blob: 74dd5ad9b99d185bbcb4f985eae22c483ac5fbdb [file] [log] [blame]
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Semi-Intrusive unordered associative containers: unordered_set, unordered_multiset</title>
<link rel="stylesheet" href="../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../index.html" title="The Boost C++ Libraries BoostBook Documentation Subset">
<link rel="up" href="../intrusive.html" title="Chapter&#160;10.&#160;Boost.Intrusive">
<link rel="prev" href="set_multiset.html" title="Intrusive associative containers: set, multiset, rbtree">
<link rel="next" href="splay_set_multiset.html" title="Intrusive splay tree based associative containers: splay_set, splay_multiset and , splay_tree">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../boost.png"></td>
<td align="center"><a href="../../../index.html">Home</a></td>
<td align="center"><a href="../../../libs/libraries.htm">Libraries</a></td>
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
<td align="center"><a href="../../../more/index.htm">More</a></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="set_multiset.html"><img src="../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../intrusive.html"><img src="../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="splay_set_multiset.html"><img src="../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="intrusive.unordered_set_unordered_multiset"></a><a class="link" href="unordered_set_unordered_multiset.html" title="Semi-Intrusive unordered associative containers: unordered_set, unordered_multiset">Semi-Intrusive
unordered associative containers: unordered_set, unordered_multiset</a>
</h2></div></div></div>
<div class="toc"><dl>
<dt><span class="section"><a href="unordered_set_unordered_multiset.html#intrusive.unordered_set_unordered_multiset.unordered_set_unordered_multiset_performance">unordered_set
and unordered_multiset performance notes</a></span></dt>
<dt><span class="section"><a href="unordered_set_unordered_multiset.html#intrusive.unordered_set_unordered_multiset.unordered_set_unordered_multiset_hooks">unordered_set
and unordered_multiset hooks</a></span></dt>
<dt><span class="section"><a href="unordered_set_unordered_multiset.html#intrusive.unordered_set_unordered_multiset.unordered_set_unordered_multiset_containers">unordered_set
and unordered_multiset containers</a></span></dt>
<dt><span class="section"><a href="unordered_set_unordered_multiset.html#intrusive.unordered_set_unordered_multiset.unordered_set_unordered_multiset_example">Example</a></span></dt>
<dt><span class="section"><a href="unordered_set_unordered_multiset.html#intrusive.unordered_set_unordered_multiset.custom_bucket_traits">Custom
bucket traits</a></span></dt>
</dl></div>
<p>
<span class="bold"><strong>Boost.Intrusive</strong></span> also offers hashed containers
that can be very useful to implement fast-lookup containers. These containers
(<code class="computeroutput"><a class="link" href="../boost/intrusive/unordered_set.html" title="Class template unordered_set">unordered_set</a></code>
and <code class="computeroutput"><a class="link" href="../boost/intrusive/unordered_multiset.html" title="Class template unordered_multiset">unordered_multiset</a></code>)
are semi-intrusive containers: they need additional memory apart from the hook
stored in the <code class="computeroutput"><span class="identifier">value_type</span></code>. This
additional memory must be passed in the constructor of the container.
</p>
<p>
Unlike C++ TR1 unordered associative containers (which are also hashed containers),
the contents of these semi-intrusive containers are not rehashed to maintain
a load factor: that would require memory management and intrusive containers
don't implement any memory management at all. However, the user can request
an explicit rehashing passing a new bucket array. This also offers an additional
guarantee over TR1 unordered associative containers: <span class="bold"><strong>iterators
are not invalidated when inserting an element</strong></span> in the container.
</p>
<p>
As with TR1 unordered associative containers, rehashing invalidates iterators,
changes ordering between elements and changes which buckets elements appear
in, but does not invalidate pointers or references to elements.
</p>
<p>
Apart from expected hash and equality function objects, <span class="bold"><strong>Boost.Intrusive</strong></span>
unordered associative containers' constructors take an argument specifying
an auxiliary bucket vector to be used by the container.
</p>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="intrusive.unordered_set_unordered_multiset.unordered_set_unordered_multiset_performance"></a><a class="link" href="unordered_set_unordered_multiset.html#intrusive.unordered_set_unordered_multiset.unordered_set_unordered_multiset_performance" title="unordered_set and unordered_multiset performance notes">unordered_set
and unordered_multiset performance notes</a>
</h3></div></div></div>
<p>
The size overhead for a hashed container is moderate: 1 pointer per value
plus a bucket array per container. The size of an element of the bucket array
is usually one pointer. To obtain a good performance hashed container, the
bucket length is usually the same as the number of elements that the container
contains, so a well-balanced hashed container (<code class="computeroutput"><span class="identifier">bucket_count</span><span class="special">()</span></code> is equal to <code class="computeroutput"><span class="identifier">size</span><span class="special">()</span></code> ) will have an equivalent overhead of two
pointers per element.
</p>
<p>
An empty, non constant-time size <code class="computeroutput"><a class="link" href="../boost/intrusive/unordered_set.html" title="Class template unordered_set">unordered_set</a></code>
or <code class="computeroutput"><a class="link" href="../boost/intrusive/unordered_multiset.html" title="Class template unordered_multiset">unordered_multiset</a></code>
has also the size of <code class="computeroutput"><span class="identifier">bucket_count</span><span class="special">()</span></code> pointers.
</p>
<p>
Insertions, erasures, and searches, have amortized constant-time complexity
in hashed containers. However, some worst-case guarantees are linear. See
<code class="computeroutput"><a class="link" href="../boost/intrusive/unordered_set.html" title="Class template unordered_set">unordered_set</a></code>
or <code class="computeroutput"><a class="link" href="../boost/intrusive/unordered_multiset.html" title="Class template unordered_multiset">unordered_multiset</a></code>
for complexity guarantees of each operation.
</p>
<p>
<span class="bold"><strong>Be careful with non constant-time size hashed containers</strong></span>:
some operations, like <code class="computeroutput"><span class="identifier">empty</span><span class="special">()</span></code>, have linear complexity, unlike other
<span class="bold"><strong>Boost.Intrusive</strong></span> containers.
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="intrusive.unordered_set_unordered_multiset.unordered_set_unordered_multiset_hooks"></a><a class="link" href="unordered_set_unordered_multiset.html#intrusive.unordered_set_unordered_multiset.unordered_set_unordered_multiset_hooks" title="unordered_set and unordered_multiset hooks">unordered_set
and unordered_multiset hooks</a>
</h3></div></div></div>
<p>
<code class="computeroutput"><a class="link" href="../boost/intrusive/unordered_set.html" title="Class template unordered_set">unordered_set</a></code>
and <code class="computeroutput"><a class="link" href="../boost/intrusive/unordered_multiset.html" title="Class template unordered_multiset">unordered_multiset</a></code>
share the same hooks. This is an advantage, because the same user type can
be inserted first in a <code class="computeroutput"><a class="link" href="../boost/intrusive/unordered_multiset.html" title="Class template unordered_multiset">unordered_multiset</a></code>
and after that in <code class="computeroutput"><a class="link" href="../boost/intrusive/unordered_set.html" title="Class template unordered_set">unordered_set</a></code>
without changing the definition of the user class.
</p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="special">...</span><span class="identifier">Options</span><span class="special">&gt;</span>
<span class="keyword">class</span> <span class="identifier">unordered_set_base_hook</span><span class="special">;</span>
</pre>
<div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
<code class="computeroutput"><a class="link" href="../boost/intrusive/unordered_set_base_hook.html" title="Class template unordered_set_base_hook">unordered_set_base_hook</a></code>:
the user class derives publicly from <code class="computeroutput"><a class="link" href="../boost/intrusive/unordered_set_base_hook.html" title="Class template unordered_set_base_hook">unordered_set_base_hook</a></code>
to make it <code class="computeroutput"><a class="link" href="../boost/intrusive/unordered_set.html" title="Class template unordered_set">unordered_set</a></code>/<code class="computeroutput"><a class="link" href="../boost/intrusive/unordered_multiset.html" title="Class template unordered_multiset">unordered_multiset</a></code>-compatible.
</li></ul></div>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="special">...</span><span class="identifier">Options</span><span class="special">&gt;</span>
<span class="keyword">class</span> <span class="identifier">unordered_set_member_hook</span><span class="special">;</span>
</pre>
<div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
<code class="computeroutput"><a class="link" href="../boost/intrusive/unordered_set_member_hook.html" title="Class template unordered_set_member_hook">unordered_set_member_hook</a></code>:
the user class contains a public <code class="computeroutput"><a class="link" href="../boost/intrusive/unordered_set_member_hook.html" title="Class template unordered_set_member_hook">unordered_set_member_hook</a></code>
to make it <code class="computeroutput"><a class="link" href="../boost/intrusive/unordered_set.html" title="Class template unordered_set">unordered_set</a></code>/<code class="computeroutput"><a class="link" href="../boost/intrusive/unordered_multiset.html" title="Class template unordered_multiset">unordered_multiset</a></code>-compatible.
</li></ul></div>
<p>
<code class="computeroutput"><a class="link" href="../boost/intrusive/unordered_set_base_hook.html" title="Class template unordered_set_base_hook">unordered_set_base_hook</a></code>
and <code class="computeroutput"><a class="link" href="../boost/intrusive/unordered_set_member_hook.html" title="Class template unordered_set_member_hook">unordered_set_member_hook</a></code>
receive the same options explained in the section <a class="link" href="usage.html" title="How to use Boost.Intrusive">How
to use Boost.Intrusive</a>:
</p>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
<span class="bold"><strong><code class="computeroutput"><span class="identifier">tag</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Tag</span><span class="special">&gt;</span></code></strong></span>
(for base hooks only): This argument serves as a tag, so you can derive
from more than one base hook. Default: <code class="computeroutput"><span class="identifier">tag</span><span class="special">&lt;</span><span class="identifier">default_tag</span><span class="special">&gt;</span></code>.
</li>
<li class="listitem">
<span class="bold"><strong><code class="computeroutput"><span class="identifier">link_mode</span><span class="special">&lt;</span><span class="identifier">link_mode_type</span>
<span class="identifier">LinkMode</span><span class="special">&gt;</span></code></strong></span>:
The linking policy. Default: <code class="computeroutput"><span class="identifier">link_mode</span><span class="special">&lt;</span><span class="identifier">safe_link</span><span class="special">&gt;</span></code>.
</li>
<li class="listitem">
<span class="bold"><strong><code class="computeroutput"><span class="identifier">void_pointer</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">VoidPointer</span><span class="special">&gt;</span></code></strong></span>:
The pointer type to be used internally in the hook and propagated to
the container. Default: <code class="computeroutput"><span class="identifier">void_pointer</span><span class="special">&lt;</span><span class="keyword">void</span><span class="special">*&gt;</span></code>.
</li>
</ul></div>
<p>
Apart from them, these hooks offer additional options:
</p>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
<span class="bold"><strong><code class="computeroutput"><span class="identifier">store_hash</span><span class="special">&lt;</span><span class="keyword">bool</span> <span class="identifier">Enabled</span><span class="special">&gt;</span></code></strong></span>:
This option reserves additional space in the hook to store the hash value
of the object once it's introduced in the container. When this option
is used, the unordered container will store the calculated hash value
in the hook and rehashing operations won't need to recalculate the hash
of the value. This option will improve the performance of unordered containers
when rehashing is frequent or hashing the value is a slow operation.
Default: <code class="computeroutput"><span class="identifier">store_hash</span><span class="special">&lt;</span><span class="keyword">false</span><span class="special">&gt;</span></code>.
</li>
<li class="listitem">
<span class="bold"><strong><code class="computeroutput"><span class="identifier">optimize_multikey</span><span class="special">&lt;</span><span class="keyword">bool</span> <span class="identifier">Enabled</span><span class="special">&gt;</span></code></strong></span>:
This option reserves additional space in the hook that will be used to
group equal elements in unordered multisets, improving significantly
the performance when many equal values are inserted in these containers.
Default: <code class="computeroutput"><span class="identifier">optimize_multikey</span><span class="special">&lt;</span><span class="keyword">false</span><span class="special">&gt;</span></code>.
</li>
</ul></div>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="intrusive.unordered_set_unordered_multiset.unordered_set_unordered_multiset_containers"></a><a class="link" href="unordered_set_unordered_multiset.html#intrusive.unordered_set_unordered_multiset.unordered_set_unordered_multiset_containers" title="unordered_set and unordered_multiset containers">unordered_set
and unordered_multiset containers</a>
</h3></div></div></div>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="special">...</span><span class="identifier">Options</span><span class="special">&gt;</span>
<span class="keyword">class</span> <span class="identifier">unordered_set</span><span class="special">;</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="special">...</span><span class="identifier">Options</span><span class="special">&gt;</span>
<span class="keyword">class</span> <span class="identifier">unordered_multiset</span><span class="special">;</span>
</pre>
<p>
As mentioned, unordered containers need an auxiliary array to work. <span class="bold"><strong>Boost.Intrusive</strong></span> unordered containers receive this
auxiliary array packed in a type called <code class="computeroutput"><span class="identifier">bucket_traits</span></code>
(which can be also customized by a container option). All unordered containers
receive a <code class="computeroutput"><span class="identifier">bucket_traits</span></code> object
in their constructors. The default <code class="computeroutput"><span class="identifier">bucket_traits</span></code>
class is initialized with a pointer to an array of buckets and its size:
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">intrusive</span><span class="special">/</span><span class="identifier">unordered_set</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">intrusive</span><span class="special">;</span>
<span class="keyword">struct</span> <span class="identifier">MyClass</span> <span class="special">:</span> <span class="keyword">public</span> <span class="identifier">unordered_set_base_hook</span><span class="special">&lt;&gt;</span>
<span class="special">{};</span>
<span class="keyword">typedef</span> <span class="identifier">unordered_set</span><span class="special">&lt;</span><span class="identifier">MyClass</span><span class="special">&gt;::</span><span class="identifier">bucket_type</span> <span class="identifier">bucket_type</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">unordered_set</span><span class="special">&lt;</span><span class="identifier">MyClass</span><span class="special">&gt;::</span><span class="identifier">bucket_traits</span> <span class="identifier">bucket_traits</span><span class="special">;</span>
<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
<span class="special">{</span>
<span class="identifier">bucket_type</span> <span class="identifier">buckets</span><span class="special">[</span><span class="number">100</span><span class="special">];</span>
<span class="identifier">unordered_set</span><span class="special">&lt;</span><span class="identifier">MyClass</span><span class="special">&gt;</span> <span class="identifier">uset</span><span class="special">(</span><span class="identifier">bucket_traits</span><span class="special">(</span><span class="identifier">buckets</span><span class="special">,</span> <span class="number">100</span><span class="special">));</span>
<span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
<span class="special">}</span>
</pre>
<p>
Each hashed container needs <span class="bold"><strong>its own bucket traits</strong></span>,
that is, <span class="bold"><strong>its own bucket vector</strong></span>. Two hashed
containers <span class="bold"><strong>can't</strong></span> share the same <code class="computeroutput"><span class="identifier">bucket_type</span></code> elements. The bucket array
<span class="bold"><strong>must</strong></span> be destroyed <span class="bold"><strong>after</strong></span>
the container using it is destroyed, otherwise, the result is undefined.
</p>
<p>
<code class="computeroutput"><a class="link" href="../boost/intrusive/unordered_set.html" title="Class template unordered_set">unordered_set</a></code>
and <code class="computeroutput"><a class="link" href="../boost/intrusive/unordered_multiset.html" title="Class template unordered_multiset">unordered_multiset</a></code>
receive the same options explained in the section <a class="link" href="usage.html" title="How to use Boost.Intrusive">How
to use Boost.Intrusive</a>:
</p>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
<span class="bold"><strong><code class="computeroutput"><span class="identifier">base_hook</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Hook</span><span class="special">&gt;</span></code></strong></span>
/ <span class="bold"><strong><code class="computeroutput"><span class="identifier">member_hook</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Hook</span><span class="special">,</span> <span class="identifier">Hook</span> <span class="identifier">T</span><span class="special">::*</span> <span class="identifier">PtrToMember</span><span class="special">&gt;</span></code></strong></span>
/ <span class="bold"><strong><code class="computeroutput"><span class="identifier">value_traits</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">ValueTraits</span><span class="special">&gt;</span></code></strong></span>:
To specify the hook type or value traits used to configure the container.
(To learn about value traits go to the section <a class="link" href="value_traits.html" title="Containers with custom ValueTraits">Containers
with custom ValueTraits</a>.)
</li>
<li class="listitem">
<span class="bold"><strong><code class="computeroutput"><span class="identifier">constant_time_size</span><span class="special">&lt;</span><span class="keyword">bool</span> <span class="identifier">Enabled</span><span class="special">&gt;</span></code></strong></span>:
To activate the constant-time <code class="computeroutput"><span class="identifier">size</span><span class="special">()</span></code> operation. Default: <code class="computeroutput"><span class="identifier">constant_time_size</span><span class="special">&lt;</span><span class="keyword">true</span><span class="special">&gt;</span></code>
</li>
<li class="listitem">
<span class="bold"><strong><code class="computeroutput"><span class="identifier">size_type</span><span class="special">&lt;</span><span class="keyword">bool</span> <span class="identifier">Enabled</span><span class="special">&gt;</span></code></strong></span>:
To specify the type that will be used to store the size of the container.
Default: <code class="computeroutput"><span class="identifier">size_type</span><span class="special">&lt;</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span><span class="special">&gt;</span></code>
</li>
</ul></div>
<p>
And they also can receive additional options:
</p>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
<span class="bold"><strong><code class="computeroutput"><span class="identifier">equal</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Equal</span><span class="special">&gt;</span></code></strong></span>:
Equality function for the objects to be inserted in containers. Default:
<code class="computeroutput"><span class="identifier">equal</span><span class="special">&lt;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">equal_to</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&gt;</span></code>
</li>
<li class="listitem">
<span class="bold"><strong><code class="computeroutput"><span class="identifier">hash</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Hash</span><span class="special">&gt;</span></code></strong></span>:
Hash function to be used in the container. Default: <code class="computeroutput"><span class="identifier">hash</span><span class="special">&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">hash</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&gt;</span></code>
</li>
<li class="listitem">
<span class="bold"><strong><code class="computeroutput"><span class="identifier">bucket_traits</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">BucketTraits</span><span class="special">&gt;</span></code></strong></span>:
A type that wraps the bucket vector to be used by the unordered container.
Default: a type initialized by the address and size of a bucket array
and stores both variables internally.
</li>
<li class="listitem">
<span class="bold"><strong><code class="computeroutput"><span class="identifier">power_2_buckets</span><span class="special">&lt;</span><span class="keyword">bool</span> <span class="identifier">Enabled</span><span class="special">&gt;</span></code></strong></span>:
The user guarantees that only bucket arrays with power of two length
will be used. The container will then use masks instead of modulo operations
to obtain the bucket number from the hash value. Masks are faster than
modulo operations and for some applications modulo operations can impose
a considerable overhead. In debug mode an assertion will be raised if
the user provides a bucket length that is not power of two. Default:
<code class="computeroutput"><span class="identifier">power_2_buckets</span><span class="special">&lt;</span><span class="keyword">false</span><span class="special">&gt;</span></code>.
</li>
<li class="listitem">
<span class="bold"><strong><code class="computeroutput"><span class="identifier">cache_begin</span><span class="special">&lt;</span><span class="keyword">bool</span> <span class="identifier">Enabled</span><span class="special">&gt;</span></code></strong></span>:
<span class="bold"><strong>Note: this option is not compatible with <code class="computeroutput"><span class="identifier">auto_unlink</span></code> hooks</strong></span>. Due to
its internal structure, finding the first element of an unordered container
(<code class="computeroutput"><span class="identifier">begin</span><span class="special">()</span></code>
operation) is amortized constant-time. It's possible to speed up <code class="computeroutput"><span class="identifier">begin</span><span class="special">()</span></code>
and other operations related to it (like <code class="computeroutput"><span class="identifier">clear</span><span class="special">()</span></code>) if the container caches internally
the position of the first element. This imposes the overhead of one pointer
to the size of the container. Default: <code class="computeroutput"><span class="identifier">cache_begin</span><span class="special">&lt;</span><span class="keyword">false</span><span class="special">&gt;</span></code>.
</li>
<li class="listitem">
<span class="bold"><strong><code class="computeroutput"><span class="identifier">compare_hash</span><span class="special">&lt;</span><span class="keyword">bool</span> <span class="identifier">Enabled</span><span class="special">&gt;</span></code></strong></span>:
<span class="bold"><strong>Note: this option requires <code class="computeroutput"><span class="identifier">store_hash</span><span class="special">&lt;</span><span class="keyword">true</span><span class="special">&gt;</span></code> option in the hook</strong></span>. When
the comparison function is expensive, (e.g. strings with a long common
predicate) sometimes (specially when the load factor is high or we have
many equivalent elements in an <code class="computeroutput"><a class="link" href="../boost/intrusive/unordered_multiset.html" title="Class template unordered_multiset">unordered_multiset</a></code>
and no <code class="computeroutput"><span class="identifier">optimize_multikey</span><span class="special">&lt;&gt;</span></code> is activated in the hook) the
equality function is a performance problem. Two equal values must have
equal hashes, so comparing the hash values of two elements before using
the comparison functor can speed up some implementations.
</li>
<li class="listitem">
<span class="bold"><strong><code class="computeroutput"><span class="identifier">incremental</span><span class="special">&lt;</span><span class="keyword">bool</span> <span class="identifier">Enabled</span><span class="special">&gt;</span></code></strong></span>:
Activates incremental hashing (also known as Linear Hashing). This option
implies <code class="computeroutput"><span class="identifier">power_2_buckets</span><span class="special">&lt;</span><span class="keyword">true</span><span class="special">&gt;</span></code> and the container will require power
of two buckets. For more information on incremental hashing, see <a href="http://en.wikipedia.org/wiki/Linear_hashing" target="_top"><code class="computeroutput"><span class="identifier">Linear</span>
<span class="identifier">hash</span></code> on Wikipedia</a> Default:
<code class="computeroutput"><span class="identifier">incremental</span><span class="special">&lt;</span><span class="keyword">false</span><span class="special">&gt;</span></code>
</li>
</ul></div>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="intrusive.unordered_set_unordered_multiset.unordered_set_unordered_multiset_example"></a><a class="link" href="unordered_set_unordered_multiset.html#intrusive.unordered_set_unordered_multiset.unordered_set_unordered_multiset_example" title="Example">Example</a>
</h3></div></div></div>
<p>
Now let's see a small example using both hooks and both containers:
</p>
<p>
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">intrusive</span><span class="special">/</span><span class="identifier">unordered_set</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">vector</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">algorithm</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">functional</span><span class="special">/</span><span class="identifier">hash</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">intrusive</span><span class="special">;</span>
<span class="keyword">class</span> <span class="identifier">MyClass</span> <span class="special">:</span> <span class="keyword">public</span> <span class="identifier">unordered_set_base_hook</span><span class="special">&lt;&gt;</span>
<span class="special">{</span> <span class="comment">//This is a derivation hook
</span> <span class="keyword">int</span> <span class="identifier">int_</span><span class="special">;</span>
<span class="keyword">public</span><span class="special">:</span>
<span class="identifier">unordered_set_member_hook</span><span class="special">&lt;&gt;</span> <span class="identifier">member_hook_</span><span class="special">;</span> <span class="comment">//This is a member hook
</span>
<span class="identifier">MyClass</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">i</span><span class="special">)</span>
<span class="special">:</span> <span class="identifier">int_</span><span class="special">(</span><span class="identifier">i</span><span class="special">)</span>
<span class="special">{}</span>
<span class="keyword">friend</span> <span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">==</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">MyClass</span> <span class="special">&amp;</span><span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">MyClass</span> <span class="special">&amp;</span><span class="identifier">b</span><span class="special">)</span>
<span class="special">{</span> <span class="keyword">return</span> <span class="identifier">a</span><span class="special">.</span><span class="identifier">int_</span> <span class="special">==</span> <span class="identifier">b</span><span class="special">.</span><span class="identifier">int_</span><span class="special">;</span> <span class="special">}</span>
<span class="keyword">friend</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">hash_value</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">MyClass</span> <span class="special">&amp;</span><span class="identifier">value</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">size_t</span><span class="special">(</span><span class="identifier">value</span><span class="special">.</span><span class="identifier">int_</span><span class="special">);</span> <span class="special">}</span>
<span class="special">};</span>
<span class="comment">//Define an unordered_set that will store MyClass objects using the base hook
</span><span class="keyword">typedef</span> <span class="identifier">unordered_set</span><span class="special">&lt;</span><span class="identifier">MyClass</span><span class="special">&gt;</span> <span class="identifier">BaseSet</span><span class="special">;</span>
<span class="comment">//Define an unordered_multiset that will store MyClass using the member hook
</span><span class="keyword">typedef</span> <span class="identifier">member_hook</span><span class="special">&lt;</span><span class="identifier">MyClass</span><span class="special">,</span> <span class="identifier">unordered_set_member_hook</span><span class="special">&lt;&gt;,</span> <span class="special">&amp;</span><span class="identifier">MyClass</span><span class="special">::</span><span class="identifier">member_hook_</span><span class="special">&gt;</span>
<span class="identifier">MemberOption</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">unordered_multiset</span><span class="special">&lt;</span> <span class="identifier">MyClass</span><span class="special">,</span> <span class="identifier">MemberOption</span><span class="special">&gt;</span> <span class="identifier">MemberMultiSet</span><span class="special">;</span>
<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
<span class="special">{</span>
<span class="keyword">typedef</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="identifier">MyClass</span><span class="special">&gt;::</span><span class="identifier">iterator</span> <span class="identifier">VectIt</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="identifier">MyClass</span><span class="special">&gt;::</span><span class="identifier">reverse_iterator</span> <span class="identifier">VectRit</span><span class="special">;</span>
<span class="comment">//Create a vector with 100 different MyClass objects
</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="identifier">MyClass</span><span class="special">&gt;</span> <span class="identifier">values</span><span class="special">;</span>
<span class="keyword">for</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special">&lt;</span> <span class="number">100</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> <span class="identifier">values</span><span class="special">.</span><span class="identifier">push_back</span><span class="special">(</span><span class="identifier">MyClass</span><span class="special">(</span><span class="identifier">i</span><span class="special">));</span>
<span class="comment">//Create a copy of the vector
</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="identifier">MyClass</span><span class="special">&gt;</span> <span class="identifier">values2</span><span class="special">(</span><span class="identifier">values</span><span class="special">);</span>
<span class="comment">//Create a bucket array for base_set
</span> <span class="identifier">BaseSet</span><span class="special">::</span><span class="identifier">bucket_type</span> <span class="identifier">base_buckets</span><span class="special">[</span><span class="number">100</span><span class="special">];</span>
<span class="comment">//Create a bucket array for member_multi_set
</span> <span class="identifier">MemberMultiSet</span><span class="special">::</span><span class="identifier">bucket_type</span> <span class="identifier">member_buckets</span><span class="special">[</span><span class="number">200</span><span class="special">];</span>
<span class="comment">//Create unordered containers taking buckets as arguments
</span> <span class="identifier">BaseSet</span> <span class="identifier">base_set</span><span class="special">(</span><span class="identifier">BaseSet</span><span class="special">::</span><span class="identifier">bucket_traits</span><span class="special">(</span><span class="identifier">base_buckets</span><span class="special">,</span> <span class="number">100</span><span class="special">));</span>
<span class="identifier">MemberMultiSet</span> <span class="identifier">member_multi_set</span>
<span class="special">(</span><span class="identifier">MemberMultiSet</span><span class="special">::</span><span class="identifier">bucket_traits</span><span class="special">(</span><span class="identifier">member_buckets</span><span class="special">,</span> <span class="number">200</span><span class="special">));</span>
<span class="comment">//Now insert values's elements in the unordered_set
</span> <span class="keyword">for</span><span class="special">(</span><span class="identifier">VectIt</span> <span class="identifier">it</span><span class="special">(</span><span class="identifier">values</span><span class="special">.</span><span class="identifier">begin</span><span class="special">()),</span> <span class="identifier">itend</span><span class="special">(</span><span class="identifier">values</span><span class="special">.</span><span class="identifier">end</span><span class="special">());</span> <span class="identifier">it</span> <span class="special">!=</span> <span class="identifier">itend</span><span class="special">;</span> <span class="special">++</span><span class="identifier">it</span><span class="special">)</span>
<span class="identifier">base_set</span><span class="special">.</span><span class="identifier">insert</span><span class="special">(*</span><span class="identifier">it</span><span class="special">);</span>
<span class="comment">//Now insert values's and values2's elements in the unordered_multiset
</span> <span class="keyword">for</span><span class="special">(</span><span class="identifier">VectIt</span> <span class="identifier">it</span><span class="special">(</span><span class="identifier">values</span><span class="special">.</span><span class="identifier">begin</span><span class="special">()),</span> <span class="identifier">itend</span><span class="special">(</span><span class="identifier">values</span><span class="special">.</span><span class="identifier">end</span><span class="special">()),</span>
<span class="identifier">it2</span><span class="special">(</span><span class="identifier">values2</span><span class="special">.</span><span class="identifier">begin</span><span class="special">()),</span><span class="identifier">itend2</span><span class="special">(</span><span class="identifier">values2</span><span class="special">.</span><span class="identifier">end</span><span class="special">())</span>
<span class="special">;</span> <span class="identifier">it</span> <span class="special">!=</span> <span class="identifier">itend</span><span class="special">;</span> <span class="special">++</span><span class="identifier">it</span><span class="special">,</span> <span class="special">++</span><span class="identifier">it2</span><span class="special">){</span>
<span class="identifier">member_multi_set</span><span class="special">.</span><span class="identifier">insert</span><span class="special">(*</span><span class="identifier">it</span><span class="special">);</span>
<span class="identifier">member_multi_set</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="special">}</span>
<span class="comment">//Now find every element
</span> <span class="special">{</span>
<span class="identifier">VectIt</span> <span class="identifier">it</span><span class="special">(</span><span class="identifier">values</span><span class="special">.</span><span class="identifier">begin</span><span class="special">()),</span> <span class="identifier">itend</span><span class="special">(</span><span class="identifier">values</span><span class="special">.</span><span class="identifier">end</span><span class="special">());</span>
<span class="keyword">for</span><span class="special">(;</span> <span class="identifier">it</span> <span class="special">!=</span> <span class="identifier">itend</span><span class="special">;</span> <span class="special">++</span><span class="identifier">it</span><span class="special">){</span>
<span class="comment">//base_set should contain one element for each key
</span> <span class="keyword">if</span><span class="special">(</span><span class="identifier">base_set</span><span class="special">.</span><span class="identifier">count</span><span class="special">(*</span><span class="identifier">it</span><span class="special">)</span> <span class="special">!=</span> <span class="number">1</span><span class="special">)</span> <span class="keyword">return</span> <span class="number">1</span><span class="special">;</span>
<span class="comment">//member_multi_set should contain two elements for each key
</span> <span class="keyword">if</span><span class="special">(</span><span class="identifier">member_multi_set</span><span class="special">.</span><span class="identifier">count</span><span class="special">(*</span><span class="identifier">it</span><span class="special">)</span> <span class="special">!=</span> <span class="number">2</span><span class="special">)</span> <span class="keyword">return</span> <span class="number">1</span><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span>
<span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
<span class="special">}</span>
</pre>
<p>
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="intrusive.unordered_set_unordered_multiset.custom_bucket_traits"></a><a class="link" href="unordered_set_unordered_multiset.html#intrusive.unordered_set_unordered_multiset.custom_bucket_traits" title="Custom bucket traits">Custom
bucket traits</a>
</h3></div></div></div>
<p>
Instead of using the default <code class="computeroutput"><span class="identifier">bucket_traits</span></code>
class to store the bucket array, a user can define his own class to store
the bucket array using the <span class="bold"><strong><span class="emphasis"><em>bucket_traits&lt;&gt;</em></span></strong></span>
option. A user-defined bucket-traits must fulfill the following interface:
</p>
<pre class="programlisting"><span class="keyword">class</span> <span class="identifier">my_bucket_traits</span>
<span class="special">{</span>
<span class="identifier">bucket_ptr</span> <span class="identifier">bucket_begin</span><span class="special">();</span>
<span class="identifier">const_bucket_ptr</span> <span class="identifier">bucket_begin</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">bucket_count</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">};</span>
</pre>
<p>
The following bucket traits just stores a pointer to the bucket array but
the size is a compile-time constant. Note the use of the auxiliary <code class="computeroutput">unordered_bucket</code> and
<code class="computeroutput">unordered_bucket_ptr</code>
utilities to obtain the type of the bucket and its pointer before defining
the unordered container:
</p>
<p>
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">intrusive</span><span class="special">/</span><span class="identifier">unordered_set</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">functional</span><span class="special">/</span><span class="identifier">hash</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">vector</span><span class="special">&gt;</span>
<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">intrusive</span><span class="special">;</span>
<span class="comment">//A class to be inserted in an unordered_set
</span><span class="keyword">class</span> <span class="identifier">MyClass</span> <span class="special">:</span> <span class="keyword">public</span> <span class="identifier">unordered_set_base_hook</span><span class="special">&lt;&gt;</span>
<span class="special">{</span>
<span class="keyword">int</span> <span class="identifier">int_</span><span class="special">;</span>
<span class="keyword">public</span><span class="special">:</span>
<span class="identifier">MyClass</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">)</span> <span class="special">:</span> <span class="identifier">int_</span><span class="special">(</span><span class="identifier">i</span><span class="special">)</span>
<span class="special">{}</span>
<span class="keyword">friend</span> <span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">==(</span><span class="keyword">const</span> <span class="identifier">MyClass</span> <span class="special">&amp;</span><span class="identifier">l</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">MyClass</span> <span class="special">&amp;</span><span class="identifier">r</span><span class="special">)</span>
<span class="special">{</span> <span class="keyword">return</span> <span class="identifier">l</span><span class="special">.</span><span class="identifier">int_</span> <span class="special">==</span> <span class="identifier">r</span><span class="special">.</span><span class="identifier">int_</span><span class="special">;</span> <span class="special">}</span>
<span class="keyword">friend</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">hash_value</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">MyClass</span> <span class="special">&amp;</span><span class="identifier">v</span><span class="special">)</span>
<span class="special">{</span> <span class="keyword">return</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">hash_value</span><span class="special">(</span><span class="identifier">v</span><span class="special">.</span><span class="identifier">int_</span><span class="special">);</span> <span class="special">}</span>
<span class="special">};</span>
<span class="comment">//Define the base hook option
</span><span class="keyword">typedef</span> <span class="identifier">base_hook</span><span class="special">&lt;</span> <span class="identifier">unordered_set_base_hook</span><span class="special">&lt;&gt;</span> <span class="special">&gt;</span> <span class="identifier">BaseHookOption</span><span class="special">;</span>
<span class="comment">//Obtain the types of the bucket and the bucket pointer
</span><span class="keyword">typedef</span> <span class="identifier">unordered_bucket</span><span class="special">&lt;</span><span class="identifier">BaseHookOption</span><span class="special">&gt;::</span><span class="identifier">type</span> <span class="identifier">BucketType</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">unordered_bucket_ptr</span><span class="special">&lt;</span><span class="identifier">BaseHookOption</span><span class="special">&gt;::</span><span class="identifier">type</span> <span class="identifier">BucketPtr</span><span class="special">;</span>
<span class="comment">//The custom bucket traits.
</span><span class="keyword">class</span> <span class="identifier">custom_bucket_traits</span>
<span class="special">{</span>
<span class="keyword">public</span><span class="special">:</span>
<span class="keyword">static</span> <span class="keyword">const</span> <span class="keyword">int</span> <span class="identifier">NumBuckets</span> <span class="special">=</span> <span class="number">100</span><span class="special">;</span>
<span class="identifier">custom_bucket_traits</span><span class="special">(</span><span class="identifier">BucketPtr</span> <span class="identifier">buckets</span><span class="special">)</span>
<span class="special">:</span> <span class="identifier">buckets_</span><span class="special">(</span><span class="identifier">buckets</span><span class="special">)</span>
<span class="special">{}</span>
<span class="comment">//Functions to be implemented by custom bucket traits
</span> <span class="identifier">BucketPtr</span> <span class="identifier">bucket_begin</span><span class="special">()</span> <span class="keyword">const</span> <span class="special">{</span> <span class="keyword">return</span> <span class="identifier">buckets_</span><span class="special">;</span> <span class="special">}</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">bucket_count</span><span class="special">()</span> <span class="keyword">const</span> <span class="special">{</span> <span class="keyword">return</span> <span class="identifier">NumBuckets</span><span class="special">;}</span>
<span class="keyword">private</span><span class="special">:</span>
<span class="identifier">BucketPtr</span> <span class="identifier">buckets_</span><span class="special">;</span>
<span class="special">};</span>
<span class="comment">//Define the container using the custom bucket traits
</span><span class="keyword">typedef</span> <span class="identifier">unordered_set</span><span class="special">&lt;</span><span class="identifier">MyClass</span><span class="special">,</span> <span class="identifier">bucket_traits</span><span class="special">&lt;</span><span class="identifier">custom_bucket_traits</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">BucketTraitsUset</span><span class="special">;</span>
<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
<span class="special">{</span>
<span class="keyword">typedef</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="identifier">MyClass</span><span class="special">&gt;::</span><span class="identifier">iterator</span> <span class="identifier">VectIt</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="identifier">MyClass</span><span class="special">&gt;</span> <span class="identifier">values</span><span class="special">;</span>
<span class="comment">//Fill values
</span> <span class="keyword">for</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special">&lt;</span> <span class="number">100</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> <span class="identifier">values</span><span class="special">.</span><span class="identifier">push_back</span><span class="special">(</span><span class="identifier">MyClass</span><span class="special">(</span><span class="identifier">i</span><span class="special">));</span>
<span class="comment">//Now create the bucket array and the custom bucket traits object
</span> <span class="identifier">BucketType</span> <span class="identifier">buckets</span><span class="special">[</span><span class="identifier">custom_bucket_traits</span><span class="special">::</span><span class="identifier">NumBuckets</span><span class="special">];</span>
<span class="identifier">custom_bucket_traits</span> <span class="identifier">btraits</span><span class="special">(</span><span class="identifier">buckets</span><span class="special">);</span>
<span class="comment">//Now create the unordered set
</span> <span class="identifier">BucketTraitsUset</span> <span class="identifier">uset</span><span class="special">(</span><span class="identifier">btraits</span><span class="special">);</span>
<span class="comment">//Insert the values in the unordered set
</span> <span class="keyword">for</span><span class="special">(</span><span class="identifier">VectIt</span> <span class="identifier">it</span><span class="special">(</span><span class="identifier">values</span><span class="special">.</span><span class="identifier">begin</span><span class="special">()),</span> <span class="identifier">itend</span><span class="special">(</span><span class="identifier">values</span><span class="special">.</span><span class="identifier">end</span><span class="special">());</span> <span class="identifier">it</span> <span class="special">!=</span> <span class="identifier">itend</span><span class="special">;</span> <span class="special">++</span><span class="identifier">it</span><span class="special">)</span>
<span class="identifier">uset</span><span class="special">.</span><span class="identifier">insert</span><span class="special">(*</span><span class="identifier">it</span><span class="special">);</span>
<span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
<span class="special">}</span>
</pre>
<p>
</p>
</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; 2005 Olaf Krzikalla, 2006-2010 Ion Gaztanaga<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt 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>
</div></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="set_multiset.html"><img src="../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../intrusive.html"><img src="../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="splay_set_multiset.html"><img src="../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>