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<h1>Non-Unique Mapping Containers</h1>
<p>
This section describes the design of non-unique mapping containers
(multimaps and multisets). It is organized as follows:
</p>
<ol>
<li> The <a href = "#general">Main Points</a> Section describes the main points.
</li>
<li>
The <a href = "#types">Mapped Data Types and Mapped Value Types</a> Section
describes some additional types that each associative container defines.
</li>
<li> The <a href = "generics">Generics</a> Section describes some classes for
generic programming.
</li>
<li> The <a href = "#compound_keys">Compound Keys</a> Section describes an
alternative to the STL's design of using equivalent, non-identical, keys.
</li>
</ol>
<h2><a name = "general">Main Points</a></h2>
<p>
In <tt>pb_assoc</tt>, all associative containers have a unique-key design;
each container can have at most one entry for any given key. Multimaps
are designed as maps from keys to sets; multisets are designed as maps from
keys to non-negative integral types.
</p>
<h2><a name = "types">Mapped Data Types and Mapped Value Types</a></h2>
<p>
The STL's design of associative containers elegantly allows
generic manipulation of containers: each container defines
<tt>data_type</tt> as the domain of its data;
<tt>value_type</tt> as the domain of its relationship. This is not
directly applicable in <tt>pb_assoc</tt>. Consider
a multimap mapping <tt>Key</tt> objects to
<tt>Data_Coll</tt> objects, where
<tt>Data_Coll</tt> is some set-type of <tt>Data</tt>.
Then should the multimap's <tt>value_type</tt> should be
<tt>std::pair<Key, Data></tt> or
<tt>std::pair<Key, Data_Coll></tt>, for example?.
</p>
<p>
<tt>pb_assoc</tt> addresses this by differentiating
between the <i>domain</i> and the <i>type</i> of relationship.
All associative containers define <tt>value_type</tt> as
the relationship's <i>domain</i>, and <tt>mapped_value_type</tt> as its
<i>type</i>. <i>E.g.</i>, both
map types and multimap types may share the same <tt>value_type</tt>,
if they map from the same key domain to
the same data domain. In this case, however, they will not share
the same <tt>mapped_value_type</tt>, since the multimap type maps from the
key domain to the domain of collections of data. The same
differentiation exists between the domain and type of mapped data.
</p>
<p>
In general, the following types describe the relationships
of each associative container:
</p>
<ol>
<li>
<tt>key_type</tt>- This describes the domain of the keys of the container. All
associative containers define this type.
</li>
<li>
<tt>data_type</tt>- This describes the <i>domain</i> of the data mapped by a
key. It is identical to the <tt>data_type</tt> defined by <tt>std::map</tt>, <tt>std::set</tt>,
<tt>std::multimap</tt>, and <tt>std::multiset</tt>. Sets and multisets do not
define this type, since they map each key to the abstract fact that the key is
stored by them.
</li>
<li>
<tt>mapped_data_type</tt>- This describes the <i>type</i> of the data mapped by
a key. For maps, this is the same as <tt>data_type</tt>. For multimaps, this is
not the same as <tt>data_type</tt>; The <tt>mapped_data_type</tt> describes the
collection of <tt>data_type</tt>s used. Sets do not define this type. For
multisets, the <tt>mapped_data_type</tt> describes the unsigned integral type
used to indicate the number of occurrences of a key.
</li>
<li>
<tt>value_type</tt>- This describes the <i>domain</i> of relationships store in
a container. It is identical to the <tt>value_type</tt> defined by <tt>std::map</tt>,
<tt>std::set</tt>, <tt>std::multimap</tt>, and <tt>std::multiset</tt>.
</li>
<li>
<tt>mapped_value_type</tt>- This describes the <i>type</i> of relationships
store in a container. It consists of information on the <tt>key_type</tt> and <tt>mapped_data_type</tt>
(except for sets).
</li>
</ol>
<p>
The following table defines the above types for a map
mapping from <tt>Key</tt> types to <tt>Data</tt> types:
</p>
<TABLE WIDTH="100%" BORDER="1" ID="Table1">
<TR>
<TD Width="50%" ALIGN="left"><b>type</b></TD>
<TD Width="50%" ALIGN="left"><b>Description / Definition</b></TD>
</TR>
<TR>
<TD ALIGN="left"><pre>key_type</pre>
</TD>
<TD ALIGN="left"><pre>Key</pre>
</TD>
</TR>
<TR>
<TD ALIGN="left"><pre>data_type</pre>
</TD>
<TD ALIGN="left"><pre>Data</pre>
</TD>
</TR>
<TR>
<TD ALIGN="left"><pre>mapped_data_type</pre>
</TD>
<TD ALIGN="left"><pre>Data</pre>
</TD>
</TR>
<TR>
<TD ALIGN="left"><pre>value_type</pre>
</TD>
<TD ALIGN="left"><pre>std::pair<<b>const</b> Key, Data></pre>
</TD>
</TR>
<TR>
<TD ALIGN="left"><pre>mapped_value_type</pre>
</TD>
<TD ALIGN="left"><pre>std::pair<<b>const</b> Key, Data></pre>
</TD>
</TR>
</TABLE>
<p>The following table defines the above types for a
set storing <tt>Key</tt> types:</p>
<TABLE WIDTH="100%" BORDER="1" ID="Table2">
<TR>
<TD Width="50%" ALIGN="left"><b>type</b></TD>
<TD Width="50%" ALIGN="left"><b>Description / Definition</b></TD>
</TR>
<TR>
<TD ALIGN="left"><pre>key_type</pre>
</TD>
<TD ALIGN="left"><pre>Key</pre>
</TD>
</TR>
<TR>
<TD ALIGN="left"><pre>data_type</pre>
</TD>
<TD ALIGN="left">-</TD>
</TR>
<TR>
<TD ALIGN="left"><pre>mapped_data_type</pre>
</TD>
<TD ALIGN="left">-</TD>
</TR>
<TR>
<TD ALIGN="left"><pre>value_type</pre>
</TD>
<TD ALIGN="left"><pre><b>const</b> Key</pre>
</TD>
</TR>
<TR>
<TD ALIGN="left"><pre>mapped_value_type</pre>
</TD>
<TD ALIGN="left"><pre><b>const</b> Key</pre>
</TD>
</TR>
</TABLE>
<p>The following table defines the above types for a multimap
mapping from <tt>Key</tt> types to <tt>Data_Coll<Data></tt>
types, where <tt>Data_Coll<Data></tt>
is a set of <tt>Data</tt> types:</p>
<TABLE WIDTH="100%" BORDER="1" ID="Table3">
<TR>
<TD Width="50%" ALIGN="left"><b>type</b></TD>
<TD Width="50%" ALIGN="left"><b>Description / Definition</b></TD>
</TR>
<TR>
<TD ALIGN="left"><pre>key_type</pre>
</TD>
<TD ALIGN="left"><pre>Key</pre>
</TD>
</TR>
<TR>
<TD ALIGN="left"><pre>data_type</pre>
</TD>
<TD ALIGN="left"><pre>Data</pre>
</TD>
</TR>
<TR>
<TD ALIGN="left"><pre>mapped_data_type</pre>
</TD>
<TD ALIGN="left"><pre>Data_Coll<Data></pre>
</TD>
</TR>
<TR>
<TD ALIGN="left"><pre>value_type</pre>
</TD>
<TD ALIGN="left"><pre>std::pair<<b>const</b> Key, Data></pre>
</TD>
</TR>
<TR>
<TD ALIGN="left"><pre>mapped_value_type</pre>
</TD>
<TD ALIGN="left"><pre>std::pair<<b>const</b> Key, Data_Coll<Data> ></pre>
</TD>
</TR>
</TABLE>
<p>The following table defines the above types for a multiset
storing <tt>Key</tt> types:</p>
<TABLE WIDTH="100%" BORDER="1" ID="Table4">
<TR>
<TD Width="50%" ALIGN="left"><b>type</b></TD>
<TD Width="50%" ALIGN="left"><b>Description / Definition</b></TD>
</TR>
<TR>
<TD ALIGN="left"><pre>key_type</pre>
</TD>
<TD ALIGN="left"><pre>Key</pre>
</TD>
</TR>
<TR>
<TD ALIGN="left"><pre>data_type</pre>
</TD>
<TD ALIGN="left">-</TD>
</TR>
<TR>
<TD ALIGN="left"><pre>mapped_data_type</pre>
</TD>
<TD ALIGN="left"><pre>size_type</pre>
</TD>
</TR>
<TR>
<TD ALIGN="left"><pre>value_type</pre>
</TD>
<TD ALIGN="left"><pre>std::pair<<b>const</b> Key, size_type></pre>
</TD>
</TR>
<TR>
<TD ALIGN="left"><pre>mapped_value_type</pre>
</TD>
<TD ALIGN="left"><pre><b>const</b> Key</pre>
</TD>
</TR>
</TABLE>
<p>
The above types allow to define simple invariants on the interfaces of
containers. For example, each container defines both an <tt>insert</tt> method
which takes a const reference to a <tt>value_type</tt>, and an <tt>insert</tt> method
which takes a const reference to a <tt>mapped_value_type</tt>. Containers for
which both these types are synonymous (<i>i.e.</i>, maps and sets), consequently
have a
single <tt>insert</tt> method. Containers for which these types are distinct (<i>i.e.</i>,
multimaps and multisets), use overloading.
</p>
<h2><a name="generics">Generics</a></h2>
<p>
<tt>pb_assoc</tt> contains a number of utility classes to ease generic
programming.
</p>
<p>
There are four container-type identifiers, <a href="is_map_type.html"><tt>is_map_type</tt></a>,
<a href="is_set_type.html"><tt>is_set_type</tt></a>, <a href="is_multimap_type.html">
<tt>is_multimap_type</tt></a>, and <a href="is_multiset_type.html"><tt>is_multiset_type</tt></a>.
Given a container <tt>T</tt>, for example, it is possible to query at compile
time whether it is a a multimap type by writing <tt>is_multimap_type<T>::value</tt>.
(This is probably very similar to [<a href="references.html#boost_concept_check">boost_concept_check</a>]
and [<a href="references.html#boost_type_traits">boost_type_traits</a>].)
</p>
<p>
In some cases, it is necessary, given a container and an iterator, to query the
iterator' <tt>value_type</tt> to the container's <tt>value_type</tt> and <tt>mapped_value_type</tt>.
The classes
<a href="is_mapped_value_iterator.html"><tt>is_mapped_value_iterator</tt></a>
and <a href="iterator_key.html"><tt>iterator_key</tt></a> can be used for this.
</p>
<p>
The STL's <tt>std::multimap</tt> and <tt>std::multiset</tt> allow iterating
over all <tt>value_type</tt>s stored in them, which is convenient. The library
provides a <a href="value_iterators.html"><tt>value_iterator</tt></a> for this.
This is an iterator adapter over the containers' native iterators.
</p>
<h2><a name = "compound_keys">Compound Keys</a></h2>
<p>
The STL allows using equivalent, non-identical, keys.
For example, let <tt>interval</tt> be a line-interval class,
<tt>color</tt> be a
color type, <tt>thickness</tt> be a thickness type, and <tt>colored_interval</tt>
be a class composed of an <tt>interval</tt> and a <tt>color</tt>.
</p>
<p>
Suppose one wants to store <tt>colored_interval</tt>
objects using a comparison predicate ignoring colors. Then
in the STL's design, one would use
<tt>multiset<colored_interval></tt>; in <tt>pb_assoc</tt>'s design,
one would use one of the following:
</p>
<ol>
<li>
A map mapping <tt>interval</tt> objects to
<tt>color</tt> objects. This, however, assumes that
<tt>colored_interval</tt> is decomposable to, and constructible from,
<tt>interval</tt> and <tt>color</tt>.
</li>
<li>
A map mapping <tt>colored_interval</tt> objects to
<tt>color</tt> objects. In this (less efficient) case, a <tt>colored_interval</tt> object
is a "representative" of all colored intervals with the same endpoints.
</li>
</ol>
<p>
Suppose one wants to map <tt>colored_interval</tt>
objects to <tt>thickness</tt> objects
using a comparison predicate ignoring colors. Then
in the STL's design, one would use
<tt>multimap<colored_interval, thickness></tt>; in <tt>pb_assoc</tt>'s design,
one would use one of the following:
</p>
<ol>
<li> A map mapping <tt>interval</tt> objects to
<tt>std::pair<color, thickness></tt> objects. This, however, assumes that
<tt>colored_interval</tt> is decomposable to, and constructible from,
<tt>interval</tt> and <tt>color</tt>.
</li>
<li> A map mapping <tt>colored_interval</tt> objects to
<tt>std::pair<color, thickness></tt> objects. In this (less efficient) case, a <tt>colored_interval</tt> object
is a "representative" of all colored intervals with the same endpoints.
</li>
</ol>
<p>
(From the above, it is apparent that the STL's design has an advantage
over <tt>pb_assoc</tt>'s design in terms of convenience. Nonethless, there
are efficiency limitation in the STL's design (see
<a href = "motivation.html#unique_key">Unique-Key Design for Multimaps and Multisets</a>).)
</p>
<p>
The above example, using intervals, colors and thicknesses, can be generalized.
Let
<tt>key_unique_part</tt> be a unique part of some key
(<i>e.g.</i>, <tt>interval</tt> in the above),
<tt>key_non_unique_part</tt> be a non-unique part of some key
(<i>e.g.</i>, <tt>color</tt> in the above),
<tt>key</tt> be some key composed of unique and non-uniqe parts
(<i>e.g.</i>, <tt>colored_interval</tt> in the above),
and
<tt>data</tt> be some data
(<i>e.g.</i>, <tt>thickness</tt> in the above).
Then the <a href = "#stl_to_pb_assoc_non_unique_mapping">
figure shows some
STL containers and the <tt>pb_assoc</tt> counterparts.
</a>
</p>
<h6 align = "center">
<a name = "stl_to_pb_assoc_non_unique_mapping">
<img src = "stl_to_pb_assoc_non_unique_mapping.jpg" alt = "no-image" width = "60%">
</a>
</h6>
<h6 align = "center">
STL containers and <tt>pb_assoc</tt> counterparts.
</h6>
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