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1043 lines
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<a name="boost_icl.function_reference.addition"></a><a class="link" href="addition.html" title="Addition">Addition</a>
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<div class="toc"><dl class="toc">
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<dt><span class="section"><a href="addition.html#boost_icl.function_reference.addition.synopsis">Synopsis</a></span></dt>
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<dt><span class="section"><a href="addition.html#boost_icl.function_reference.addition.functions">Functions</a></span></dt>
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<dt><span class="section"><a href="addition.html#boost_icl.function_reference.addition.inplace_operators">Inplace
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operators</a></span></dt>
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<dt><span class="section"><a href="addition.html#boost_icl.function_reference.addition.infix_operators">Infix
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operators</a></span></dt>
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<div class="titlepage"><div><div><h4 class="title">
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<a name="boost_icl.function_reference.addition.synopsis"></a><a class="link" href="addition.html#boost_icl.function_reference.addition.synopsis" title="Synopsis">Synopsis</a>
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</h4></div></div></div>
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<div class="informaltable"><table class="table">
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<colgroup>
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<col>
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<thead><tr>
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<p>
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Addition
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</p>
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</th>
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<th>
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<p>
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interval<br> sets
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</p>
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</th>
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<th>
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<p>
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interval<br> maps
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</p>
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</th>
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<th>
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<p>
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element<br> sets
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</p>
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</th>
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<th>
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<p>
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element<br> maps
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</p>
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</th>
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</tr></thead>
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<tbody>
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<tr>
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<td>
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<p>
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<code class="computeroutput"><span class="identifier">T</span><span class="special">&</span>
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<span class="identifier">T</span><span class="special">::</span><span class="identifier">add</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">P</span><span class="special">&)</span></code>
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</p>
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</td>
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<td>
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<p>
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<a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
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<a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a>
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</p>
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</td>
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<td>
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<p>
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<a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
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<a class="link" href="../interface/function_synopsis.html#interval_mapping_type"><span class="bold"><strong>p</strong></span></a>
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</p>
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</td>
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<td>
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</td>
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<td>
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<p>
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<a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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<code class="computeroutput"><span class="identifier">T</span><span class="special">&</span>
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||
<span class="identifier">add</span><span class="special">(</span><span class="identifier">T</span><span class="special">&,</span>
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<span class="keyword">const</span> <span class="identifier">P</span><span class="special">&)</span></code>
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</p>
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</td>
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<td>
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<p>
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<a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
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<a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a>
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</p>
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</td>
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<td>
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<p>
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<a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
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<a class="link" href="../interface/function_synopsis.html#interval_mapping_type"><span class="bold"><strong>p</strong></span></a>
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</p>
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</td>
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<td>
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<p>
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<a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
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</p>
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</td>
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<td>
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<p>
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<a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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<code class="computeroutput"><span class="identifier">J</span> <span class="identifier">T</span><span class="special">::</span><span class="identifier">add</span><span class="special">(</span><span class="identifier">J</span>
|
||
<span class="identifier">pos</span><span class="special">,</span>
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<span class="keyword">const</span> <span class="identifier">P</span><span class="special">&)</span></code>
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</p>
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</td>
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<td>
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<p>
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<a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a>
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</p>
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||
</td>
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<td>
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<p>
|
||
<a class="link" href="../interface/function_synopsis.html#interval_mapping_type"><span class="bold"><strong>p</strong></span></a>
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||
</p>
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||
</td>
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||
<td>
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||
</td>
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||
<td>
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<p>
|
||
<a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
|
||
</p>
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||
</td>
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||
</tr>
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<tr>
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<td>
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<p>
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<code class="computeroutput"><span class="identifier">J</span> <span class="identifier">add</span><span class="special">(</span><span class="identifier">T</span><span class="special">&,</span> <span class="identifier">J</span>
|
||
<span class="identifier">pos</span><span class="special">,</span>
|
||
<span class="keyword">const</span> <span class="identifier">P</span><span class="special">&)</span></code>
|
||
</p>
|
||
</td>
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||
<td>
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||
<p>
|
||
<a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a>
|
||
</p>
|
||
</td>
|
||
<td>
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||
<p>
|
||
<a class="link" href="../interface/function_synopsis.html#interval_mapping_type"><span class="bold"><strong>p</strong></span></a>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
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||
</p>
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||
</td>
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||
</tr>
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||
<tr>
|
||
<td>
|
||
<p>
|
||
<code class="computeroutput"><span class="identifier">T</span><span class="special">&</span>
|
||
<span class="keyword">operator</span> <span class="special">+=(</span><span class="identifier">T</span><span class="special">&,</span>
|
||
<span class="keyword">const</span> <span class="identifier">P</span><span class="special">&)</span></code>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
|
||
<a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a>
|
||
<a class="link" href="../interface/function_synopsis.html#interval_set_types"><span class="bold"><strong>S</strong></span></a>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
|
||
<a class="link" href="../interface/function_synopsis.html#interval_mapping_type"><span class="bold"><strong>p</strong></span></a>
|
||
<a class="link" href="../interface/function_synopsis.html#interval_map_types"><span class="bold"><strong>M</strong></span></a>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
|
||
<a class="link" href="../interface/function_synopsis.html#itl_set_type"><span class="bold"><strong>s</strong></span></a>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
|
||
<a class="link" href="../interface/function_synopsis.html#itl_map_type"><span class="bold"><strong>m</strong></span></a>
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
<code class="computeroutput"><span class="identifier">T</span> <span class="keyword">operator</span>
|
||
<span class="special">+</span> <span class="special">(</span><span class="identifier">T</span><span class="special">,</span>
|
||
<span class="keyword">const</span> <span class="identifier">P</span><span class="special">&)</span></code><br> <code class="computeroutput"><span class="identifier">T</span>
|
||
<span class="keyword">operator</span> <span class="special">+</span>
|
||
<span class="special">(</span><span class="keyword">const</span>
|
||
<span class="identifier">P</span><span class="special">&,</span>
|
||
<span class="identifier">T</span><span class="special">)</span></code>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
|
||
<a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a>
|
||
<a class="link" href="../interface/function_synopsis.html#interval_set_types"><span class="bold"><strong>S</strong></span></a>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
|
||
<a class="link" href="../interface/function_synopsis.html#interval_mapping_type"><span class="bold"><strong>p</strong></span></a>
|
||
<a class="link" href="../interface/function_synopsis.html#interval_map_types"><span class="bold"><strong>M</strong></span></a>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
|
||
<a class="link" href="../interface/function_synopsis.html#itl_set_type"><span class="bold"><strong>s</strong></span></a>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
|
||
<a class="link" href="../interface/function_synopsis.html#itl_map_type"><span class="bold"><strong>m</strong></span></a>
|
||
</p>
|
||
</td>
|
||
</tr>
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||
<tr>
|
||
<td>
|
||
<p>
|
||
<code class="computeroutput"><span class="identifier">T</span><span class="special">&</span>
|
||
<span class="keyword">operator</span> <span class="special">|=(</span>
|
||
<span class="identifier">T</span><span class="special">&,</span>
|
||
<span class="keyword">const</span> <span class="identifier">P</span><span class="special">&)</span></code>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
|
||
<a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a>
|
||
<a class="link" href="../interface/function_synopsis.html#interval_set_types"><span class="bold"><strong>S</strong></span></a>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
|
||
<a class="link" href="../interface/function_synopsis.html#interval_mapping_type"><span class="bold"><strong>p</strong></span></a>
|
||
<a class="link" href="../interface/function_synopsis.html#interval_map_types"><span class="bold"><strong>M</strong></span></a>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
|
||
<a class="link" href="../interface/function_synopsis.html#itl_set_type"><span class="bold"><strong>s</strong></span></a>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
|
||
<a class="link" href="../interface/function_synopsis.html#itl_map_type"><span class="bold"><strong>m</strong></span></a>
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
<code class="computeroutput"><span class="identifier">T</span> <span class="keyword">operator</span>
|
||
<span class="special">|</span> <span class="special">(</span><span class="identifier">T</span><span class="special">,</span>
|
||
<span class="keyword">const</span> <span class="identifier">P</span><span class="special">&)</span></code><br> <code class="computeroutput"><span class="identifier">T</span>
|
||
<span class="keyword">operator</span> <span class="special">|</span>
|
||
<span class="special">(</span><span class="keyword">const</span>
|
||
<span class="identifier">P</span><span class="special">&,</span>
|
||
<span class="identifier">T</span><span class="special">)</span></code>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
|
||
<a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a>
|
||
<a class="link" href="../interface/function_synopsis.html#interval_set_types"><span class="bold"><strong>S</strong></span></a>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
|
||
<a class="link" href="../interface/function_synopsis.html#interval_mapping_type"><span class="bold"><strong>p</strong></span></a>
|
||
<a class="link" href="../interface/function_synopsis.html#interval_map_types"><span class="bold"><strong>M</strong></span></a>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
|
||
<a class="link" href="../interface/function_synopsis.html#itl_set_type"><span class="bold"><strong>s</strong></span></a>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
|
||
<a class="link" href="../interface/function_synopsis.html#itl_map_type"><span class="bold"><strong>m</strong></span></a>
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
Functions and operators that implement <span class="emphasis"><em><span class="bold"><strong>Addition</strong></span></em></span>
|
||
on <span class="bold"><strong>icl</strong></span> objects are given in the table
|
||
above. <code class="computeroutput"><span class="keyword">operator</span> <span class="special">|=</span></code>
|
||
and <code class="computeroutput"><span class="keyword">operator</span> <span class="special">|</span></code>
|
||
are behavioral identical to <code class="computeroutput"><span class="keyword">operator</span>
|
||
<span class="special">+=</span></code> and <code class="computeroutput"><span class="keyword">operator</span>
|
||
<span class="special">+</span></code>. This is a redundancy that has
|
||
been introduced deliberately, because a <span class="emphasis"><em>set union</em></span>
|
||
semantics is often attached <code class="computeroutput"><span class="identifier">operators</span>
|
||
<span class="special">|=</span></code> and <code class="computeroutput"><span class="special">|</span></code>.
|
||
</p>
|
||
<div class="informaltable"><table class="table">
|
||
<colgroup>
|
||
<col>
|
||
<col>
|
||
</colgroup>
|
||
<thead><tr>
|
||
<th>
|
||
</th>
|
||
<th>
|
||
<p>
|
||
Description of Addition
|
||
</p>
|
||
</th>
|
||
</tr></thead>
|
||
<tbody>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
<code class="computeroutput"><span class="identifier">Sets</span></code>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
Addition on Sets implements <span class="emphasis"><em><span class="bold"><strong>set
|
||
union</strong></span></em></span>
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
<code class="computeroutput"><span class="identifier">Maps</span></code>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
Addition on Maps implements a <span class="emphasis"><em><span class="bold"><strong>map
|
||
union</strong></span></em></span> function similar to <span class="emphasis"><em>set
|
||
union</em></span>. If, on insertion of an element value pair
|
||
<code class="computeroutput"><span class="special">(</span><span class="identifier">k</span><span class="special">,</span><span class="identifier">v</span><span class="special">)</span></code> it's key <code class="computeroutput"><span class="identifier">k</span></code>
|
||
is in the map already, the addition function is propagated to
|
||
the associated value. This functionality has been introduced
|
||
as <span class="emphasis"><em>aggregate on collision</em></span> for element maps
|
||
and <span class="emphasis"><em>aggregate on overlap</em></span> for interval maps.
|
||
</p>
|
||
<p>
|
||
Find more on <a class="link" href="../concepts/aggrovering.html" title="Addability, Subtractability and Aggregate on Overlap"><span class="emphasis"><em>addability
|
||
of maps</em></span></a> and related <a class="link" href="../semantics/maps.html" title="Maps"><span class="emphasis"><em>semantic
|
||
issues</em></span></a> following the links.
|
||
</p>
|
||
<p>
|
||
Examples, demonstrating Addition on interval containers are
|
||
<a class="link" href="../examples/overlap_counter.html" title="Overlap counter"><span class="emphasis"><em>overlap
|
||
counter</em></span></a>, <a class="link" href="../examples/party.html" title="Party"><span class="emphasis"><em>party</em></span></a>
|
||
and <a class="link" href="../examples/partys_height_average.html" title="Party's height average"><span class="emphasis"><em>party's
|
||
height average.</em></span></a>
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
For <code class="computeroutput"><span class="identifier">Sets</span></code> <span class="emphasis"><em><span class="bold"><strong>addition</strong></span></em></span> and <span class="emphasis"><em><span class="bold"><strong>insertion</strong></span></em></span>
|
||
are implemented identically. Functions <code class="computeroutput"><span class="identifier">add</span></code>
|
||
and <code class="computeroutput"><span class="identifier">insert</span></code> collapse to
|
||
the same function. For <code class="computeroutput"><span class="identifier">Maps</span></code>
|
||
<span class="emphasis"><em><span class="bold"><strong>addition</strong></span></em></span> and <span class="emphasis"><em><span class="bold"><strong>insertion</strong></span></em></span> work differently. Function
|
||
<code class="computeroutput"><span class="identifier">add</span></code> performs aggregations
|
||
on collision or overlap, while function <code class="computeroutput"><span class="identifier">insert</span></code>
|
||
only inserts values that do not yet have key values.
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h4 class="title">
|
||
<a name="boost_icl.function_reference.addition.functions"></a><a class="link" href="addition.html#boost_icl.function_reference.addition.functions" title="Functions">Functions</a>
|
||
</h4></div></div></div>
|
||
<p>
|
||
The admissible combinations of types for member function <code class="computeroutput"><span class="identifier">T</span><span class="special">&</span> <span class="identifier">T</span><span class="special">::</span><span class="identifier">add</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">P</span><span class="special">&)</span></code>
|
||
can be summarized in the <span class="emphasis"><em><span class="bold"><strong>overload table</strong></span></em></span>
|
||
below:
|
||
</p>
|
||
<p>
|
||
</p>
|
||
<pre class="programlisting"><span class="comment">// overload table for T\P| e i b p </span>
|
||
<span class="identifier">T</span><span class="special">&</span> <span class="identifier">T</span><span class="special">::</span><span class="identifier">add</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">P</span><span class="special">&)</span> <span class="special">---+--------</span>
|
||
<span class="identifier">T</span><span class="special">&</span> <span class="identifier">add</span><span class="special">(</span><span class="identifier">T</span><span class="special">&,</span> <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&)</span> <span class="identifier">s</span> <span class="special">|</span> <span class="identifier">s</span>
|
||
<span class="identifier">m</span> <span class="special">|</span> <span class="identifier">m</span>
|
||
<span class="identifier">S</span> <span class="special">|</span> <span class="identifier">S</span> <span class="identifier">S</span>
|
||
<span class="identifier">M</span> <span class="special">|</span> <span class="identifier">M</span> <span class="identifier">M</span>
|
||
</pre>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
The next table contains complexity characteristics for <code class="computeroutput"><span class="identifier">add</span></code>.
|
||
</p>
|
||
<div class="table">
|
||
<a name="boost_icl.function_reference.addition.functions.t0"></a><p class="title"><b>Table 1.21. Time Complexity for member function add on icl containers</b></p>
|
||
<div class="table-contents"><table class="table" summary="Time Complexity for member function add on icl containers">
|
||
<colgroup>
|
||
<col>
|
||
<col>
|
||
<col>
|
||
<col>
|
||
<col>
|
||
</colgroup>
|
||
<thead><tr>
|
||
<th>
|
||
<p>
|
||
<code class="computeroutput"><span class="identifier">T</span><span class="special">&</span>
|
||
<span class="identifier">T</span><span class="special">::</span><span class="identifier">add</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">P</span><span class="special">&)</span></code><br> <code class="computeroutput"><span class="identifier">T</span><span class="special">&</span> <span class="identifier">add</span><span class="special">(</span><span class="identifier">T</span><span class="special">&,</span> <span class="keyword">const</span>
|
||
<span class="identifier">P</span><span class="special">&)</span></code>
|
||
</p>
|
||
</th>
|
||
<th>
|
||
<p>
|
||
domain<br> type
|
||
</p>
|
||
</th>
|
||
<th>
|
||
<p>
|
||
interval<br> type
|
||
</p>
|
||
</th>
|
||
<th>
|
||
<p>
|
||
domain<br> mapping<br> type
|
||
</p>
|
||
</th>
|
||
<th>
|
||
<p>
|
||
interval<br> mapping<br> type
|
||
</p>
|
||
</th>
|
||
</tr></thead>
|
||
<tbody>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
<a href="http://www.cplusplus.com/reference/stl/set/" target="_top"><code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">set</span></code> </a>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<span class="emphasis"><em>O(log n)</em></span>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
<code class="computeroutput"><a class="link" href="../../boost/icl/map.html" title="Class template map">icl::map</a></code>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<span class="emphasis"><em>O(log n)</em></span>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
<code class="computeroutput"><a class="link" href="../../boost/icl/interval_set.html" title="Class template interval_set">interval_set</a></code><br>
|
||
<code class="computeroutput"><a class="link" href="../../boost/icl/separate_interval_set.html" title="Class template separate_interval_set">separate_interval_set</a></code>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<span class="emphasis"><em>O(log n)</em></span>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<span class="emphasis"><em>amortized<br> O(log n)</em></span>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
<code class="computeroutput"><a class="link" href="../../boost/icl/split_interval_set.html" title="Class template split_interval_set">split_interval_set</a></code>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<span class="emphasis"><em>O(log n)</em></span>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<span class="emphasis"><em>O(n)</em></span>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
<code class="computeroutput"><a class="link" href="../../boost/icl/interval_map.html" title="Class template interval_map">interval_map</a></code><br>
|
||
<code class="computeroutput"><a class="link" href="../../boost/icl/split_interval_map.html" title="Class template split_interval_map">split_interval_map</a></code>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<span class="emphasis"><em>O(log n)</em></span>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<span class="emphasis"><em>O(n)</em></span>
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
</div>
|
||
<br class="table-break"><h6>
|
||
<a name="boost_icl.function_reference.addition.functions.h0"></a>
|
||
<span class="phrase"><a name="boost_icl.function_reference.addition.functions.hinted_addition"></a></span><a class="link" href="addition.html#boost_icl.function_reference.addition.functions.hinted_addition">Hinted
|
||
addition</a>
|
||
</h6>
|
||
<p>
|
||
Function <code class="computeroutput"><span class="identifier">J</span> <span class="identifier">T</span><span class="special">::</span><span class="identifier">add</span><span class="special">(</span><span class="identifier">J</span> <span class="identifier">prior</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&</span> <span class="identifier">addend</span><span class="special">)</span></code>
|
||
allows for an addition in <span class="emphasis"><em><span class="bold"><strong>constant time</strong></span></em></span>,
|
||
if <code class="computeroutput"><span class="identifier">addend</span></code> can be inserted
|
||
right after iterator <code class="computeroutput"><span class="identifier">prior</span></code>
|
||
without collision. If this is not possible the complexity characteristics
|
||
are as stated for the non hinted addition above. Hinted addition is available
|
||
for these combinations of types:
|
||
</p>
|
||
<pre class="programlisting"><span class="comment">// overload table for addition with hint T\P| e i b p </span>
|
||
<span class="identifier">J</span> <span class="identifier">T</span><span class="special">::</span><span class="identifier">add</span><span class="special">(</span><span class="identifier">J</span> <span class="identifier">prior</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&)</span> <span class="special">---+--------</span>
|
||
<span class="identifier">J</span> <span class="identifier">add</span><span class="special">(</span><span class="identifier">T</span><span class="special">&,</span> <span class="identifier">J</span> <span class="identifier">prior</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&)</span> <span class="identifier">s</span> <span class="special">|</span> <span class="identifier">s</span>
|
||
<span class="identifier">m</span> <span class="special">|</span> <span class="identifier">m</span>
|
||
<span class="identifier">S</span> <span class="special">|</span> <span class="identifier">S</span>
|
||
<span class="identifier">M</span> <span class="special">|</span> <span class="identifier">M</span>
|
||
</pre>
|
||
<p>
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h4 class="title">
|
||
<a name="boost_icl.function_reference.addition.inplace_operators"></a><a class="link" href="addition.html#boost_icl.function_reference.addition.inplace_operators" title="Inplace operators">Inplace
|
||
operators</a>
|
||
</h4></div></div></div>
|
||
<p>
|
||
The possible overloads of inplace <code class="computeroutput"><span class="identifier">T</span><span class="special">&</span> <span class="keyword">operator</span>
|
||
<span class="special">+=</span> <span class="special">(</span><span class="identifier">T</span><span class="special">&,</span> <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&)</span></code> are given by two tables, that show
|
||
admissible combinations of types. Row types show instantiations of argument
|
||
type <code class="computeroutput"><span class="identifier">T</span></code>. Columns types show
|
||
show instantiations of argument type <code class="computeroutput"><span class="identifier">P</span></code>.
|
||
If a combination of argument types is possible, the related table cell
|
||
contains the result type of the operation. <a class="link" href="../interface/function_synopsis.html#element_type">Placeholders</a>
|
||
<a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
|
||
<a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a>
|
||
<a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
|
||
<a class="link" href="../interface/function_synopsis.html#interval_mapping_type"><span class="bold"><strong>p</strong></span></a>
|
||
<a class="link" href="../interface/function_synopsis.html#itl_set_type"><span class="bold"><strong>s</strong></span></a>
|
||
<a class="link" href="../interface/function_synopsis.html#interval_set_types"><span class="bold"><strong>S</strong></span></a>
|
||
<a class="link" href="../interface/function_synopsis.html#itl_map_type"><span class="bold"><strong>m</strong></span></a>
|
||
<a class="link" href="../interface/function_synopsis.html#interval_map_types"><span class="bold"><strong>M</strong></span></a>
|
||
will be used to denote <span class="emphasis"><em>elements, intervals, element value pairs,
|
||
interval value pairs, element sets, interval sets, element maps</em></span>
|
||
and <span class="emphasis"><em>interval maps</em></span>. The first table shows the overloads
|
||
of <code class="computeroutput"><span class="special">+=</span></code> for <span class="emphasis"><em>element
|
||
containers</em></span> the second table refers to <span class="emphasis"><em>interval containers</em></span>.
|
||
</p>
|
||
<p>
|
||
</p>
|
||
<pre class="programlisting"><span class="comment">// overload tables for element containers: interval containers: </span>
|
||
<span class="identifier">T</span><span class="special">&</span> <span class="keyword">operator</span> <span class="special">+=</span> <span class="special">(</span><span class="identifier">T</span><span class="special">&,</span> <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&)</span> <span class="special">+=</span> <span class="special">|</span> <span class="identifier">e</span> <span class="identifier">b</span> <span class="identifier">s</span> <span class="identifier">m</span> <span class="special">+=</span> <span class="special">|</span> <span class="identifier">e</span> <span class="identifier">i</span> <span class="identifier">b</span> <span class="identifier">p</span> <span class="identifier">S</span> <span class="identifier">M</span>
|
||
<span class="special">---+--------</span> <span class="special">---+------------</span>
|
||
<span class="identifier">s</span> <span class="special">|</span> <span class="identifier">s</span> <span class="identifier">s</span> <span class="identifier">S</span> <span class="special">|</span> <span class="identifier">S</span> <span class="identifier">S</span> <span class="identifier">S</span>
|
||
<span class="identifier">m</span> <span class="special">|</span> <span class="identifier">m</span> <span class="identifier">m</span> <span class="identifier">M</span> <span class="special">|</span> <span class="identifier">M</span> <span class="identifier">M</span> <span class="identifier">M</span>
|
||
</pre>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
For the definition of admissible overloads we separate <span class="emphasis"><em>element
|
||
containers</em></span> from <span class="emphasis"><em>interval containers</em></span>. Within
|
||
each group all combinations of types are supported for an operation, that
|
||
are in line with the <span class="bold"><strong>icl's</strong></span> design and
|
||
the sets of laws, that establish the <span class="bold"><strong>icl's</strong></span>
|
||
<a class="link" href="../semantics.html" title="Semantics">semantics</a>.
|
||
</p>
|
||
<p>
|
||
Overloads between <span class="emphasis"><em>element containers</em></span> and <span class="emphasis"><em>interval
|
||
containers</em></span> could also be defined. But this has not been done
|
||
for pragmatical reasons: Each additional combination of types for an operation
|
||
enlarges the space of possible overloads. This makes the overload resolution
|
||
by compilers more complex, error prone and slows down compilation speed.
|
||
Error messages for unresolvable or ambiguous overloads are difficult to
|
||
read and understand. Therefore overloading of namespace global functions
|
||
in the <span class="bold"><strong>icl</strong></span> are limited to a reasonable
|
||
field of combinations, that are described here.
|
||
</p>
|
||
</div>
|
||
<h5>
|
||
<a name="boost_icl.function_reference.addition.h0"></a>
|
||
<span class="phrase"><a name="boost_icl.function_reference.addition.complexity"></a></span><a class="link" href="addition.html#boost_icl.function_reference.addition.complexity">Complexity</a>
|
||
</h5>
|
||
<p>
|
||
For different combinations of argument types <code class="computeroutput"><span class="identifier">T</span></code>
|
||
and <code class="computeroutput"><span class="identifier">P</span></code> different implementations
|
||
of the <code class="computeroutput"><span class="keyword">operator</span> <span class="special">+=</span></code>
|
||
are selected. These implementations show different complexity characteristics.
|
||
If <code class="computeroutput"><span class="identifier">T</span></code> is a container type,
|
||
the combination of domain elements (<a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>) or element value pairs (<a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>) is faster than a combination of intervals
|
||
(<a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a>)
|
||
or interval value pairs (<a class="link" href="../interface/function_synopsis.html#interval_mapping_type"><span class="bold"><strong>p</strong></span></a>) which in turn is faster than the combination
|
||
of element or interval containers. The next table shows <span class="emphasis"><em>time complexities</em></span>
|
||
of addition for <span class="bold"><strong>icl's</strong></span> element containers.
|
||
</p>
|
||
<p>
|
||
Sizes <code class="computeroutput"><span class="identifier">n</span></code> and <code class="computeroutput"><span class="identifier">m</span></code> are in the complexity statements are
|
||
sizes of objects <code class="computeroutput"><span class="identifier">T</span> <span class="identifier">y</span></code>
|
||
and <code class="computeroutput"><span class="identifier">P</span> <span class="identifier">x</span></code>:
|
||
</p>
|
||
<pre class="programlisting"><span class="identifier">n</span> <span class="special">=</span> <span class="identifier">iterative_size</span><span class="special">(</span><span class="identifier">y</span><span class="special">);</span>
|
||
<span class="identifier">m</span> <span class="special">=</span> <span class="identifier">iterative_size</span><span class="special">(</span><span class="identifier">x</span><span class="special">);</span> <span class="comment">//if P is a container type</span>
|
||
</pre>
|
||
<p>
|
||
Note, that for an interval container the number of elements <code class="computeroutput"><span class="identifier">T</span><span class="special">::</span><span class="identifier">size</span></code>
|
||
is different from the number of intervals that you can iterate over. Therefore
|
||
a function <code class="computeroutput"><span class="identifier">T</span><span class="special">::</span><span class="identifier">iterative_size</span><span class="special">()</span></code>
|
||
is used that provides the desired kind of size.
|
||
</p>
|
||
<div class="table">
|
||
<a name="boost_icl.function_reference.addition.t0"></a><p class="title"><b>Table 1.22. Time Complexity for inplace Addition on element containers</b></p>
|
||
<div class="table-contents"><table class="table" summary="Time Complexity for inplace Addition on element containers">
|
||
<colgroup>
|
||
<col>
|
||
<col>
|
||
<col>
|
||
<col>
|
||
<col>
|
||
</colgroup>
|
||
<thead><tr>
|
||
<th>
|
||
<p>
|
||
<code class="computeroutput"><span class="identifier">T</span><span class="special">&</span>
|
||
<span class="keyword">operator</span> <span class="special">+=</span>
|
||
<span class="special">(</span><span class="identifier">T</span><span class="special">&</span> <span class="identifier">y</span><span class="special">,</span> <span class="keyword">const</span>
|
||
<span class="identifier">P</span><span class="special">&</span>
|
||
<span class="identifier">x</span><span class="special">)</span></code>
|
||
</p>
|
||
</th>
|
||
<th>
|
||
<p>
|
||
domain<br> type
|
||
</p>
|
||
</th>
|
||
<th>
|
||
<p>
|
||
domain<br> mapping<br> type
|
||
</p>
|
||
</th>
|
||
<th>
|
||
<p>
|
||
__ch_icl_sets__
|
||
</p>
|
||
</th>
|
||
<th>
|
||
<p>
|
||
__ch_icl_maps__
|
||
</p>
|
||
</th>
|
||
</tr></thead>
|
||
<tbody>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
<a href="http://www.cplusplus.com/reference/stl/set/" target="_top"><code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">set</span></code> </a>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<span class="emphasis"><em>O(log n)</em></span>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<span class="emphasis"><em>O(m)</em></span>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
<code class="computeroutput"><a class="link" href="../../boost/icl/map.html" title="Class template map">icl::map</a></code>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<span class="emphasis"><em>O(log n)</em></span>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<span class="emphasis"><em>O(m)</em></span>
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
</div>
|
||
<br class="table-break"><p>
|
||
Time complexity characteristics of inplace addition for interval containers
|
||
is given by this table.
|
||
</p>
|
||
<div class="table">
|
||
<a name="boost_icl.function_reference.addition.t1"></a><p class="title"><b>Table 1.23. Time Complexity for inplace Addition on interval containers</b></p>
|
||
<div class="table-contents"><table class="table" summary="Time Complexity for inplace Addition on interval containers">
|
||
<colgroup>
|
||
<col>
|
||
<col>
|
||
<col>
|
||
<col>
|
||
<col>
|
||
<col>
|
||
<col>
|
||
<col>
|
||
</colgroup>
|
||
<thead><tr>
|
||
<th>
|
||
<p>
|
||
<code class="computeroutput"><span class="identifier">T</span><span class="special">&</span>
|
||
<span class="keyword">operator</span> <span class="special">+=</span>
|
||
<span class="special">(</span><span class="identifier">T</span><span class="special">&</span> <span class="identifier">y</span><span class="special">,</span> <span class="keyword">const</span>
|
||
<span class="identifier">P</span><span class="special">&</span>
|
||
<span class="identifier">x</span><span class="special">)</span></code>
|
||
</p>
|
||
</th>
|
||
<th>
|
||
</th>
|
||
<th>
|
||
<p>
|
||
domain<br> type
|
||
</p>
|
||
</th>
|
||
<th>
|
||
<p>
|
||
interval<br> type
|
||
</p>
|
||
</th>
|
||
<th>
|
||
<p>
|
||
domain<br> mapping<br> type
|
||
</p>
|
||
</th>
|
||
<th>
|
||
<p>
|
||
interval<br> mapping<br> type
|
||
</p>
|
||
</th>
|
||
<th>
|
||
<p>
|
||
interval<br> sets
|
||
</p>
|
||
</th>
|
||
<th>
|
||
<p>
|
||
interval<br> maps
|
||
</p>
|
||
</th>
|
||
</tr></thead>
|
||
<tbody>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
interval_sets
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<code class="computeroutput"><a class="link" href="../../boost/icl/interval_set.html" title="Class template interval_set">interval_set</a></code><br>
|
||
<code class="computeroutput"><a class="link" href="../../boost/icl/separate_interval_set.html" title="Class template separate_interval_set">separate_interval_set</a></code>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<span class="emphasis"><em>O(log n)</em></span>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<span class="emphasis"><em>amortized<br> O(log n)</em></span>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<span class="emphasis"><em>O(m log(n+m))</em></span>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<code class="computeroutput"><a class="link" href="../../boost/icl/split_interval_set.html" title="Class template split_interval_set">split_interval_set</a></code>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<span class="emphasis"><em>O(log n)</em></span>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<span class="emphasis"><em>O(n)</em></span>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<span class="emphasis"><em>O(m log(n+m))</em></span>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
interval_maps
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<span class="emphasis"><em>O(log n)</em></span>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<span class="emphasis"><em>O(n)</em></span>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<span class="emphasis"><em>O(m log(n+m))</em></span>
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
</div>
|
||
<br class="table-break"><p>
|
||
Since the implementation of element and interval containers is based on the
|
||
<a class="link" href="../implementation.html" title="Implementation">link red-black tree implementation</a>
|
||
of std::AssociativeContainers, we have a logarithmic complexity for addition
|
||
of elements. Addition of intervals or interval value pairs is amortized logarithmic
|
||
for <code class="computeroutput"><a class="link" href="../../boost/icl/interval_set.html" title="Class template interval_set">interval_sets</a></code> and
|
||
<code class="computeroutput"><a class="link" href="../../boost/icl/separate_interval_set.html" title="Class template separate_interval_set">separate_interval_sets</a></code>
|
||
and linear for <code class="computeroutput"><a class="link" href="../../boost/icl/split_interval_set.html" title="Class template split_interval_set">split_interval_sets</a></code>
|
||
and <code class="computeroutput"><a class="link" href="../../boost/icl/interval_map.html" title="Class template interval_map">interval_maps</a></code>.
|
||
Addition is linear for element containers and loglinear for interval containers.
|
||
</p>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h4 class="title">
|
||
<a name="boost_icl.function_reference.addition.infix_operators"></a><a class="link" href="addition.html#boost_icl.function_reference.addition.infix_operators" title="Infix operators">Infix
|
||
operators</a>
|
||
</h4></div></div></div>
|
||
<p>
|
||
The admissible type combinations for infix <code class="computeroutput"><span class="keyword">operator</span>
|
||
<span class="special">+</span></code> are defined by the overload tables
|
||
below.
|
||
</p>
|
||
<p>
|
||
</p>
|
||
<pre class="programlisting"><span class="comment">// overload tables for element containers: interval containers:</span>
|
||
<span class="identifier">T</span> <span class="keyword">operator</span> <span class="special">+</span> <span class="special">(</span><span class="identifier">T</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&)</span> <span class="special">+</span> <span class="special">|</span> <span class="identifier">e</span> <span class="identifier">b</span> <span class="identifier">s</span> <span class="identifier">m</span> <span class="special">+</span> <span class="special">|</span> <span class="identifier">e</span> <span class="identifier">i</span> <span class="identifier">b</span> <span class="identifier">p</span> <span class="identifier">S1</span> <span class="identifier">S2</span> <span class="identifier">S3</span> <span class="identifier">M1</span> <span class="identifier">M3</span>
|
||
<span class="identifier">T</span> <span class="keyword">operator</span> <span class="special">+</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">P</span><span class="special">&,</span> <span class="identifier">T</span><span class="special">)</span> <span class="special">---+--------</span> <span class="special">---+---------------------------</span>
|
||
<span class="identifier">e</span> <span class="special">|</span> <span class="identifier">s</span> <span class="identifier">e</span> <span class="special">|</span> <span class="identifier">S1</span> <span class="identifier">S2</span> <span class="identifier">S3</span>
|
||
<span class="identifier">b</span> <span class="special">|</span> <span class="identifier">m</span> <span class="identifier">i</span> <span class="special">|</span> <span class="identifier">S1</span> <span class="identifier">S2</span> <span class="identifier">S3</span>
|
||
<span class="identifier">s</span> <span class="special">|</span> <span class="identifier">s</span> <span class="identifier">s</span> <span class="identifier">b</span> <span class="special">|</span> <span class="identifier">M1</span> <span class="identifier">M3</span>
|
||
<span class="identifier">m</span> <span class="special">|</span> <span class="identifier">m</span> <span class="identifier">m</span> <span class="identifier">p</span> <span class="special">|</span> <span class="identifier">M1</span> <span class="identifier">M3</span>
|
||
<span class="identifier">S1</span> <span class="special">|</span> <span class="identifier">S1</span> <span class="identifier">S1</span> <span class="identifier">S1</span> <span class="identifier">S2</span> <span class="identifier">S3</span>
|
||
<span class="identifier">S2</span> <span class="special">|</span> <span class="identifier">S2</span> <span class="identifier">S2</span> <span class="identifier">S2</span> <span class="identifier">S2</span> <span class="identifier">S3</span>
|
||
<span class="identifier">S3</span> <span class="special">|</span> <span class="identifier">S3</span> <span class="identifier">S3</span> <span class="identifier">S3</span> <span class="identifier">S3</span> <span class="identifier">S3</span>
|
||
<span class="identifier">M1</span> <span class="special">|</span> <span class="identifier">M1</span> <span class="identifier">M1</span> <span class="identifier">M1</span> <span class="identifier">M3</span>
|
||
<span class="identifier">M3</span> <span class="special">|</span> <span class="identifier">M3</span> <span class="identifier">M3</span> <span class="identifier">M3</span> <span class="identifier">M3</span>
|
||
</pre>
|
||
<p>
|
||
</p>
|
||
</div>
|
||
<p>
|
||
<span class="emphasis"><em><span class="bold"><strong>See also . . .</strong></span></em></span>
|
||
</p>
|
||
<div class="informaltable"><table class="table">
|
||
<colgroup><col></colgroup>
|
||
<thead><tr></tr></thead>
|
||
<tbody>
|
||
<tr><td>
|
||
<p>
|
||
<a class="link" href="subtraction.html" title="Subtraction"><span class="emphasis"><em><span class="bold"><strong>Subtraction</strong></span></em></span></a>
|
||
</p>
|
||
</td></tr>
|
||
<tr><td>
|
||
<p>
|
||
<a class="link" href="insertion.html" title="Insertion"><span class="emphasis"><em><span class="bold"><strong>Insertion</strong></span></em></span></a>
|
||
</p>
|
||
</td></tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
<span class="emphasis"><em><span class="bold"><strong>Back to section . . .</strong></span></em></span>
|
||
</p>
|
||
<div class="informaltable"><table class="table">
|
||
<colgroup><col></colgroup>
|
||
<thead><tr></tr></thead>
|
||
<tbody>
|
||
<tr><td>
|
||
<p>
|
||
<a class="link" href="../interface/function_synopsis.html#function_synopsis_table"><span class="emphasis"><em><span class="bold"><strong>Function
|
||
Synopsis</strong></span></em></span></a>
|
||
</p>
|
||
</td></tr>
|
||
<tr><td>
|
||
<p>
|
||
<a class="link" href="../interface.html" title="Interface"><span class="emphasis"><em><span class="bold"><strong>Interface</strong></span></em></span></a>
|
||
</p>
|
||
</td></tr>
|
||
</tbody>
|
||
</table></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 © 2007-2010 Joachim
|
||
Faulhaber<br>Copyright © 1999-2006 Cortex Software
|
||
GmbH<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>
|
||
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