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<title>Permutation Iterator</title>
<meta name="author" content="Toon Knapen, David Abrahams, Roland Richter, Jeremy Siek" />
<meta name="organization" content="Boost Consulting, Indiana University Open Systems Lab" />
<meta name="date" content="2006-09-11" />
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<div class="document" id="permutation-iterator">
<h1 class="title">Permutation Iterator</h1>
<table class="docinfo" frame="void" rules="none">
<col class="docinfo-name" />
<col class="docinfo-content" />
<tbody valign="top">
<tr><th class="docinfo-name">Author:</th>
<td>Toon Knapen, David Abrahams, Roland Richter, Jeremy Siek</td></tr>
<tr><th class="docinfo-name">Contact:</th>
<td><a class="first reference external" href="mailto:dave&#64;boost-consulting.com">dave&#64;boost-consulting.com</a>, <a class="last reference external" href="mailto:jsiek&#64;osl.iu.edu">jsiek&#64;osl.iu.edu</a></td></tr>
<tr><th class="docinfo-name">Organization:</th>
<td><a class="first reference external" href="http://www.boost-consulting.com">Boost Consulting</a>, Indiana University <a class="last reference external" href="http://www.osl.iu.edu">Open Systems
Lab</a></td></tr>
<tr><th class="docinfo-name">Date:</th>
<td>2006-09-11</td></tr>
<tr><th class="docinfo-name">Copyright:</th>
<td>Copyright Toon Knapen, David Abrahams, Roland Richter, and Jeremy Siek 2003.</td></tr>
</tbody>
</table>
<!-- Distributed under the Boost -->
<!-- Software License, Version 1.0. (See accompanying -->
<!-- file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -->
<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">abstract:</th><td class="field-body"><!-- Copyright David Abrahams 2006. Distributed under the Boost -->
<!-- Software License, Version 1.0. (See accompanying -->
<!-- file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -->
The permutation iterator adaptor provides a permuted view of a given
range. That is, the view includes every element of the given range but
in a potentially different order.</td>
</tr>
</tbody>
</table>
<div class="contents topic" id="table-of-contents">
<p class="topic-title first">Table of Contents</p>
<ul class="simple">
<li><a class="reference internal" href="#introduction" id="id2">Introduction</a></li>
<li><a class="reference internal" href="#reference" id="id3">Reference</a><ul>
<li><a class="reference internal" href="#permutation-iterator-requirements" id="id4"><tt class="docutils literal"><span class="pre">permutation_iterator</span></tt> requirements</a></li>
<li><a class="reference internal" href="#permutation-iterator-models" id="id5"><tt class="docutils literal"><span class="pre">permutation_iterator</span></tt> models</a></li>
<li><a class="reference internal" href="#permutation-iterator-operations" id="id6"><tt class="docutils literal"><span class="pre">permutation_iterator</span></tt> operations</a></li>
</ul>
</li>
<li><a class="reference internal" href="#example" id="id7">Example</a></li>
</ul>
</div>
<div class="section" id="introduction">
<h1><a class="toc-backref" href="#id2">Introduction</a></h1>
<!-- Copyright David Abrahams 2006. Distributed under the Boost -->
<!-- Software License, Version 1.0. (See accompanying -->
<!-- file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -->
<p>The adaptor takes two arguments:</p>
<blockquote>
<ul class="simple">
<li>an iterator to the range V on which the permutation
will be applied</li>
<li>the reindexing scheme that defines how the
elements of V will be permuted.</li>
</ul>
</blockquote>
<p>Note that the permutation iterator is not limited to strict
permutations of the given range V.  The distance between begin and end
of the reindexing iterators is allowed to be smaller compared to the
size of the range V, in which case the permutation iterator only
provides a permutation of a subrange of V.  The indexes neither need
to be unique. In this same context, it must be noted that the past the
end permutation iterator is completely defined by means of the
past-the-end iterator to the indices.</p>
</div>
<div class="section" id="reference">
<h1><a class="toc-backref" href="#id3">Reference</a></h1>
<!-- Copyright David Abrahams 2006. Distributed under the Boost -->
<!-- Software License, Version 1.0. (See accompanying -->
<!-- file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -->
<pre class="literal-block">
template&lt; class ElementIterator
        , class IndexIterator
        , class ValueT        = use_default
        , class CategoryT     = use_default
        , class ReferenceT    = use_default
        , class DifferenceT   = use_default &gt;
class permutation_iterator
{
public:
  permutation_iterator();
  explicit permutation_iterator(ElementIterator x, IndexIterator y);

  template&lt; class OEIter, class OIIter, class V, class C, class R, class D &gt;
  permutation_iterator(
      permutation_iterator&lt;OEIter, OIIter, V, C, R, D&gt; const&amp; r
      , typename enable_if_convertible&lt;OEIter, ElementIterator&gt;::type* = 0
      , typename enable_if_convertible&lt;OIIter, IndexIterator&gt;::type* = 0
      );
  reference operator*() const;
  permutation_iterator&amp; operator++();
  ElementIterator const&amp; base() const;
private:
  ElementIterator m_elt;      // exposition only
  IndexIterator m_order;      // exposition only
};

template &lt;class ElementIterator, class IndexIterator&gt;
permutation_iterator&lt;ElementIterator, IndexIterator&gt;
make_permutation_iterator( ElementIterator e, IndexIterator i);
</pre>
<div class="section" id="permutation-iterator-requirements">
<h2><a class="toc-backref" href="#id4"><tt class="docutils literal"><span class="pre">permutation_iterator</span></tt> requirements</a></h2>
<p><tt class="docutils literal"><span class="pre">ElementIterator</span></tt> shall model Random Access Traversal Iterator.
<tt class="docutils literal"><span class="pre">IndexIterator</span></tt> shall model Readable Iterator.  The value type of
the <tt class="docutils literal"><span class="pre">IndexIterator</span></tt> must be convertible to the difference type of
<tt class="docutils literal"><span class="pre">ElementIterator</span></tt>.</p>
</div>
<div class="section" id="permutation-iterator-models">
<h2><a class="toc-backref" href="#id5"><tt class="docutils literal"><span class="pre">permutation_iterator</span></tt> models</a></h2>
<p><tt class="docutils literal"><span class="pre">permutation_iterator</span></tt> models the same iterator traversal concepts
as <tt class="docutils literal"><span class="pre">IndexIterator</span></tt> and the same iterator access concepts as
<tt class="docutils literal"><span class="pre">ElementIterator</span></tt>.</p>
<p>If <tt class="docutils literal"><span class="pre">IndexIterator</span></tt> models Single Pass Iterator and
<tt class="docutils literal"><span class="pre">ElementIterator</span></tt> models Readable Iterator then
<tt class="docutils literal"><span class="pre">permutation_iterator</span></tt> models Input Iterator.</p>
<p>If <tt class="docutils literal"><span class="pre">IndexIterator</span></tt> models Forward Traversal Iterator and
<tt class="docutils literal"><span class="pre">ElementIterator</span></tt> models Readable Lvalue Iterator then
<tt class="docutils literal"><span class="pre">permutation_iterator</span></tt> models Forward Iterator.</p>
<p>If <tt class="docutils literal"><span class="pre">IndexIterator</span></tt> models Bidirectional Traversal Iterator and
<tt class="docutils literal"><span class="pre">ElementIterator</span></tt> models Readable Lvalue Iterator then
<tt class="docutils literal"><span class="pre">permutation_iterator</span></tt> models Bidirectional Iterator.</p>
<p>If <tt class="docutils literal"><span class="pre">IndexIterator</span></tt> models Random Access Traversal Iterator and
<tt class="docutils literal"><span class="pre">ElementIterator</span></tt> models Readable Lvalue Iterator then
<tt class="docutils literal"><span class="pre">permutation_iterator</span></tt> models Random Access Iterator.</p>
<p><tt class="docutils literal"><span class="pre">permutation_iterator&lt;E1,</span> <span class="pre">X,</span> <span class="pre">V1,</span> <span class="pre">C2,</span> <span class="pre">R1,</span> <span class="pre">D1&gt;</span></tt> is interoperable
with <tt class="docutils literal"><span class="pre">permutation_iterator&lt;E2,</span> <span class="pre">Y,</span> <span class="pre">V2,</span> <span class="pre">C2,</span> <span class="pre">R2,</span> <span class="pre">D2&gt;</span></tt> if and only if
<tt class="docutils literal"><span class="pre">X</span></tt> is interoperable with <tt class="docutils literal"><span class="pre">Y</span></tt> and <tt class="docutils literal"><span class="pre">E1</span></tt> is convertible
to <tt class="docutils literal"><span class="pre">E2</span></tt>.</p>
</div>
<div class="section" id="permutation-iterator-operations">
<h2><a class="toc-backref" href="#id6"><tt class="docutils literal"><span class="pre">permutation_iterator</span></tt> operations</a></h2>
<p>In addition to those operations required by the concepts that
<tt class="docutils literal"><span class="pre">permutation_iterator</span></tt> models, <tt class="docutils literal"><span class="pre">permutation_iterator</span></tt> provides the
following operations.</p>
<p><tt class="docutils literal"><span class="pre">permutation_iterator();</span></tt></p>
<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">Effects:</th><td class="field-body">Default constructs <tt class="docutils literal"><span class="pre">m_elt</span></tt> and <tt class="docutils literal"><span class="pre">m_order</span></tt>.</td>
</tr>
</tbody>
</table>
<p><tt class="docutils literal"><span class="pre">explicit</span> <span class="pre">permutation_iterator(ElementIterator</span> <span class="pre">x,</span> <span class="pre">IndexIterator</span> <span class="pre">y);</span></tt></p>
<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">Effects:</th><td class="field-body">Constructs <tt class="docutils literal"><span class="pre">m_elt</span></tt> from <tt class="docutils literal"><span class="pre">x</span></tt> and <tt class="docutils literal"><span class="pre">m_order</span></tt> from <tt class="docutils literal"><span class="pre">y</span></tt>.</td>
</tr>
</tbody>
</table>
<pre class="literal-block">
template&lt; class OEIter, class OIIter, class V, class C, class R, class D &gt;
permutation_iterator(
    permutation_iterator&lt;OEIter, OIIter, V, C, R, D&gt; const&amp; r
    , typename enable_if_convertible&lt;OEIter, ElementIterator&gt;::type* = 0
    , typename enable_if_convertible&lt;OIIter, IndexIterator&gt;::type* = 0
    );
</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">Effects:</th><td class="field-body">Constructs <tt class="docutils literal"><span class="pre">m_elt</span></tt> from <tt class="docutils literal"><span class="pre">r.m_elt</span></tt> and
<tt class="docutils literal"><span class="pre">m_order</span></tt> from <tt class="docutils literal"><span class="pre">y.m_order</span></tt>.</td>
</tr>
</tbody>
</table>
<p><tt class="docutils literal"><span class="pre">reference</span> <span class="pre">operator*()</span> <span class="pre">const;</span></tt></p>
<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">Returns:</th><td class="field-body"><tt class="docutils literal"><span class="pre">*(m_elt</span> <span class="pre">+</span> <span class="pre">*m_order)</span></tt></td>
</tr>
</tbody>
</table>
<p><tt class="docutils literal"><span class="pre">permutation_iterator&amp;</span> <span class="pre">operator++();</span></tt></p>
<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">Effects:</th><td class="field-body"><tt class="docutils literal"><span class="pre">++m_order</span></tt></td>
</tr>
<tr class="field"><th class="field-name">Returns:</th><td class="field-body"><tt class="docutils literal"><span class="pre">*this</span></tt></td>
</tr>
</tbody>
</table>
<p><tt class="docutils literal"><span class="pre">ElementIterator</span> <span class="pre">const&amp;</span> <span class="pre">base()</span> <span class="pre">const;</span></tt></p>
<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">Returns:</th><td class="field-body"><tt class="docutils literal"><span class="pre">m_order</span></tt></td>
</tr>
</tbody>
</table>
<pre class="literal-block">
template &lt;class ElementIterator, class IndexIterator&gt;
permutation_iterator&lt;ElementIterator, IndexIterator&gt;
make_permutation_iterator(ElementIterator e, IndexIterator i);
</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">Returns:</th><td class="field-body"><tt class="docutils literal"><span class="pre">permutation_iterator&lt;ElementIterator,</span> <span class="pre">IndexIterator&gt;(e,</span> <span class="pre">i)</span></tt></td>
</tr>
</tbody>
</table>
</div>
</div>
<div class="section" id="example">
<h1><a class="toc-backref" href="#id7">Example</a></h1>
<!-- Copyright David Abrahams 2006. Distributed under the Boost -->
<!-- Software License, Version 1.0. (See accompanying -->
<!-- file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -->
<pre class="literal-block">
using namespace boost;
int i = 0;

typedef std::vector&lt; int &gt; element_range_type;
typedef std::list&lt; int &gt; index_type;

static const int element_range_size = 10;
static const int index_size = 4;

element_range_type elements( element_range_size );
for(element_range_type::iterator el_it = elements.begin() ; el_it != elements.end() ; ++el_it)
  *el_it = std::distance(elements.begin(), el_it);

index_type indices( index_size );
for(index_type::iterator i_it = indices.begin() ; i_it != indices.end() ; ++i_it )
  *i_it = element_range_size - index_size + std::distance(indices.begin(), i_it);
std::reverse( indices.begin(), indices.end() );

typedef permutation_iterator&lt; element_range_type::iterator, index_type::iterator &gt; permutation_type;
permutation_type begin = make_permutation_iterator( elements.begin(), indices.begin() );
permutation_type it = begin;
permutation_type end = make_permutation_iterator( elements.begin(), indices.end() );

std::cout &lt;&lt; &quot;The original range is : &quot;;
std::copy( elements.begin(), elements.end(), std::ostream_iterator&lt; int &gt;( std::cout, &quot; &quot; ) );
std::cout &lt;&lt; &quot;\n&quot;;

std::cout &lt;&lt; &quot;The reindexing scheme is : &quot;;
std::copy( indices.begin(), indices.end(), std::ostream_iterator&lt; int &gt;( std::cout, &quot; &quot; ) );
std::cout &lt;&lt; &quot;\n&quot;;

std::cout &lt;&lt; &quot;The permutated range is : &quot;;
std::copy( begin, end, std::ostream_iterator&lt; int &gt;( std::cout, &quot; &quot; ) );
std::cout &lt;&lt; &quot;\n&quot;;

std::cout &lt;&lt; &quot;Elements at even indices in the permutation : &quot;;
it = begin;
for(i = 0; i &lt; index_size / 2 ; ++i, it+=2 ) std::cout &lt;&lt; *it &lt;&lt; &quot; &quot;;
std::cout &lt;&lt; &quot;\n&quot;;

std::cout &lt;&lt; &quot;Permutation backwards : &quot;;
it = begin + (index_size);
assert( it != begin );
for( ; it-- != begin ; ) std::cout &lt;&lt; *it &lt;&lt; &quot; &quot;;
std::cout &lt;&lt; &quot;\n&quot;;

std::cout &lt;&lt; &quot;Iterate backward with stride 2 : &quot;;
it = begin + (index_size - 1);
for(i = 0 ; i &lt; index_size / 2 ; ++i, it-=2 ) std::cout &lt;&lt; *it &lt;&lt; &quot; &quot;;
std::cout &lt;&lt; &quot;\n&quot;;
</pre>
<p>The output is:</p>
<pre class="literal-block">
The original range is : 0 1 2 3 4 5 6 7 8 9
The reindexing scheme is : 9 8 7 6
The permutated range is : 9 8 7 6
Elements at even indices in the permutation : 9 7
Permutation backwards : 6 7 8 9
Iterate backward with stride 2 : 6 8
</pre>
<p>The source code for this example can be found <a class="reference external" href="../example/permutation_iter_example.cpp">here</a>.</p>
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