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<div class="section boost_icl_function_reference_equivalences_and_orderings" lang="en">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_icl.function_reference.equivalences_and_orderings"></a><a class="link" href="equivalences_and_orderings.html" title="Equivalences and Orderings">Equivalences
and Orderings</a>
</h3></div></div></div>
<div class="toc"><dl>
<dt><span class="section"><a href="equivalences_and_orderings.html#boost_icl.function_reference.equivalences_and_orderings.synopsis">Synopsis</a></span></dt>
<dt><span class="section"><a href="equivalences_and_orderings.html#boost_icl.function_reference.equivalences_and_orderings.less_on_intervals">Less
on Intervals</a></span></dt>
<dt><span class="section"><a href="equivalences_and_orderings.html#boost_icl.function_reference.equivalences_and_orderings.lexicographical_ordering">Lexicographical
Ordering</a></span></dt>
<dt><span class="section"><a href="equivalences_and_orderings.html#boost_icl.function_reference.equivalences_and_orderings.sequential_element_ordering">Sequential
Element Ordering</a></span></dt>
<dt><span class="section"><a href="equivalences_and_orderings.html#boost_icl.function_reference.equivalences_and_orderings.distinct_equality">Distinct
Equality</a></span></dt>
</dl></div>
<div class="section boost_icl_function_reference_equivalences_and_orderings_synopsis" lang="en">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_icl.function_reference.equivalences_and_orderings.synopsis"></a><a class="link" href="equivalences_and_orderings.html#boost_icl.function_reference.equivalences_and_orderings.synopsis" title="Synopsis">Synopsis</a>
</h4></div></div></div>
<div class="informaltable"><table class="table">
<colgroup>
<col>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
<span class="emphasis"><em><span class="bold"><strong>Equivalences and Orderings</strong></span></em></span>
</p>
</th>
<th>
<p>
intervals
</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>
<span class="emphasis"><em>Segment Ordering</em></span>
</p>
</td>
<td>
<p>
</p>
</td>
<td>
<p>
</p>
</td>
<td>
<p>
</p>
</td>
<td>
<p>
</p>
</td>
<td>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="keyword">bool</span> <span class="keyword">operator</span>
<span class="special">==</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span>
<span class="identifier">T</span><span class="special">&amp;)</span></code>
</p>
</td>
<td>
<p>
1
</p>
</td>
<td>
<p>
1
</p>
</td>
<td>
<p>
1
</p>
</td>
<td>
<p>
1
</p>
</td>
<td>
<p>
1
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="keyword">bool</span> <span class="keyword">operator</span>
<span class="special">!=</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span>
<span class="identifier">T</span><span class="special">&amp;)</span></code>
</p>
</td>
<td>
<p>
1
</p>
</td>
<td>
<p>
1
</p>
</td>
<td>
<p>
1
</p>
</td>
<td>
<p>
1
</p>
</td>
<td>
<p>
1
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="keyword">bool</span> <span class="keyword">operator</span>
<span class="special">&lt;</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span>
<span class="identifier">T</span><span class="special">&amp;)</span></code>
</p>
</td>
<td>
<p>
1
</p>
</td>
<td>
<p>
1
</p>
</td>
<td>
<p>
1
</p>
</td>
<td>
<p>
1
</p>
</td>
<td>
<p>
1
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="keyword">bool</span> <span class="keyword">operator</span>
<span class="special">&gt;</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span>
<span class="identifier">T</span><span class="special">&amp;)</span></code>
</p>
</td>
<td>
<p>
1
</p>
</td>
<td>
<p>
1
</p>
</td>
<td>
<p>
1
</p>
</td>
<td>
<p>
1
</p>
</td>
<td>
<p>
1
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="keyword">bool</span> <span class="keyword">operator</span>
<span class="special">&lt;=</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span>
<span class="identifier">T</span><span class="special">&amp;)</span></code>
</p>
</td>
<td>
<p>
1
</p>
</td>
<td>
<p>
1
</p>
</td>
<td>
<p>
1
</p>
</td>
<td>
<p>
1
</p>
</td>
<td>
<p>
1
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="keyword">bool</span> <span class="keyword">operator</span>
<span class="special">&gt;=</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span>
<span class="identifier">T</span><span class="special">&amp;)</span></code>
</p>
</td>
<td>
<p>
1
</p>
</td>
<td>
<p>
1
</p>
</td>
<td>
<p>
1
</p>
</td>
<td>
<p>
1
</p>
</td>
<td>
<p>
1
</p>
</td>
</tr>
<tr>
<td>
<p>
<span class="emphasis"><em>Element Ordering</em></span>
</p>
</td>
<td>
<p>
</p>
</td>
<td>
<p>
</p>
</td>
<td>
<p>
</p>
</td>
<td>
<p>
</p>
</td>
<td>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="keyword">bool</span> <span class="identifier">is_element_equal</span><span class="special">(</span><span class="keyword">const</span>
<span class="identifier">T</span><span class="special">&amp;,</span>
<span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span></code>
</p>
</td>
<td>
<p>
</p>
</td>
<td>
<p>
<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#interval_map_types"><span class="bold"><strong>M</strong></span></a>
</p>
</td>
<td>
<p>
1
</p>
</td>
<td>
<p>
1
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="keyword">bool</span> <span class="identifier">is_element_less</span><span class="special">(</span><span class="keyword">const</span>
<span class="identifier">T</span><span class="special">&amp;,</span>
<span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span></code>
</p>
</td>
<td>
<p>
</p>
</td>
<td>
<p>
<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#interval_map_types"><span class="bold"><strong>M</strong></span></a>
</p>
</td>
<td>
<p>
1
</p>
</td>
<td>
<p>
1
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="keyword">bool</span> <span class="identifier">is_element_greater</span><span class="special">(</span><span class="keyword">const</span>
<span class="identifier">T</span><span class="special">&amp;,</span>
<span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span></code>
</p>
</td>
<td>
<p>
</p>
</td>
<td>
<p>
<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#interval_map_types"><span class="bold"><strong>M</strong></span></a>
</p>
</td>
<td>
<p>
1
</p>
</td>
<td>
<p>
1
</p>
</td>
</tr>
<tr>
<td>
<p>
<span class="emphasis"><em>Distinct Equality</em></span>
</p>
</td>
<td>
<p>
</p>
</td>
<td>
<p>
</p>
</td>
<td>
<p>
</p>
</td>
<td>
<p>
</p>
</td>
<td>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="keyword">bool</span> <span class="identifier">is_distinct_equal</span><span class="special">(</span><span class="keyword">const</span>
<span class="identifier">T</span><span class="special">&amp;,</span>
<span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span></code>
</p>
</td>
<td>
<p>
</p>
</td>
<td>
<p>
</p>
</td>
<td>
<p>
<a class="link" href="../interface/function_synopsis.html#interval_map_types"><span class="bold"><strong>M</strong></span></a>
</p>
</td>
<td>
<p>
</p>
</td>
<td>
<p>
1
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<div class="section boost_icl_function_reference_equivalences_and_orderings_less_on_intervals" lang="en">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_icl.function_reference.equivalences_and_orderings.less_on_intervals"></a><a class="link" href="equivalences_and_orderings.html#boost_icl.function_reference.equivalences_and_orderings.less_on_intervals" title="Less on Intervals">Less
on Intervals</a>
</h4></div></div></div>
<div class="informaltable"><table class="table">
<colgroup>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
</p>
</th>
<th>
<p>
Types
</p>
</th>
<th>
<p>
</p>
</th>
</tr></thead>
<tbody><tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">x</span> <span class="special">&lt;</span>
<span class="identifier">y</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>
<code class="computeroutput"><span class="identifier">x</span></code> begins before
<code class="computeroutput"><span class="identifier">y</span></code> or, for equal
beginnings <code class="computeroutput"><span class="identifier">x</span></code> ends
before <code class="computeroutput"><span class="identifier">y</span></code>
</p>
</td>
</tr></tbody>
</table></div>
</div>
<div class="section boost_icl_function_reference_equivalences_and_orderings_lexicographical_ordering" lang="en">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_icl.function_reference.equivalences_and_orderings.lexicographical_ordering"></a><a class="link" href="equivalences_and_orderings.html#boost_icl.function_reference.equivalences_and_orderings.lexicographical_ordering" title="Lexicographical Ordering">Lexicographical
Ordering</a>
</h4></div></div></div>
<p>
All common equality and compare operators are defined for all objects of
the <span class="bold"><strong>icl</strong></span>. For all <span class="bold"><strong>icl</strong></span>
containers equality and compare operators implement lexicographical equality
and lexicographical comparison, that depends on the equality of template
parameter <code class="computeroutput"><span class="identifier">Compare</span></code>. This
includes the less ordering on intervals, that can be perceived as the sequence
of elements between their lower and upper bound. This generalized lexicogrphical
comparison in intervals can also be specified this way:
</p>
<div class="informaltable"><table class="table">
<colgroup>
<col>
<col>
<col>
</colgroup>
<thead><tr></tr></thead>
<tbody>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">x</span> <span class="special">&lt;</span>
<span class="identifier">y</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="special">:=</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">x</span></code> begins before
<code class="computeroutput"><span class="identifier">y</span></code> or, for equal
beginnings <code class="computeroutput"><span class="identifier">x</span></code> ends
before <code class="computeroutput"><span class="identifier">y</span></code>.
</p>
</td>
</tr>
<tr>
<td>
<p>
</p>
</td>
<td>
<p>
</p>
</td>
<td>
<p>
The other operators can be deduced in the usual way
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">x</span> <span class="special">&gt;</span>
<span class="identifier">y</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="special">:=</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">y</span> <span class="special">&lt;</span>
<span class="identifier">x</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">x</span> <span class="special">&lt;=</span>
<span class="identifier">y</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="special">:=</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="special">!(</span><span class="identifier">y</span>
<span class="special">&lt;</span> <span class="identifier">x</span><span class="special">)</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">x</span> <span class="special">&gt;=</span>
<span class="identifier">y</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="special">:=</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="special">!(</span><span class="identifier">x</span>
<span class="special">&lt;</span> <span class="identifier">y</span><span class="special">)</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">x</span> <span class="special">==</span>
<span class="identifier">y</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="special">:=</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="special">!(</span><span class="identifier">x</span>
<span class="special">&lt;</span> <span class="identifier">y</span><span class="special">)</span> <span class="special">&amp;&amp;</span>
<span class="special">!(</span><span class="identifier">y</span>
<span class="special">&lt;</span> <span class="identifier">x</span><span class="special">)</span></code> induced equivalence
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">x</span> <span class="special">!=</span>
<span class="identifier">y</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="special">:=</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="special">!(</span><span class="identifier">x</span>
<span class="special">==</span> <span class="identifier">y</span><span class="special">)</span></code>
</p>
</td>
</tr>
</tbody>
</table></div>
<p>
Equality and compare operators are defined for all <span class="bold"><strong>icl</strong></span>
objects but there are no overloads between different types.
</p>
<p>
Containers of different segmentation are different, even if their elements
are the same:
</p>
<pre class="programlisting"><span class="identifier">split_interval_set</span><span class="special">&lt;</span><span class="identifier">time</span><span class="special">&gt;</span> <span class="identifier">w1</span><span class="special">,</span> <span class="identifier">w2</span><span class="special">;</span> <span class="comment">//Pseudocode
</span><span class="identifier">w1</span> <span class="special">=</span> <span class="special">{[</span><span class="identifier">Mon</span> <span class="special">..</span> <span class="identifier">Sun</span><span class="special">)};</span> <span class="comment">//split_interval_set containing a week
</span><span class="identifier">w2</span> <span class="special">=</span> <span class="special">{[</span><span class="identifier">Mon</span> <span class="special">..</span> <span class="identifier">Fri</span><span class="special">)[</span><span class="identifier">Sat</span> <span class="special">..</span> <span class="identifier">Sun</span><span class="special">)};</span> <span class="comment">//Same week split in work and week end parts.
</span><span class="identifier">w1</span> <span class="special">==</span> <span class="identifier">w2</span><span class="special">;</span> <span class="comment">//false: Different segmentation
</span><span class="identifier">is_element_equal</span><span class="special">(</span><span class="identifier">w1</span><span class="special">,</span><span class="identifier">w2</span><span class="special">);</span> <span class="comment">//true: Same elements contained
</span></pre>
<p>
</p>
<p>
<span class="bold"><strong>Complexity</strong></span> is <span class="emphasis"><em><span class="bold"><strong>linear</strong></span></em></span>
in the <code class="computeroutput"><span class="identifier">iterative_size</span></code> of
the shorter container to compare.
</p>
</div>
<div class="section boost_icl_function_reference_equivalences_and_orderings_sequential_element_ordering" lang="en">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_icl.function_reference.equivalences_and_orderings.sequential_element_ordering"></a><a class="link" href="equivalences_and_orderings.html#boost_icl.function_reference.equivalences_and_orderings.sequential_element_ordering" title="Sequential Element Ordering">Sequential
Element Ordering</a>
</h4></div></div></div>
<p>
The <span class="emphasis"><em><span class="bold"><strong>Sequential Element Ordering</strong></span></em></span>
abstracts from the way in which elements of interval containers are clustered
into intervals: it's <span class="emphasis"><em><span class="bold"><strong>segmentation</strong></span></em></span>.
</p>
<p>
So these equality and compare operations can be applied within interval
container types. The admissible type combinations are summarized in the
next overload table.
</p>
<p>
</p>
<pre class="programlisting"><span class="comment">// overload tables for
</span><span class="keyword">bool</span> <span class="identifier">is_element_equal</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span>
<span class="keyword">bool</span> <span class="identifier">is_element_less</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span>
<span class="keyword">bool</span> <span class="identifier">is_element_greater</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span>
<span class="identifier">element</span> <span class="identifier">containers</span><span class="special">:</span> <span class="identifier">interval</span> <span class="identifier">containers</span><span class="special">:</span>
<span class="identifier">T</span><span class="special">\</span><span class="identifier">P</span><span class="special">|</span> <span class="identifier">s</span> <span class="identifier">m</span> <span class="identifier">T</span><span class="special">\</span><span class="identifier">P</span><span class="special">|</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="special">---+----</span> <span class="special">---+---------------</span>
<span class="identifier">s</span> <span class="special">|</span> <span class="number">1</span> <span class="identifier">S1</span> <span class="special">|</span> <span class="number">1</span> <span class="number">1</span> <span class="number">1</span>
<span class="identifier">m</span> <span class="special">|</span> <span class="number">1</span> <span class="identifier">S2</span> <span class="special">|</span> <span class="number">1</span> <span class="number">1</span> <span class="number">1</span>
<span class="identifier">S3</span> <span class="special">|</span> <span class="number">1</span> <span class="number">1</span> <span class="number">1</span>
<span class="identifier">M1</span> <span class="special">|</span> <span class="number">1</span> <span class="number">1</span>
<span class="identifier">M3</span> <span class="special">|</span> <span class="number">1</span> <span class="number">1</span>
</pre>
<p>
</p>
<p>
For element containers lexicographical equality and sequential element
equality are identical.
</p>
<p>
The <span class="bold"><strong>complexity</strong></span> of sequential element comparison
functions is <span class="emphasis"><em><span class="bold"><strong>linear</strong></span></em></span>
in the <code class="computeroutput"><span class="identifier">iterative_size</span></code> of
the larger container.
</p>
</div>
<div class="section boost_icl_function_reference_equivalences_and_orderings_distinct_equality" lang="en">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_icl.function_reference.equivalences_and_orderings.distinct_equality"></a><a class="link" href="equivalences_and_orderings.html#boost_icl.function_reference.equivalences_and_orderings.distinct_equality" title="Distinct Equality">Distinct
Equality</a>
</h4></div></div></div>
<p>
<span class="emphasis"><em><span class="bold"><strong>Distinct Equality</strong></span></em></span>
is an equality predicate that is available for <code class="computeroutput"><a class="link" href="../../boost/icl/map.html" title="Class template map">icl::maps</a></code>
and <code class="computeroutput"><a class="link" href="../../boost/icl/interval_map.html" title="Class template interval_map">interval_maps</a></code>.
It yields true, if two maps are sequential element equal except for value
pairs whose associated values are identity elements.
</p>
<p>
<span class="bold"><strong>Complexity</strong></span> is linear in the <code class="computeroutput"><span class="identifier">iterative_size</span></code> of the larger container
to compare.
</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="../semantics.html#boost_icl.semantics.orderings_and_equivalences" title="Orderings and Equivalences"><span class="emphasis"><em><span class="bold"><strong>Semantics</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>
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<td align="right"><div class="copyright-footer">Copyright &#169; 2007 -2010 Joachim Faulhaber<br>Copyright &#169; 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>)
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