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<a name="optional"></a>Chapter&#160;1.&#160;Boost.Icl</h2></div>
<div><div class="author"><h3 class="author">
<span class="firstname">Joachim</span> <span class="surname">Faulhaber</span>
</h3></div></div>
<div><p class="copyright">Copyright &#169; 2007-2010 Joachim
      Faulhaber</p></div>
<div><p class="copyright">Copyright &#169; 1999-2006 Cortex Software
      GmbH</p></div>
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<a name="optional.legal"></a><p>
        Distributed under the Boost Software License, Version 1.0. (See accompanying
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<div class="toc">
<p><b>Table of Contents</b></p>
<dl class="toc">
<dt><span class="section"><a href="index.html#boost_icl.introduction">Introduction</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="index.html#boost_icl.introduction.definition_and_basic_example">Definition
      and Basic Example</a></span></dt>
<dt><span class="section"><a href="index.html#boost_icl.introduction.icl_s_class_templates">Icl's class
      templates</a></span></dt>
<dt><span class="section"><a href="index.html#boost_icl.introduction.interval_combining_styles">Interval
      Combining Styles</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="boost_icl/examples.html">Examples</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="boost_icl/examples.html#boost_icl.examples.overview">Overview</a></span></dt>
<dt><span class="section"><a href="boost_icl/examples/party.html">Party</a></span></dt>
<dt><span class="section"><a href="boost_icl/examples/interval.html">Interval</a></span></dt>
<dt><span class="section"><a href="boost_icl/examples/dynamic_interval.html">Dynamic interval</a></span></dt>
<dt><span class="section"><a href="boost_icl/examples/static_interval.html">Static interval</a></span></dt>
<dt><span class="section"><a href="boost_icl/examples/interval_container.html">Interval container</a></span></dt>
<dt><span class="section"><a href="boost_icl/examples/overlap_counter.html">Overlap counter</a></span></dt>
<dt><span class="section"><a href="boost_icl/examples/partys_height_average.html">Party's height
      average</a></span></dt>
<dt><span class="section"><a href="boost_icl/examples/partys_tallest_guests.html">Party's tallest
      guests</a></span></dt>
<dt><span class="section"><a href="boost_icl/examples/time_grids.html">Time grids for months
      and weeks</a></span></dt>
<dt><span class="section"><a href="boost_icl/examples/man_power.html">Man power</a></span></dt>
<dt><span class="section"><a href="boost_icl/examples/user_groups.html">User groups</a></span></dt>
<dt><span class="section"><a href="boost_icl/examples/std_copy.html">Std copy</a></span></dt>
<dt><span class="section"><a href="boost_icl/examples/std_transform.html">Std transform</a></span></dt>
<dt><span class="section"><a href="boost_icl/examples/custom_interval.html">Custom interval</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="boost_icl/projects.html">Projects</a></span></dt>
<dd><dl><dt><span class="section"><a href="boost_icl/projects.html#boost_icl.projects.large_bitset">Large Bitset</a></span></dt></dl></dd>
<dt><span class="section"><a href="boost_icl/concepts.html">Concepts</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="boost_icl/concepts.html#boost_icl.concepts.naming">Naming</a></span></dt>
<dt><span class="section"><a href="boost_icl/concepts/aspects.html">Aspects</a></span></dt>
<dt><span class="section"><a href="boost_icl/concepts/sets_and_maps.html">Sets and Maps</a></span></dt>
<dt><span class="section"><a href="boost_icl/concepts/aggrovering.html">Addability, Subtractability
      and Aggregate on Overlap</a></span></dt>
<dt><span class="section"><a href="boost_icl/concepts/map_traits.html">Map Traits</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="boost_icl/semantics.html">Semantics</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="boost_icl/semantics.html#boost_icl.semantics.orderings_and_equivalences">Orderings
      and Equivalences</a></span></dt>
<dt><span class="section"><a href="boost_icl/semantics/sets.html">Sets</a></span></dt>
<dt><span class="section"><a href="boost_icl/semantics/maps.html">Maps</a></span></dt>
<dt><span class="section"><a href="boost_icl/semantics/collectors__maps_of_sets.html">Collectors:
      Maps of Sets</a></span></dt>
<dt><span class="section"><a href="boost_icl/semantics/quantifiers__maps_of_numbers.html">Quantifiers:
      Maps of Numbers</a></span></dt>
<dt><span class="section"><a href="boost_icl/semantics/concept_induction.html">Concept Induction</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="boost_icl/interface.html">Interface</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="boost_icl/interface.html#boost_icl.interface.class_templates">Class templates</a></span></dt>
<dt><span class="section"><a href="boost_icl/interface/required_concepts.html">Required Concepts</a></span></dt>
<dt><span class="section"><a href="boost_icl/interface/associated_types.html">Associated Types</a></span></dt>
<dt><span class="section"><a href="boost_icl/interface/function_synopsis.html">Function Synopsis</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="boost_icl/customization.html">Customization</a></span></dt>
<dd><dl><dt><span class="section"><a href="boost_icl/customization.html#boost_icl.customization.intervals">Intervals</a></span></dt></dl></dd>
<dt><span class="section"><a href="boost_icl/implementation.html">Implementation</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="boost_icl/implementation.html#boost_icl.implementation.iterative_size">Iterative size</a></span></dt>
<dt><span class="section"><a href="boost_icl/implementation/complexity.html">Complexity</a></span></dt>
<dt><span class="section"><a href="boost_icl/implementation/inplace_and_infix_operators.html">Inplace
      and infix operators</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="boost_icl/function_reference.html">Function Reference</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="boost_icl/function_reference.html#boost_icl.function_reference.overload_tables">Overload
      tables</a></span></dt>
<dt><span class="section"><a href="boost_icl/function_reference/segmentational_fineness.html">Segmentational
      Fineness</a></span></dt>
<dt><span class="section"><a href="boost_icl/function_reference/key_types.html">Key Types</a></span></dt>
<dt><span class="section"><a href="boost_icl/function_reference/construct__copy__destruct.html">Construct,
      copy, destruct</a></span></dt>
<dt><span class="section"><a href="boost_icl/function_reference/containedness.html">Containedness</a></span></dt>
<dt><span class="section"><a href="boost_icl/function_reference/equivalences_and_orderings.html">Equivalences
      and Orderings</a></span></dt>
<dt><span class="section"><a href="boost_icl/function_reference/size.html">Size</a></span></dt>
<dt><span class="section"><a href="boost_icl/function_reference/range.html">Range</a></span></dt>
<dt><span class="section"><a href="boost_icl/function_reference/selection.html">Selection</a></span></dt>
<dt><span class="section"><a href="boost_icl/function_reference/addition.html">Addition</a></span></dt>
<dt><span class="section"><a href="boost_icl/function_reference/subtraction.html">Subtraction</a></span></dt>
<dt><span class="section"><a href="boost_icl/function_reference/insertion.html">Insertion</a></span></dt>
<dt><span class="section"><a href="boost_icl/function_reference/erasure.html">Erasure</a></span></dt>
<dt><span class="section"><a href="boost_icl/function_reference/intersection.html">Intersection</a></span></dt>
<dt><span class="section"><a href="boost_icl/function_reference/symmetric_difference.html">Symmetric
      Difference</a></span></dt>
<dt><span class="section"><a href="boost_icl/function_reference/iterator_related.html">Iterator
      related</a></span></dt>
<dt><span class="section"><a href="boost_icl/function_reference/element_iteration.html">Element
      iteration</a></span></dt>
<dt><span class="section"><a href="boost_icl/function_reference/streaming__conversion.html">Streaming,
      conversion</a></span></dt>
<dt><span class="section"><a href="boost_icl/function_reference/interval_construction.html">Interval
      Construction</a></span></dt>
<dt><span class="section"><a href="boost_icl/function_reference/additional_interval_orderings.html">Additional
      Interval Orderings</a></span></dt>
<dt><span class="section"><a href="boost_icl/function_reference/miscellaneous_interval_functions.html">Miscellaneous
      Interval Functions</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="boost_icl/acknowledgments.html">Acknowledgments</a></span></dt>
<dt><span class="section"><a href="interval_container_library_reference.html">Interval Container Library Reference</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="interval_container_library_reference.html#header.boost.icl.closed_interval_hpp">Header &lt;boost/icl/closed_interval.hpp&gt;</a></span></dt>
<dt><span class="section"><a href="header/boost/icl/continuous_interval_hpp.html">Header &lt;boost/icl/continuous_interval.hpp&gt;</a></span></dt>
<dt><span class="section"><a href="header/boost/icl/discrete_interval_hpp.html">Header &lt;boost/icl/discrete_interval.hpp&gt;</a></span></dt>
<dt><span class="section"><a href="header/boost/icl/dynamic_interval_traits_hpp.html">Header &lt;boost/icl/dynamic_interval_traits.hpp&gt;</a></span></dt>
<dt><span class="section"><a href="header/boost/icl/functors_hpp.html">Header &lt;boost/icl/functors.hpp&gt;</a></span></dt>
<dt><span class="section"><a href="header/boost/icl/gregorian_hpp.html">Header &lt;boost/icl/gregorian.hpp&gt;</a></span></dt>
<dt><span class="section"><a href="header/boost/icl/impl_config_hpp.html">Header &lt;boost/icl/impl_config.hpp&gt;</a></span></dt>
<dt><span class="section"><a href="header/boost/icl/interval_hpp.html">Header &lt;boost/icl/interval.hpp&gt;</a></span></dt>
<dt><span class="section"><a href="header/boost/icl/interval_base_map_hpp.html">Header &lt;boost/icl/interval_base_map.hpp&gt;</a></span></dt>
<dt><span class="section"><a href="header/boost/icl/interval_base_set_hpp.html">Header &lt;boost/icl/interval_base_set.hpp&gt;</a></span></dt>
<dt><span class="section"><a href="header/boost/icl/interval_bounds_hpp.html">Header &lt;boost/icl/interval_bounds.hpp&gt;</a></span></dt>
<dt><span class="section"><a href="header/boost/icl/interval_combining_style_hpp.html">Header &lt;boost/icl/interval_combining_style.hpp&gt;</a></span></dt>
<dt><span class="section"><a href="header/boost/icl/interval_map_hpp.html">Header &lt;boost/icl/interval_map.hpp&gt;</a></span></dt>
<dt><span class="section"><a href="header/boost/icl/interval_set_hpp.html">Header &lt;boost/icl/interval_set.hpp&gt;</a></span></dt>
<dt><span class="section"><a href="header/boost/icl/interval_traits_hpp.html">Header &lt;boost/icl/interval_traits.hpp&gt;</a></span></dt>
<dt><span class="section"><a href="header/boost/icl/iterator_hpp.html">Header &lt;boost/icl/iterator.hpp&gt;</a></span></dt>
<dt><span class="section"><a href="header/boost/icl/left_open_interval_hpp.html">Header &lt;boost/icl/left_open_interval.hpp&gt;</a></span></dt>
<dt><span class="section"><a href="header/boost/icl/map_hpp.html">Header &lt;boost/icl/map.hpp&gt;</a></span></dt>
<dt><span class="section"><a href="header/boost/icl/open_interval_hpp.html">Header &lt;boost/icl/open_interval.hpp&gt;</a></span></dt>
<dt><span class="section"><a href="header/boost/icl/ptime_hpp.html">Header &lt;boost/icl/ptime.hpp&gt;</a></span></dt>
<dt><span class="section"><a href="header/boost/icl/rational_hpp.html">Header &lt;boost/icl/rational.hpp&gt;</a></span></dt>
<dt><span class="section"><a href="header/boost/icl/right_open_interval_hpp.html">Header &lt;boost/icl/right_open_interval.hpp&gt;</a></span></dt>
<dt><span class="section"><a href="header/boost/icl/separate_interval_set_hpp.html">Header &lt;boost/icl/separate_interval_set.hpp&gt;</a></span></dt>
<dt><span class="section"><a href="header/boost/icl/split_interval_map_hpp.html">Header &lt;boost/icl/split_interval_map.hpp&gt;</a></span></dt>
<dt><span class="section"><a href="header/boost/icl/split_interval_set_hpp.html">Header &lt;boost/icl/split_interval_set.hpp&gt;</a></span></dt>
</dl></dd>
</dl>
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="boost_icl.introduction"></a><a class="link" href="index.html#boost_icl.introduction" title="Introduction">Introduction</a>
</h2></div></div></div>
<div class="toc"><dl class="toc">
<dt><span class="section"><a href="index.html#boost_icl.introduction.definition_and_basic_example">Definition
      and Basic Example</a></span></dt>
<dt><span class="section"><a href="index.html#boost_icl.introduction.icl_s_class_templates">Icl's class
      templates</a></span></dt>
<dt><span class="section"><a href="index.html#boost_icl.introduction.interval_combining_styles">Interval
      Combining Styles</a></span></dt>
</dl></div>
<p>
      <span class="quote">&#8220;<span class="quote">A bug crawls across the boost docs on my laptop screen. Let him be!
      We need all the readers we can get.</span>&#8221;</span> -- Freely adapted from <a href="http://en.wikipedia.org/wiki/Jack_Kornfield" target="_top">Jack
      Kornfield</a>
    </p>
<p>
      Intervals are almost ubiquitous in software development. Yet they are very
      easily coded into user defined classes by a pair of numbers so they are only
      <span class="emphasis"><em>implicitly</em></span> used most of the time. The meaning of an interval
      is simple. They represent all the elements between their lower and upper bound
      and thus a set. But unlike sets, intervals usually can not be added to a single
      new interval. If you want to add intervals to a collection of intervals that
      does still represent a <span class="emphasis"><em>set</em></span>, you arrive at the idea of
      <span class="emphasis"><em>interval_sets</em></span> provided by this library.
    </p>
<p>
      Interval containers of the <span class="bold"><strong>ICL</strong></span> have been developed
      initially at <a href="http://www.cortex-software.de/desktopdefault.aspx" target="_top">Cortex
      Software GmbH</a> to solve problems related to date and time interval computations
      in the context of a Hospital Information System. Time intervals with associated
      values like <span class="emphasis"><em>amount of invoice</em></span> or <span class="emphasis"><em>set of therapies</em></span>
      had to be manipulated in statistics, billing programs and therapy scheduling
      programs. So the <span class="bold"><strong>ICL</strong></span> emerged out of those
      industrial use cases. It extracts generic code that helps to solve common problems
      from the date and time problem domain and can be beneficial in other fields
      as well.
    </p>
<p>
      One of the most advantageous aspects of interval containers is their very compact
      representation of sets and maps. Working with sets and maps <span class="emphasis"><em>of elements</em></span>
      can be very inefficient, if in a given problem domain, elements are typically
      occurring in contiguous chunks. Besides a compact representation of associative
      containers, that can reduce the cost of space and time drastically, the ICL
      comes with a universal mechanism of aggregation, that allows to combine associated
      values in meaningful ways when intervals overlap on insertion.
    </p>
<p>
      For a condensed introduction and overview you may want to look at the <a href="http://www.herold-faulhaber.de/boost_icl/doc/libs/icl/doc/boostcon09/intro_to_itl.pdf" target="_top">presentation
      material on the <span class="bold"><strong>ICL</strong></span> from <span class="emphasis"><em><span class="bold"><strong>BoostCon2009</strong></span></em></span></a>.
    </p>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_icl.introduction.definition_and_basic_example"></a><a class="link" href="index.html#boost_icl.introduction.definition_and_basic_example" title="Definition and Basic Example">Definition
      and Basic Example</a>
</h3></div></div></div>
<p>
        The <span class="bold"><strong>Interval Container Library (ICL)</strong></span> provides
        <code class="computeroutput"><a class="link" href="boost/icl/interval.html" title="Struct template interval">intervals</a></code> and two kinds
        of interval containers: <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/interval_map.html" title="Class template interval_map">interval_maps</a></code>.
      </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
            An <code class="computeroutput"><a class="link" href="boost/icl/interval_base_set.html" title="Class template interval_base_set">interval_set</a></code>
            is a <span class="bold"><strong>set</strong></span> that is implemented as a set
            of intervals.
          </li>
<li class="listitem">
            An <code class="computeroutput"><a class="link" href="boost/icl/interval_base_map.html" title="Class template interval_base_map">interval_map</a></code>
            is a <span class="bold"><strong>map</strong></span> that is implemented as a map
            of interval value pairs.
          </li>
</ul></div>
<h5>
<a name="boost_icl.introduction.definition_and_basic_example.h0"></a>
        <span class="phrase"><a name="boost_icl.introduction.definition_and_basic_example.two_aspects"></a></span><a class="link" href="index.html#boost_icl.introduction.definition_and_basic_example.two_aspects">Two
        Aspects</a>
      </h5>
<p>
        <code class="computeroutput"><a class="link" href="boost/icl/interval_base_set.html" title="Class template interval_base_set">Interval_sets</a></code>
        and <code class="computeroutput"><a class="link" href="boost/icl/interval_base_map.html" title="Class template interval_base_map">interval_maps</a></code>
        expose two different aspects in their interfaces: (1) The functionality of
        a set or a map, which is the more <span class="emphasis"><em><span class="bold"><strong>abstract
        aspect</strong></span></em></span>. And (2) the functionality of a container of
        intervals which is the more specific and <span class="emphasis"><em><span class="bold"><strong>implementation
        related aspect</strong></span></em></span>. In practice both aspects are useful
        and are therefore supported.
      </p>
<p>
        The first aspect, that will be called <span class="emphasis"><em><span class="bold"><strong>fundamental</strong></span></em></span>
        <span class="emphasis"><em><span class="bold"><strong>aspect</strong></span></em></span>, is the more
        important one. It means that we can use an <code class="computeroutput"><a class="link" href="boost/icl/interval_set.html" title="Class template interval_set">interval_set</a></code>
        or <code class="computeroutput"><a class="link" href="boost/icl/interval_map.html" title="Class template interval_map">interval_map</a></code> like
        a set or map <span class="emphasis"><em><span class="bold"><strong>of elements</strong></span></em></span>.
        It exposes the same functions.
</p>
<pre class="programlisting"><span class="identifier">interval_set</span><span class="special">&lt;</span><span class="keyword">int</span><span class="special">&gt;</span> <span class="identifier">mySet</span><span class="special">;</span>
<span class="identifier">mySet</span><span class="special">.</span><span class="identifier">insert</span><span class="special">(</span><span class="number">42</span><span class="special">);</span>
<span class="keyword">bool</span> <span class="identifier">has_answer</span> <span class="special">=</span> <span class="identifier">contains</span><span class="special">(</span><span class="identifier">mySet</span><span class="special">,</span> <span class="number">42</span><span class="special">);</span>
</pre>
<p>
      </p>
<p>
        The second aspect, that will be called <span class="emphasis"><em><span class="bold"><strong>segmental</strong></span></em></span>
        <span class="emphasis"><em><span class="bold"><strong>aspect</strong></span></em></span>, allows to exploit
        the fact, that the elements of <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/interval_map.html" title="Class template interval_map">interval_maps</a></code> are
        clustered in <span class="emphasis"><em><span class="bold"><strong>intervals</strong></span></em></span>
        or <span class="emphasis"><em><span class="bold"><strong>segments</strong></span></em></span> that we
        can iterate over.
      </p>
<p>
</p>
<pre class="programlisting"><span class="comment">// Switch on my favorite telecasts using an interval_set</span>
<span class="identifier">interval</span><span class="special">&lt;</span><span class="identifier">seconds</span><span class="special">&gt;::</span><span class="identifier">type</span> <span class="identifier">news</span><span class="special">(</span><span class="identifier">make_seconds</span><span class="special">(</span><span class="string">"20:00:00"</span><span class="special">),</span> <span class="identifier">make_seconds</span><span class="special">(</span><span class="string">"20:15:00"</span><span class="special">));</span>
<span class="identifier">interval</span><span class="special">&lt;</span><span class="identifier">seconds</span><span class="special">&gt;::</span><span class="identifier">type</span> <span class="identifier">talk_show</span><span class="special">(</span><span class="identifier">make_seconds</span><span class="special">(</span><span class="string">"22:45:30"</span><span class="special">),</span> <span class="identifier">make_seconds</span><span class="special">(</span><span class="string">"23:30:50"</span><span class="special">));</span>
<span class="identifier">interval_set</span><span class="special">&lt;</span><span class="identifier">seconds</span><span class="special">&gt;</span> <span class="identifier">myTvProgram</span><span class="special">;</span>
<span class="identifier">myTvProgram</span><span class="special">.</span><span class="identifier">add</span><span class="special">(</span><span class="identifier">news</span><span class="special">).</span><span class="identifier">add</span><span class="special">(</span><span class="identifier">talk_show</span><span class="special">);</span>

<span class="comment">// Iterating over elements (seconds) would be silly ...</span>
<span class="keyword">for</span><span class="special">(</span><span class="identifier">interval_set</span><span class="special">&lt;</span><span class="identifier">seconds</span><span class="special">&gt;::</span><span class="identifier">iterator</span> <span class="identifier">telecast</span> <span class="special">=</span> <span class="identifier">myTvProgram</span><span class="special">.</span><span class="identifier">begin</span><span class="special">();</span>
    <span class="identifier">telecast</span> <span class="special">!=</span> <span class="identifier">myTvProgram</span><span class="special">.</span><span class="identifier">end</span><span class="special">();</span> <span class="special">++</span><span class="identifier">telecast</span><span class="special">)</span>
    <span class="comment">//...so this iterates over intervals</span>
   <span class="identifier">TV</span><span class="special">.</span><span class="identifier">switch_on</span><span class="special">(*</span><span class="identifier">telecast</span><span class="special">);</span>
</pre>
<p>
      </p>
<p>
        Working with <code class="computeroutput"><a class="link" href="boost/icl/interval_base_set.html" title="Class template interval_base_set">interval_sets</a></code>
        and <code class="computeroutput"><a class="link" href="boost/icl/interval_base_map.html" title="Class template interval_base_map">interval_maps</a></code>
        can be beneficial whenever the elements of sets appear in contiguous chunks:
        <code class="computeroutput"><a class="link" href="boost/icl/interval.html" title="Struct template interval">intervals</a></code>. This is obviously
        the case in many problem domains, particularly in fields that deal with computations
        related to date and time.
      </p>
<h5>
<a name="boost_icl.introduction.definition_and_basic_example.h1"></a>
        <span class="phrase"><a name="boost_icl.introduction.definition_and_basic_example.addabitlity_and_subtractability"></a></span><a class="link" href="index.html#boost_icl.introduction.definition_and_basic_example.addabitlity_and_subtractability">Addabitlity
        and Subtractability</a>
      </h5>
<p>
        Unlike <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">sets</span></code> and <code class="computeroutput"><span class="identifier">maps</span></code>,
        <code class="computeroutput"><a class="link" href="boost/icl/interval_base_set.html" title="Class template interval_base_set">interval_sets</a></code>
        and <code class="computeroutput"><a class="link" href="boost/icl/interval_base_map.html" title="Class template interval_base_map">interval_maps</a></code>
        implement concept <code class="computeroutput"><span class="identifier">Addable</span></code>
        and <code class="computeroutput"><span class="identifier">Subtractable</span></code>. So <code class="computeroutput"><a class="link" href="boost/icl/interval_base_set.html" title="Class template interval_base_set">interval_sets</a></code> define an
        <code class="computeroutput"><span class="keyword">operator</span> <span class="special">+=</span></code>
        that is naturally implemented as <span class="emphasis"><em><span class="bold"><strong>set union</strong></span></em></span>
        and an <code class="computeroutput"><span class="keyword">operator</span> <span class="special">-=</span></code>
        that is consequently implemented as <span class="emphasis"><em><span class="bold"><strong>set difference</strong></span></em></span>.
        In the <span class="bold"><strong>Icl</strong></span> <code class="computeroutput"><a class="link" href="boost/icl/interval_base_map.html" title="Class template interval_base_map">interval_maps</a></code>
        are addable and subtractable as well. It turned out to be a very fruitful
        concept to propagate the addition or subtraction to the <code class="computeroutput"><a class="link" href="boost/icl/interval_base_map.html" title="Class template interval_base_map">interval_map's</a></code>
        associated values in cases where the insertion of an interval value pair
        into an <code class="computeroutput"><a class="link" href="boost/icl/interval_map.html" title="Class template interval_map">interval_map</a></code>
        resulted in a collision of the inserted interval value pair with interval
        value pairs, that are already in the <code class="computeroutput"><a class="link" href="boost/icl/interval_map.html" title="Class template interval_map">interval_map</a></code>.
        This operation propagation is called <span class="emphasis"><em><span class="bold"><strong>aggregate
        on overlap</strong></span></em></span>.
      </p>
<h5>
<a name="boost_icl.introduction.definition_and_basic_example.h2"></a>
        <span class="phrase"><a name="boost_icl.introduction.definition_and_basic_example.aggregate_on_overlap"></a></span><a class="link" href="index.html#boost_icl.introduction.definition_and_basic_example.aggregate_on_overlap">Aggregate
        on Overlap</a>
      </h5>
<p>
        This is a first motivating example of a very small party, demonstrating the
        <span class="emphasis"><em><span class="bold"><strong>aggregate on overlap</strong></span></em></span>
        principle on <code class="computeroutput"><a class="link" href="boost/icl/interval_map.html" title="Class template interval_map">interval_maps</a></code>:
      </p>
<p>
        In the example Mary enters the party first. She attends during the time interval
        <code class="computeroutput"><span class="special">[</span><span class="number">20</span><span class="special">:</span><span class="number">00</span><span class="special">,</span><span class="number">22</span><span class="special">:</span><span class="number">00</span><span class="special">)</span></code>. Harry enters later. He stays within <code class="computeroutput"><span class="special">[</span><span class="number">21</span><span class="special">:</span><span class="number">00</span><span class="special">,</span><span class="number">23</span><span class="special">:</span><span class="number">00</span><span class="special">)</span></code>.
</p>
<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">set</span><span class="special">&lt;</span><span class="identifier">string</span><span class="special">&gt;</span> <span class="identifier">guests</span><span class="special">;</span>
<span class="identifier">interval_map</span><span class="special">&lt;</span><span class="identifier">time</span><span class="special">,</span> <span class="identifier">guests</span><span class="special">&gt;</span> <span class="identifier">party</span><span class="special">;</span>
<span class="identifier">party</span> <span class="special">+=</span> <span class="identifier">make_pair</span><span class="special">(</span><span class="identifier">interval</span><span class="special">&lt;</span><span class="identifier">time</span><span class="special">&gt;::</span><span class="identifier">right_open</span><span class="special">(</span><span class="identifier">time</span><span class="special">(</span><span class="string">"20:00"</span><span class="special">),</span> <span class="identifier">time</span><span class="special">(</span><span class="string">"22:00"</span><span class="special">)),</span> <span class="identifier">guests</span><span class="special">(</span><span class="string">"Mary"</span><span class="special">));</span>
<span class="identifier">party</span> <span class="special">+=</span> <span class="identifier">make_pair</span><span class="special">(</span><span class="identifier">interval</span><span class="special">&lt;</span><span class="identifier">time</span><span class="special">&gt;::</span><span class="identifier">right_open</span><span class="special">(</span><span class="identifier">time</span><span class="special">(</span><span class="string">"21:00"</span><span class="special">),</span> <span class="identifier">time</span><span class="special">(</span><span class="string">"23:00"</span><span class="special">)),</span> <span class="identifier">guests</span><span class="special">(</span><span class="string">"Harry"</span><span class="special">));</span>
<span class="comment">// party now contains</span>
<span class="special">[</span><span class="number">20</span><span class="special">:</span><span class="number">00</span><span class="special">,</span> <span class="number">21</span><span class="special">:</span><span class="number">00</span><span class="special">)-&gt;{</span><span class="string">"Mary"</span><span class="special">}</span>
<span class="special">[</span><span class="number">21</span><span class="special">:</span><span class="number">00</span><span class="special">,</span> <span class="number">22</span><span class="special">:</span><span class="number">00</span><span class="special">)-&gt;{</span><span class="string">"Harry"</span><span class="special">,</span><span class="string">"Mary"</span><span class="special">}</span> <span class="comment">//guest sets aggregated on overlap</span>
<span class="special">[</span><span class="number">22</span><span class="special">:</span><span class="number">00</span><span class="special">,</span> <span class="number">23</span><span class="special">:</span><span class="number">00</span><span class="special">)-&gt;{</span><span class="string">"Harry"</span><span class="special">}</span>
</pre>
<p>
        <span class="emphasis"><em><span class="bold"><strong>On overlap of intervals</strong></span></em></span>,
        the corresponding name sets are <span class="emphasis"><em><span class="bold"><strong>accumulated</strong></span></em></span>.
        At the <span class="emphasis"><em><span class="bold"><strong>points of overlap</strong></span></em></span>
        the intervals are <span class="emphasis"><em><span class="bold"><strong>split</strong></span></em></span>.
        The accumulation of content on overlap of intervals is done via an <code class="computeroutput"><span class="keyword">operator</span> <span class="special">+=</span></code>
        that has to be implemented for the associated values of the <code class="computeroutput"><a class="link" href="boost/icl/interval_map.html" title="Class template interval_map">interval_map</a></code>.
        In the example the associated values are <code class="computeroutput"><span class="identifier">guest</span>
        <span class="identifier">sets</span></code>. Thus a <code class="computeroutput"><span class="identifier">guest</span>
        <span class="identifier">set</span></code> has to implement <code class="computeroutput"><span class="keyword">operator</span> <span class="special">+=</span></code>
        as set union.
      </p>
<p>
        As can be seen from the example an <code class="computeroutput"><a class="link" href="boost/icl/interval_map.html" title="Class template interval_map">interval_map</a></code>
        has both a <span class="emphasis"><em><span class="bold"><strong>decompositional behavior</strong></span></em></span>
        (on the time dimension) as well as an <span class="emphasis"><em><span class="bold"><strong>accumulative
        one</strong></span></em></span> (on the associated values).
      </p>
<p>
        Addability and aggregate on overlap are useful features on <code class="computeroutput"><a class="link" href="boost/icl/interval_map.html" title="Class template interval_map">interval_maps</a></code>
        implemented via function <code class="computeroutput"><span class="identifier">add</span></code>
        and <code class="computeroutput"><span class="keyword">operator</span> <span class="special">+=</span></code>.
        But you can also use them with the <span class="emphasis"><em>traditional</em></span> <a class="link" href="boost_icl/function_reference/insertion.html" title="Insertion">insert semantics</a>
        that behaves like <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">map</span><span class="special">::</span><span class="identifier">insert</span></code>
        generalized for interval insertion.
      </p>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_icl.introduction.icl_s_class_templates"></a><a class="link" href="index.html#boost_icl.introduction.icl_s_class_templates" title="Icl's class templates">Icl's class
      templates</a>
</h3></div></div></div>
<p>
        In addition to interval containers we can work with containers of elements
        that are <span class="emphasis"><em><span class="bold"><strong>behavioral equal</strong></span></em></span>
        to the interval containers: On the fundamental aspect they have exactly the
        same functionality. An <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> of the STL is such an equivalent set implementation. Due to the
        aggregation facilities of the icl's interval maps <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">map</span></code>
        </a> is fundamentally not completely equivalent to an <code class="computeroutput"><a class="link" href="boost/icl/interval_map.html" title="Class template interval_map">interval_map</a></code>.
        Therefore there is an extra <code class="computeroutput"><a class="link" href="boost/icl/map.html" title="Class template map">icl::map</a></code>
        class template for maps of elements in the icl.
      </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
            The <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> is behavioral equal to
            <code class="computeroutput"><a class="link" href="boost/icl/interval_base_set.html" title="Class template interval_base_set">interval_sets</a></code>
            on the <span class="emphasis"><em><span class="bold"><strong>fundamental</strong></span></em></span>
            aspect.
          </li>
<li class="listitem">
            An <code class="computeroutput"><a class="link" href="boost/icl/map.html" title="Class template map">icl::map</a></code> is behavioral
            equal to <code class="computeroutput"><a class="link" href="boost/icl/interval_base_map.html" title="Class template interval_base_map">interval_maps</a></code>
            on the <span class="emphasis"><em><span class="bold"><strong>fundamental</strong></span></em></span>
            aspect. Specifically an <code class="computeroutput"><a class="link" href="boost/icl/map.html" title="Class template map">icl::map</a></code>
            implements <span class="emphasis"><em><span class="bold"><strong>aggregate on overlap</strong></span></em></span>,
            which is named <span class="emphasis"><em><span class="bold"><strong>aggregate on collision</strong></span></em></span>
            for an element container.
          </li>
</ul></div>
<p>
        The following tables give an overview over the main class templates provided
        by the <span class="bold"><strong>icl</strong></span>.
      </p>
<div class="table">
<a name="boost_icl.introduction.icl_s_class_templates.t0"></a><p class="title"><b>Table&#160;1.1.&#160;Interval class templates</b></p>
<div class="table-contents"><table class="table" summary="Interval class templates">
<colgroup>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  group
                </p>
              </th>
<th>
                <p>
                  form
                </p>
              </th>
<th>
                <p>
                  template
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  statically bounded
                </p>
              </td>
<td>
                <p>
                  asymmetric
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput"><a class="link" href="boost/icl/right_open_interval.html" title="Class template right_open_interval">right_open_interval</a></code>
                </p>
              </td>
</tr>
<tr>
<td>
              </td>
<td>
              </td>
<td>
                <p>
                  <code class="computeroutput"><a class="link" href="boost/icl/left_open_interval.html" title="Class template left_open_interval">left_open_interval</a></code>
                </p>
              </td>
</tr>
<tr>
<td>
              </td>
<td>
                <p>
                  symmetric
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput"><a class="link" href="boost/icl/closed_interval.html" title="Class template closed_interval">closed_interval</a></code>
                </p>
              </td>
</tr>
<tr>
<td>
              </td>
<td>
              </td>
<td>
                <p>
                  <code class="computeroutput"><a class="link" href="boost/icl/open_interval.html" title="Class template open_interval">open_interval</a></code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  dynamically bounded
                </p>
              </td>
<td>
              </td>
<td>
                <p>
                  <code class="computeroutput"><a class="link" href="boost/icl/discrete_interval.html" title="Class template discrete_interval">discrete_interval</a></code>
                </p>
              </td>
</tr>
<tr>
<td>
              </td>
<td>
              </td>
<td>
                <p>
                  <code class="computeroutput"><a class="link" href="boost/icl/continuous_interval.html" title="Class template continuous_interval">continuous_interval</a></code>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><p>
        Statically bounded intervals always have the same kind of interval borders,
        e.g. right open borders<code class="computeroutput"><span class="special">[</span><span class="identifier">a</span><span class="special">..</span><span class="identifier">b</span><span class="special">)</span></code>
        for <code class="computeroutput"><a class="link" href="boost/icl/right_open_interval.html" title="Class template right_open_interval">right_open_interval</a></code>.
        Dynamically bounded intervals can have different borders. Refer to the chapter
        about <a class="link" href="boost_icl/interface.html#boost_icl.interface.class_templates.intervals" title="Intervals"><span class="emphasis"><em><span class="bold"><strong>intervals</strong></span></em></span></a> for details.
      </p>
<div class="table">
<a name="boost_icl.introduction.icl_s_class_templates.t1"></a><p class="title"><b>Table&#160;1.2.&#160;Container class templates</b></p>
<div class="table-contents"><table class="table" summary="Container class templates">
<colgroup>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  granularity
                </p>
              </th>
<th>
                <p>
                  style
                </p>
              </th>
<th>
                <p>
                  sets
                </p>
              </th>
<th>
                <p>
                  maps
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  interval
                </p>
              </td>
<td>
                <p>
                  joining
                </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>
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput"><a class="link" href="boost/icl/interval_map.html" title="Class template interval_map">interval_map</a></code>
                </p>
              </td>
</tr>
<tr>
<td>
              </td>
<td>
                <p>
                  separating
                </p>
              </td>
<td>
                <p>
                  <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>
              </td>
</tr>
<tr>
<td>
              </td>
<td>
                <p>
                  splitting
                </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>
                  <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>
</tr>
<tr>
<td>
                <p>
                  element
                </p>
              </td>
<td>
              </td>
<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>
                  <code class="computeroutput"><a class="link" href="boost/icl/map.html" title="Class template map">map</a></code>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><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> is placed in paretheses, because it is not a class template of the
        <span class="bold"><strong>ICL</strong></span>. It can be used as element container
        though that is behavioral equal to the ICL's interval sets on their fundamental
        aspect. Column <span class="emphasis"><em><span class="bold"><strong>style</strong></span></em></span>
        refers to the different ways in which interval containers combine added intervals.
        These <span class="emphasis"><em><span class="bold"><strong>combining styles</strong></span></em></span>
        are described in the next section.
      </p>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_icl.introduction.interval_combining_styles"></a><a class="link" href="index.html#boost_icl.introduction.interval_combining_styles" title="Interval Combining Styles">Interval
      Combining Styles</a>
</h3></div></div></div>
<p>
        When we add intervals or interval value pairs to interval containers, the
        intervals can be added in different ways: Intervals can be joined or split
        or kept separate. The different interval combining styles are shown by example
        in the tables below.
      </p>
<div class="table">
<a name="boost_icl.introduction.interval_combining_styles.t0"></a><p class="title"><b>Table&#160;1.3.&#160;Interval container's ways to combine intervals</b></p>
<div class="table-contents"><table class="table" summary="Interval container's ways to combine intervals">
<colgroup>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  joining
                </p>
              </th>
<th>
                <p>
                  separating
                </p>
              </th>
<th>
                <p>
                  splitting
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  set
                </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>
                </p>
              </td>
<td>
                <p>
                  <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>
                  <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>
</tr>
<tr>
<td>
                <p>
                  map
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput"><a class="link" href="boost/icl/interval_map.html" title="Class template interval_map">interval_map</a></code>
                </p>
              </td>
<td>
              </td>
<td>
                <p>
                  <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>
</tr>
<tr>
<td>
              </td>
<td>
                <p>
                  Intervals are joined on overlap or touch<br> (if associated values
                  are equal).
                </p>
              </td>
<td>
                <p>
                  Intervals are joined on overlap, not on touch.
                </p>
              </td>
<td>
                <p>
                  Intervals are split on overlap.<br> All interval borders are
                  preserved.
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="boost_icl.introduction.interval_combining_styles.t1"></a><p class="title"><b>Table&#160;1.4.&#160;Interval combining styles by example</b></p>
<div class="table-contents"><table class="table" summary="Interval combining styles by example">
<colgroup>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  joining
                </p>
              </th>
<th>
                <p>
                  separating
                </p>
              </th>
<th>
                <p>
                  splitting
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  set
                </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>
                  <span class="emphasis"><em>A</em></span>
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput"><a class="link" href="boost/icl/separate_interval_set.html" title="Class template separate_interval_set">separate_interval_set</a></code>
                  <span class="emphasis"><em>B</em></span>
                </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>
                  <span class="emphasis"><em>C</em></span>
                </p>
              </td>
</tr>
<tr>
<td>
              </td>
<td>
                <p>
</p>
<pre class="programlisting">  <span class="special">{[</span><span class="number">1</span>      <span class="number">3</span><span class="special">)</span>          <span class="special">}</span>
<span class="special">+</span>       <span class="special">[</span><span class="number">2</span>      <span class="number">4</span><span class="special">)</span>
<span class="special">+</span>                 <span class="special">[</span><span class="number">4</span> <span class="number">5</span><span class="special">)</span>
<span class="special">=</span> <span class="special">{[</span><span class="number">1</span>                <span class="number">5</span><span class="special">)}</span></pre>
<p>
                </p>
              </td>
<td>
                <p>
</p>
<pre class="programlisting">  <span class="special">{[</span><span class="number">1</span>      <span class="number">3</span><span class="special">)}</span>         <span class="special">}</span>
<span class="special">+</span>       <span class="special">[</span><span class="number">2</span>      <span class="number">4</span><span class="special">)</span>
<span class="special">+</span>                 <span class="special">[</span><span class="number">4</span> <span class="number">5</span><span class="special">)</span>
<span class="special">=</span> <span class="special">{[</span><span class="number">1</span>           <span class="number">4</span><span class="special">)[</span><span class="number">4</span> <span class="number">5</span><span class="special">)}</span></pre>
<p>
                </p>
              </td>
<td>
                <p>
</p>
<pre class="programlisting">  <span class="special">{[</span><span class="number">1</span>      <span class="number">3</span><span class="special">)</span>          <span class="special">}</span>
<span class="special">+</span>       <span class="special">[</span><span class="number">2</span>      <span class="number">4</span><span class="special">)</span>
<span class="special">+</span>                 <span class="special">[</span><span class="number">4</span> <span class="number">5</span><span class="special">)</span>
<span class="special">=</span> <span class="special">{[</span><span class="number">1</span> <span class="number">2</span><span class="special">)[</span><span class="number">2</span> <span class="number">3</span><span class="special">)[</span><span class="number">3</span> <span class="number">4</span><span class="special">)[</span><span class="number">4</span> <span class="number">5</span><span class="special">)}</span></pre>
<p>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  map
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput"><a class="link" href="boost/icl/interval_map.html" title="Class template interval_map">interval_map</a></code>
                  <span class="emphasis"><em>D</em></span>
                </p>
              </td>
<td>
              </td>
<td>
                <p>
                  <code class="computeroutput"><a class="link" href="boost/icl/split_interval_map.html" title="Class template split_interval_map">split_interval_map</a></code>
                  <span class="emphasis"><em>E</em></span>
                </p>
              </td>
</tr>
<tr>
<td>
              </td>
<td>
                <p>
</p>
<pre class="programlisting">  <span class="special">{[</span><span class="number">1</span>      <span class="number">3</span><span class="special">)-&gt;</span><span class="number">1</span>          <span class="special">}</span>
<span class="special">+</span>       <span class="special">[</span><span class="number">2</span>      <span class="number">4</span><span class="special">)-&gt;</span><span class="number">1</span>
<span class="special">+</span>                 <span class="special">[</span><span class="number">4</span> <span class="number">5</span><span class="special">)-&gt;</span><span class="number">1</span>
<span class="special">=</span> <span class="special">{[</span><span class="number">1</span> <span class="number">2</span><span class="special">)[</span><span class="number">2</span> <span class="number">3</span><span class="special">)[</span><span class="number">3</span>      <span class="number">5</span><span class="special">)</span>   <span class="special">}</span>
  <span class="special">|</span> <span class="special">-&gt;</span><span class="number">1</span>  <span class="special">-&gt;</span><span class="number">2</span>     <span class="special">-&gt;</span><span class="number">1</span>      <span class="special">|</span></pre>
<p>
                </p>
              </td>
<td>
              </td>
<td>
                <p>
</p>
<pre class="programlisting">  <span class="special">{[</span><span class="number">1</span>      <span class="number">3</span><span class="special">)-&gt;</span><span class="number">1</span>          <span class="special">}</span>
<span class="special">+</span>       <span class="special">[</span><span class="number">2</span>      <span class="number">4</span><span class="special">)-&gt;</span><span class="number">1</span>
<span class="special">+</span>                 <span class="special">[</span><span class="number">4</span> <span class="number">5</span><span class="special">)-&gt;</span><span class="number">1</span>
<span class="special">=</span> <span class="special">{[</span><span class="number">1</span> <span class="number">2</span><span class="special">)[</span><span class="number">2</span> <span class="number">3</span><span class="special">)[</span><span class="number">3</span> <span class="number">4</span><span class="special">)[</span><span class="number">4</span> <span class="number">5</span><span class="special">)</span>   <span class="special">}</span>
  <span class="special">|</span> <span class="special">-&gt;</span><span class="number">1</span>  <span class="special">-&gt;</span><span class="number">2</span>  <span class="special">-&gt;</span><span class="number">1</span>  <span class="special">-&gt;</span><span class="number">1</span>    <span class="special">|</span></pre>
<p>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><p>
        Note that <code class="literal">interval_sets</code> <span class="emphasis"><em>A</em></span>, <span class="emphasis"><em>B</em></span>
        and <span class="emphasis"><em>C</em></span> represent the same set of elements <code class="literal">{1,2,3,4}</code>
        and <code class="literal">interval_maps</code> <span class="emphasis"><em>D</em></span> and <span class="emphasis"><em>E</em></span>
        represent the same map of elements <code class="literal">{1-&gt;1, 2-&gt;2, 3-&gt;1, 4-&gt;1}</code>.
        See example program <a class="link" href="boost_icl/examples/interval_container.html" title="Interval container">Interval
        container</a> for an additional demo.
      </p>
<h5>
<a name="boost_icl.introduction.interval_combining_styles.h0"></a>
        <span class="phrase"><a name="boost_icl.introduction.interval_combining_styles.joining_interval_containers"></a></span><a class="link" href="index.html#boost_icl.introduction.interval_combining_styles.joining_interval_containers">Joining
        interval containers</a>
      </h5>
<p>
        <code class="computeroutput"><a class="link" href="boost/icl/interval_set.html" title="Class template interval_set">Interval_set</a></code> and <code class="computeroutput"><a class="link" href="boost/icl/interval_map.html" title="Class template interval_map">interval_map</a></code> are always in a
        <span class="emphasis"><em><span class="bold"><strong>minimal representation</strong></span></em></span>.
        This is useful in many cases, where the points of insertion or intersection
        of intervals are not relevant. So in most instances <code class="computeroutput"><a class="link" href="boost/icl/interval_set.html" title="Class template interval_set">interval_set</a></code>
        and <code class="computeroutput"><a class="link" href="boost/icl/interval_map.html" title="Class template interval_map">interval_map</a></code> will
        be the first choice for an interval container.
      </p>
<h5>
<a name="boost_icl.introduction.interval_combining_styles.h1"></a>
        <span class="phrase"><a name="boost_icl.introduction.interval_combining_styles.splitting_interval_containers"></a></span><a class="link" href="index.html#boost_icl.introduction.interval_combining_styles.splitting_interval_containers">Splitting
        interval containers</a>
      </h5>
<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>
        and <code class="computeroutput"><a class="link" href="boost/icl/split_interval_map.html" title="Class template split_interval_map">split_interval_map</a></code>
        on the contrary have an <span class="emphasis"><em><span class="bold"><strong>insertion memory</strong></span></em></span>.
        They do accumulate interval borders both from additions and intersections.
        This is specifically useful, if we want to enrich an interval container with
        certain time grids, like e.g. months or calendar weeks or both. See example
        <a class="link" href="boost_icl/examples/time_grids.html" title="Time grids for months and weeks">time grids for months and weeks</a>.
      </p>
<h5>
<a name="boost_icl.introduction.interval_combining_styles.h2"></a>
        <span class="phrase"><a name="boost_icl.introduction.interval_combining_styles.separating_interval_containers"></a></span><a class="link" href="index.html#boost_icl.introduction.interval_combining_styles.separating_interval_containers">Separating
        interval containers</a>
      </h5>
<p>
        <code class="computeroutput"><a class="link" href="boost/icl/separate_interval_set.html" title="Class template separate_interval_set">Separate_interval_set</a></code>
        implements the separating style. This style preserves borders, that are never
        passed by an overlapping interval. So if all intervals that are inserted
        into a <code class="computeroutput"><a class="link" href="boost/icl/separate_interval_set.html" title="Class template separate_interval_set">separate_interval_set</a></code>
        are generated form a certain grid that never pass say month borders, then
        these borders are preserved in the <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>
</div>
</div>
<p>
    14:46 15.10.2010
  </p>
</div>
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