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| </div> |
| <div class="section boost_icl_function_reference_addition" lang="en"> |
| <div class="titlepage"><div><div><h3 class="title"> |
| <a name="boost_icl.function_reference.addition"></a><a class="link" href="addition.html" title="Addition">Addition</a> |
| </h3></div></div></div> |
| <div class="toc"><dl> |
| <dt><span class="section"><a href="addition.html#boost_icl.function_reference.addition.synopsis">Synopsis</a></span></dt> |
| <dt><span class="section"><a href="addition.html#boost_icl.function_reference.addition.functions">Functions</a></span></dt> |
| <dt><span class="section"><a href="addition.html#boost_icl.function_reference.addition.inplace_operators">Inplace |
| operators</a></span></dt> |
| <dt><span class="section"><a href="addition.html#boost_icl.function_reference.addition.infix_operators">Infix |
| operators</a></span></dt> |
| </dl></div> |
| <div class="section boost_icl_function_reference_addition_synopsis" lang="en"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <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> |
| </h4></div></div></div> |
| <div class="informaltable"><table class="table"> |
| <colgroup> |
| <col> |
| <col> |
| <col> |
| <col> |
| <col> |
| </colgroup> |
| <thead><tr> |
| <th> |
| <p> |
| Addition |
| </p> |
| </th> |
| <th> |
| <p> |
| interval<br> sets |
| </p> |
| </th> |
| <th> |
| <p> |
| interval<br> maps |
| </p> |
| </th> |
| <th> |
| <p> |
| element<br> sets |
| </p> |
| </th> |
| <th> |
| <p> |
| element<br> maps |
| </p> |
| </th> |
| </tr></thead> |
| <tbody> |
| <tr> |
| <td> |
| <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> |
| </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> |
| </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> |
| </p> |
| </td> |
| <td> |
| <p> |
| </p> |
| </td> |
| <td> |
| <p> |
| <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a> |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <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> |
| </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> |
| </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> |
| </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> |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <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> |
| <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#interval_type"><span class="bold"><strong>i</strong></span></a> |
| </p> |
| </td> |
| <td> |
| <p> |
| <a class="link" href="../interface/function_synopsis.html#interval_mapping_type"><span class="bold"><strong>p</strong></span></a> |
| </p> |
| </td> |
| <td> |
| <p> |
| </p> |
| </td> |
| <td> |
| <p> |
| <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a> |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <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> |
| <td> |
| <p> |
| <a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a> |
| </p> |
| </td> |
| <td> |
| <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> |
| </p> |
| </td> |
| </tr> |
| <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> |
| <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> |
| <p> |
| </p> |
| </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 boost_icl_function_reference_addition_functions" lang="en"> |
| <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="id1155216"></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> |
| <p> |
| </p> |
| </td> |
| <td> |
| <p> |
| </p> |
| </td> |
| <td> |
| <p> |
| </p> |
| </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> |
| <p> |
| </p> |
| </td> |
| <td> |
| <p> |
| </p> |
| </td> |
| <td> |
| <p> |
| <span class="emphasis"><em>O(log n)</em></span> |
| </p> |
| </td> |
| <td> |
| <p> |
| </p> |
| </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> |
| <p> |
| </p> |
| </td> |
| <td> |
| <p> |
| </p> |
| </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> |
| <p> |
| </p> |
| </td> |
| <td> |
| <p> |
| </p> |
| </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> |
| <p> |
| </p> |
| </td> |
| <td> |
| <p> |
| </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> |
| </tr> |
| </tbody> |
| </table></div> |
| </div> |
| <br class="table-break"><a name="boost_icl.function_reference.addition.functions.hinted_addition"></a><h6> |
| <a name="id1155640"></a> |
| <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 boost_icl_function_reference_addition_inplace_operators" lang="en"> |
| <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> |
| <a name="boost_icl.function_reference.addition.complexity"></a><h5> |
| <a name="id1156317"></a> |
| <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="id1157636"></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<span class="underline">sets</span><span class="underline">][</span>_ch_icl<span class="underline">maps</span>_ |
| </p> |
| </th> |
| <td class="auto-generated"> </td> |
| </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> |
| <p> |
| </p> |
| </td> |
| <td> |
| <p> |
| <span class="emphasis"><em>O(m)</em></span> |
| </p> |
| </td> |
| <td> |
| <p> |
| </p> |
| </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> |
| <p> |
| </p> |
| </td> |
| <td> |
| <p> |
| <span class="emphasis"><em>O(log n)</em></span> |
| </p> |
| </td> |
| <td> |
| <p> |
| </p> |
| </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="id1157881"></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> |
| <p> |
| </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> |
| <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> |
| <p> |
| </p> |
| </td> |
| <td> |
| <p> |
| </p> |
| </td> |
| <td> |
| <p> |
| <span class="emphasis"><em>O(m log(n+m))</em></span> |
| </p> |
| </td> |
| <td> |
| <p> |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| </p> |
| </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> |
| <p> |
| </p> |
| </td> |
| <td> |
| <p> |
| </p> |
| </td> |
| <td> |
| <p> |
| <span class="emphasis"><em>O(m log(n+m))</em></span> |
| </p> |
| </td> |
| <td> |
| <p> |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| interval_maps |
| </p> |
| </td> |
| <td> |
| <p> |
| </p> |
| </td> |
| <td> |
| <p> |
| </p> |
| </td> |
| <td> |
| <p> |
| </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> |
| <p> |
| </p> |
| </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 boost_icl_function_reference_addition_infix_operators" lang="en"> |
| <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> |
| <div class="spirit-nav"> |
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