</span></tt> invocation with arguments
<em>s</em><sub>1</sub>,<em>s</em><sub>2</sub>,...<em>s</em><sub>n</sub>,...<tt class="literal"><span class="pre">in</span></tt>.</td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="id462">
<h3><a class="subsection-title" href="#example" name="example">Example</a></h3>
<pre class="literal-block">
typedef <a href="./transform.html" class="identifier">transform</a>&lt;
      <a href="./range-c.html" class="identifier">range_c</a>&lt;int,0,10&gt;
    , <a href="./plus.html" class="identifier">plus</a>&lt;<a href="./placeholders.html" class="identifier">_1</a>,<a href="./int.html" class="identifier">int_</a>&lt;7&gt; &gt;
    , <a href="./back-inserter.html" class="identifier">back_inserter</a>&lt; vector0&lt;&gt; &gt;
    &gt;::type r1;

typedef <a href="./transform.html" class="identifier">transform</a>&lt; r1, <a href="./minus.html" class="identifier">minus</a>&lt;<a href="./placeholders.html" class="identifier">_1</a>,<a href="./int.html" class="identifier">int_</a>&lt;2&gt; &gt; &gt;::type r2;
typedef <a href="./reverse-transform.html" class="identifier">reverse_transform</a>&lt;
      r2
    , <a href="./minus.html" class="identifier">minus</a>&lt;<a href="./placeholders.html" class="identifier">_1</a>,5&gt;
    , <a href="./front-inserter.html" class="identifier">front_inserter</a>&lt; vector0&lt;&gt; &gt;
    &gt;::type r3;

<a href="./assert.html" class="identifier">BOOST_MPL_ASSERT</a>(( <a href="./equal.html" class="identifier">equal</a>&lt;r1, <a href="./range-c.html" class="identifier">range_c</a>&lt;int,7,17&gt; &gt; ));
<a href="./assert.html" class="identifier">BOOST_MPL_ASSERT</a>(( <a href="./equal.html" class="identifier">equal</a>&lt;r2, <a href="./range-c.html" class="identifier">range_c</a>&lt;int,5,15&gt; &gt; ));
<a href="./assert.html" class="identifier">BOOST_MPL_ASSERT</a>(( <a href="./equal.html" class="identifier">equal</a>&lt;r3, <a href="./range-c.html" class="identifier">range_c</a>&lt;int,0,10&gt; > ));
</pre>
</div>
<div class="section" id="id463">
<h3><a class="subsection-title" href="#models" name="models">Models</a></h3>
<ul class="simple">
<li><a class="reference internal" href="./transform.html">transform</a></li>
<li><a class="reference internal" href="./remove.html">remove</a></li>
<li><a class="reference internal" href="./replace.html">replace</a></li>
</ul>
</div>
<div class="section" id="id464">
<h3><a class="subsection-title" href="#see-also" name="see-also">See also</a></h3>
<p><a class="reference internal" href="./transformation-algorithms.html">Transformation Algorithms</a>, <a class="reference internal" href="./inserter.html">Inserter</a></p>
</div>
</div>

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