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  26 <div class="section">
  27 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
  28 <a name="intrusive.sg_set_multiset"></a><a class="link" href="sg_set_multiset.html" title="Intrusive scapegoat tree based associative containers: sg_set, sg_multiset and sgtree">Intrusive scapegoat tree based
  29     associative containers: sg_set, sg_multiset and sgtree</a>
  30 </h2></div></div></div>
  31 <div class="toc"><dl class="toc">
  32 <dt><span class="section"><a href="sg_set_multiset.html#intrusive.sg_set_multiset.sg_set_multiset_containers">sg_set,
  33       sg_multiset and sgtree containers</a></span></dt>
  34 <dt><span class="section"><a href="sg_set_multiset.html#intrusive.sg_set_multiset.sg_set_multiset_example">Example</a></span></dt>
  35 </dl></div>
  36 <p>
  37       A scapegoat tree is a self-balancing binary search tree, that provides worst-case
  38       O(log n) lookup time, and O(log n) amortized insertion and deletion time. Unlike
  39       other self-balancing binary search trees that provide worst case O(log n) lookup
  40       time, scapegoat trees have no additional per-node overhead compared to a regular
  41       binary search tree.
  42     </p>
  43 <p>
  44       A binary search tree is said to be weight balanced if half the nodes are on
  45       the left of the root, and half on the right. An a-height-balanced tree is defined
  46       with defined with the following equation:
  47     </p>
  48 <p>
  49       <span class="bold"><strong><span class="emphasis"><em>height(tree) &lt;= log1/a(tree.size())</em></span></strong></span>
  50     </p>
  51 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
  52 <li class="listitem">
  53           <span class="bold"><strong><span class="emphasis"><em>a == 1</em></span></strong></span>: A tree forming
  54           a linked list is considered balanced.
  55         </li>
  56 <li class="listitem">
  57           <span class="bold"><strong><span class="emphasis"><em>a == 0.5</em></span></strong></span>: Only a
  58           perfectly balanced binary is considered balanced.
  59         </li>
  60 </ul></div>
  61 <p>
  62       Scapegoat trees are loosely <span class="emphasis"><em>a-height-balanced</em></span> so:
  63     </p>
  64 <p>
  65       <span class="bold"><strong><span class="emphasis"><em>height(tree) &lt;= log1/a(tree.size()) + 1</em></span></strong></span>
  66     </p>
  67 <p>
  68       Scapegoat trees support any a between 0.5 and 1. If a is higher, the tree is
  69       rebalanced less often, obtaining quicker insertions but slower searches. Lower
  70       a values improve search times. Scapegoat-trees implemented in <span class="bold"><strong>Boost.Intrusive</strong></span>
  71       offer the possibility of <span class="bold"><strong>changing a at run-time</strong></span>
  72       taking advantage of the flexibility of scapegoat trees. For more information
  73       on scapegoat trees see <a href="http://en.wikipedia.org/wiki/Scapegoat_tree" target="_top">Wikipedia
  74       entry</a>.
  75     </p>
  76 <p>
  77       Scapegoat trees also have downsides:
  78     </p>
  79 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
  80 <li class="listitem">
  81           They need additional storage of data on the root (the size of the tree,
  82           for example) to achieve logarithmic complexity operations so it's not possible
  83           to offer <code class="computeroutput"><span class="identifier">auto_unlink</span></code> hooks.
  84           The size of an empty scapegoat tree is also considerably increased.
  85         </li>
  86 <li class="listitem">
  87           The operations needed to determine if the tree is unbalanced require floating-point
  88           operations like <span class="emphasis"><em>log1/a</em></span>. If the system has no floating
  89           point operations (like some embedded systems), scapegoat tree operations
  90           might become slow.
  91         </li>
  92 </ul></div>
  93 <p>
  94       <span class="bold"><strong>Boost.Intrusive</strong></span> offers 3 containers based
  95       on scapegoat trees: <code class="computeroutput"><a class="link" href="../boost/intrusive/sg_set.html" title="Class template sg_set">sg_set</a></code>,
  96       <code class="computeroutput"><a class="link" href="../boost/intrusive/sg_multiset.html" title="Class template sg_multiset">sg_multiset</a></code> and
  97       <code class="computeroutput"><a class="link" href="../boost/intrusive/sgtree.html" title="Class template sgtree">sgtree</a></code>. The first two
  98       are similar to <code class="computeroutput"><a class="link" href="../boost/intrusive/set.html" title="Class template set">set</a></code> or <code class="computeroutput"><a class="link" href="../boost/intrusive/multiset.html" title="Class template multiset">multiset</a></code> and the latter is a generalization
  99       that offers functions both to insert unique and multiple keys.
 100     </p>
 101 <p>
 102       The memory overhead of these containers with Boost.Intrusive hooks is 3 pointers.
 103     </p>
 104 <p>
 105       An empty, <code class="computeroutput"><a class="link" href="../boost/intrusive/sg_set.html" title="Class template sg_set">sg_set</a></code>, <code class="computeroutput"><a class="link" href="../boost/intrusive/sg_multiset.html" title="Class template sg_multiset">sg_multiset</a></code> or <code class="computeroutput"><a class="link" href="../boost/intrusive/sgtree.html" title="Class template sgtree">sgtree</a></code>
 106       has also the size of 3 pointers, two integers and two floating point values
 107       (equivalent to the size of 7 pointers on most systems).
 108     </p>
 109 <p>
 110       <span class="bold"><strong>Boost.Intrusive</strong></span> scapegoat associative containers
 111       don't use their own hook types but plain Binary search tree hooks. See <a class="link" href="bst_hooks.html" title="Binary search tree hooks: bs_set_base_hook and bs_set_member_hook">Binary search tree hooks: bs_set_base_hook and
 112       bs_set_member_hook</a> section for more information about these hooks.
 113     </p>
 114 <div class="section">
 115 <div class="titlepage"><div><div><h3 class="title">
 116 <a name="intrusive.sg_set_multiset.sg_set_multiset_containers"></a><a class="link" href="sg_set_multiset.html#intrusive.sg_set_multiset.sg_set_multiset_containers" title="sg_set, sg_multiset and sgtree containers">sg_set,
 117       sg_multiset and sgtree containers</a>
 118 </h3></div></div></div>
 119 <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>
 120 <span class="keyword">class</span> <span class="identifier">sg_set</span><span class="special">;</span>
 121
 122 <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>
 123 <span class="keyword">class</span> <span class="identifier">sg_multiset</span><span class="special">;</span>
 124
 125 <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>
 126 <span class="keyword">class</span> <span class="identifier">sgtree</span><span class="special">;</span>
 127 </pre>
 128 <p>
 129         These containers 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>:
 130       </p>
 131 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 132 <li class="listitem">
 133             <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>
 134             / <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>
 135             / <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>:
 136             To specify the hook type or value traits used to configure the container.
 137             (To learn about value traits go to the section <a class="link" href="value_traits.html" title="Containers with custom ValueTraits">Containers
 138             with custom ValueTraits</a>.)
 139           </li>
 140 <li class="listitem">
 141             <span class="bold"><strong><code class="computeroutput"><span class="identifier">size_type</span><span class="special">&lt;</span><span class="keyword">typename</span>
 142             <span class="identifier">SizeType</span><span class="special">&gt;</span></code></strong></span>:
 143             To specify the type that will be used to store the size of the container.
 144             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>
 145           </li>
 146 </ul></div>
 147 <p>
 148         And they also can receive additional options:
 149       </p>
 150 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 151 <li class="listitem">
 152             <span class="bold"><strong><code class="computeroutput"><span class="identifier">compare</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Compare</span><span class="special">&gt;</span></code></strong></span>:
 153             Comparison function for the objects to be inserted in containers. The
 154             comparison functor must induce a strict weak ordering. Default: <code class="computeroutput"><span class="identifier">compare</span><span class="special">&lt;</span>
 155             <span class="identifier">std</span><span class="special">::</span><span class="identifier">less</span><span class="special">&lt;</span><span class="identifier">key_type</span><span class="special">&gt;</span>
 156             <span class="special">&gt;</span></code>
 157           </li>
 158 <li class="listitem">
 159             <span class="bold"><strong><code class="computeroutput"><span class="identifier">floating_point</span><span class="special">&lt;</span><span class="keyword">bool</span> <span class="identifier">Enable</span><span class="special">&gt;</span></code></strong></span>:
 160             When this option is deactivated, the scapegoat tree loses the ability
 161             to change the balance factor a at run-time, but the size of an empty
 162             container is reduced and no floating point operations are performed,
 163             normally increasing container performance. The fixed a factor that is
 164             used when this option is activated is <span class="emphasis"><em>1/sqrt(2) ~ 0,70711</em></span>.
 165             Default: <code class="computeroutput"><span class="identifier">floating_point</span><span class="special">&lt;</span><span class="keyword">true</span><span class="special">&gt;</span></code>
 166           </li>
 167 <li class="listitem">
 168             <span class="bold"><strong><code class="computeroutput"><span class="identifier">key_of_value</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">KeyOfValueFunctionObject</span><span class="special">&gt;</span></code></strong></span>:
 169             A function object that will define the <code class="computeroutput"><span class="identifier">key_type</span></code>
 170             of the value type to be stored. This type will allow a map-like interface.
 171             See <a class="link" href="map_multimap.html" title="Map and multimap-like interface for associative containers">Map and multimap-like interface
 172             with set and multiset</a> for details. Default: <code class="computeroutput"><span class="identifier">key_type</span></code>
 173             is equal to <code class="computeroutput"><span class="identifier">value_type</span></code>
 174             (set-like interface).
 175           </li>
 176 </ul></div>
 177 </div>
 178 <div class="section">
 179 <div class="titlepage"><div><div><h3 class="title">
 180 <a name="intrusive.sg_set_multiset.sg_set_multiset_example"></a><a class="link" href="sg_set_multiset.html#intrusive.sg_set_multiset.sg_set_multiset_example" title="Example">Example</a>
 181 </h3></div></div></div>
 182 <p>
 183         Now let's see a small example using binary search tree hooks and <code class="computeroutput"><a class="link" href="../boost/intrusive/sg_set.html" title="Class template sg_set">sg_set</a></code>/ <code class="computeroutput"><a class="link" href="../boost/intrusive/sg_multiset.html" title="Class template sg_multiset">sg_multiset</a></code>
 184         containers:
 185       </p>
 186 <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">sg_set</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
 187 <span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">vector</span><span class="special">&gt;</span>
 188 <span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">functional</span><span class="special">&gt;</span>
 189 <span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">cassert</span><span class="special">&gt;</span>
 190
 191 <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>
 192
 193 <span class="keyword">class</span> <span class="identifier">MyClass</span> <span class="special">:</span> <span class="keyword">public</span> <span class="identifier">bs_set_base_hook</span><span class="special">&lt;&gt;</span>
 194 <span class="special">{</span>
 195    <span class="keyword">int</span> <span class="identifier">int_</span><span class="special">;</span>
 196
 197    <span class="keyword">public</span><span class="special">:</span>
 198    <span class="comment">//This is a member hook</span>
 199    <span class="identifier">bs_set_member_hook</span><span class="special">&lt;&gt;</span> <span class="identifier">member_hook_</span><span class="special">;</span>
 200
 201    <span class="identifier">MyClass</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">i</span><span class="special">)</span>
 202       <span class="special">:</span>  <span class="identifier">int_</span><span class="special">(</span><span class="identifier">i</span><span class="special">)</span>
 203       <span class="special">{}</span>
 204    <span class="keyword">friend</span> <span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">&lt;</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>
 205       <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">&lt;</span> <span class="identifier">b</span><span class="special">.</span><span class="identifier">int_</span><span class="special">;</span>  <span class="special">}</span>
 206    <span class="keyword">friend</span> <span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">&gt;</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>
 207       <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">&gt;</span> <span class="identifier">b</span><span class="special">.</span><span class="identifier">int_</span><span class="special">;</span>  <span class="special">}</span>
 208    <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>
 209       <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>
 210 <span class="special">};</span>
 211
 212 <span class="comment">//Define an sg_set using the base hook that will store values in reverse order</span>
 213 <span class="comment">//and won't execute floating point operations.</span>
 214 <span class="keyword">typedef</span> <span class="identifier">sg_set</span>
 215    <span class="special">&lt;</span> <span class="identifier">MyClass</span><span class="special">,</span> <span class="identifier">compare</span><span class="special">&lt;</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">greater</span><span class="special">&lt;</span><span class="identifier">MyClass</span><span class="special">&gt;</span> <span class="special">&gt;,</span> <span class="identifier">floating_point</span><span class="special">&lt;</span><span class="keyword">false</span><span class="special">&gt;</span> <span class="special">&gt;</span>   <span class="identifier">BaseSet</span><span class="special">;</span>
 216
 217 <span class="comment">//Define an multiset using the member hook</span>
 218 <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">bs_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>
 219 <span class="keyword">typedef</span> <span class="identifier">sg_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>
 220
 221 <span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
 222 <span class="special">{</span>
 223    <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>
 224
 225    <span class="comment">//Create several MyClass objects, each one with a different value</span>
 226    <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>
 227    <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>
 228
 229    <span class="identifier">BaseSet</span> <span class="identifier">baseset</span><span class="special">;</span>
 230    <span class="identifier">MemberMultiset</span> <span class="identifier">membermultiset</span><span class="special">;</span>
 231
 232    <span class="comment">//Now insert them in the reverse order in the base hook sg_set</span>
 233    <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>
 234       <span class="identifier">baseset</span><span class="special">.</span><span class="identifier">insert</span><span class="special">(*</span><span class="identifier">it</span><span class="special">);</span>
 235       <span class="identifier">membermultiset</span><span class="special">.</span><span class="identifier">insert</span><span class="special">(*</span><span class="identifier">it</span><span class="special">);</span>
 236    <span class="special">}</span>
 237
 238    <span class="comment">//Change balance factor</span>
 239    <span class="identifier">membermultiset</span><span class="special">.</span><span class="identifier">balance_factor</span><span class="special">(</span><span class="number">0.9f</span><span class="special">);</span>
 240
 241    <span class="comment">//Now test sg_sets</span>
 242    <span class="special">{</span>
 243       <span class="identifier">BaseSet</span><span class="special">::</span><span class="identifier">reverse_iterator</span> <span class="identifier">rbit</span><span class="special">(</span><span class="identifier">baseset</span><span class="special">.</span><span class="identifier">rbegin</span><span class="special">());</span>
 244       <span class="identifier">MemberMultiset</span><span class="special">::</span><span class="identifier">iterator</span> <span class="identifier">mit</span><span class="special">(</span><span class="identifier">membermultiset</span><span class="special">.</span><span class="identifier">begin</span><span class="special">());</span>
 245       <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>
 246
 247       <span class="comment">//Test the objects inserted in the base hook sg_set</span>
 248       <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="special">++</span><span class="identifier">rbit</span><span class="special">)</span>
 249          <span class="keyword">if</span><span class="special">(&amp;*</span><span class="identifier">rbit</span> <span class="special">!=</span> <span class="special">&amp;*</span><span class="identifier">it</span><span class="special">)</span>   <span class="keyword">return</span> <span class="number">1</span><span class="special">;</span>
 250
 251       <span class="comment">//Test the objects inserted in the member hook sg_set</span>
 252       <span class="keyword">for</span><span class="special">(</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">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">mit</span><span class="special">)</span>
 253          <span class="keyword">if</span><span class="special">(&amp;*</span><span class="identifier">mit</span> <span class="special">!=</span> <span class="special">&amp;*</span><span class="identifier">it</span><span class="special">)</span> <span class="keyword">return</span> <span class="number">1</span><span class="special">;</span>
 254    <span class="special">}</span>
 255    <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
 256 <span class="special">}</span>
 257 </pre>
 258 </div>
 259 </div>
 260 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 261 <td align="left"></td>
 262 <td align="right"><div class="copyright-footer">Copyright &#169; 2005 Olaf Krzikalla<br>Copyright &#169; 2006-2015 Ion Gaztanaga<p>
 263         Distributed under the Boost Software License, Version 1.0. (See accompanying
 264         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>)
 265       </p>
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