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<h1>Data-Structure Genericity</h1>

<p>
	This section describes genericity over different underlying data-structures. It is organized as follows.
</p>
<ol>
	<li><a href = "#problem">The Basic Problem</a></li>
	<li><a href = "#ds_hierarchy">Container Hierarchy</a></li>
	<li><a href = "#ds_traits">Data-Structure Tags and Traits</a></li>
	<li><a href = "#find_range">Find-Type and Range-Type Methods and Iterators</a></li>
</ol>

<h2><a name = "problem">The Basic Problem</a></h2>

<p>
	The design attempts to address the following problem. When writing a function manipulating a generic container object, what is the behaviour of the object? <i>E.g.</i>, suppose one writes
</p>
<pre>
<b>template</b>&lt;
    <b>class</b> Cntnr&gt;
<b>void</b> some_op_sequence
    (Cntnr &r_cntnr)
{
    ...
}
</pre>
then one needs to address the following questions in the body
of <tt>some_op_sequence</tt>:
<ol>
	<li> Which types and methods does <tt>Cntnr</tt> support? Containers based on hash tables can be queries for the hash-functor type and object; this is meaningless for tree-based containers. Containers based on trees can be split, joined, or can erase iterators and return the following iterator; this cannot be done by hash-based containers. </li>
	<li>
		What are the guarantees of <tt>Cntnr</tt>? A container based on a probing hash-table invalidates all iterators when it is modified; this is not the case for containers based on node-based trees. Containers based on a node-based tree can be split or joined without exceptions; this is not the case for containers based on vector-based trees.
	</li>
	<li> How does the container maintain its elements? containers based on splay trees or lists with update policies "cache" "frequently accessed" elements; containers based on most other underlying data-structures do not.</li>
</ol>

<h2><a name = "ds_hierarchy">Container Hierarchy</a></h2>

<p>
	Figure
<a href = "#cd">Class hierarchy</a>
	shows the container hierarchy.
</p>
<ol>
	<li>
<a href = "basic_assoc_cntnr.html"><tt>basic_assoc_cntnr</tt></a>
contains types and methods shared by all associative containers, <i>e.g.</i>, the type <tt>allocator</tt> and the method <tt>find</tt>.
	</li>
	<li><a href = "basic_assoc_cntnr.html"><tt>basic_hash_assoc_cntnr</tt></a> subclasses
<a href = "basic_assoc_cntnr.html"><tt>basic_assoc_cntnr</tt></a>, and contains
types and methods shared by all hash-based containers, <i>e.g.</i>, the type <tt>hash_fn</tt>.
	</li>
	<ol>
		<li>
<a href = "cc_hash_assoc_cntnr.html"><tt>cc_hash_assoc_cntnr</tt></a>
and
<a href = "gp_hash_assoc_cntnr.html"><tt>gp_hash_assoc_cntnr</tt></a>
each subclass
<a href = "basic_hash_assoc_cntnr.html"><tt>basic_hash_assoc_cntnr</tt></a>, and encapsulate collision-chaining and (general) probing hash tables, respectively. These two types of hash tables have somewhat different policies and methods (<i>i.e.</i>, constructors and policy-access methods).
		</li>
	</ol>
	<li>
<a href = "tree_assoc_cntnr.html"><tt>tree_assoc_cntnr</tt></a>
subclasses one of
<a href = "basic_tree_assoc_cntnr.html"><tt>basic_tree_assoc_cntnr</tt></a> which
subclasses
<a href = "basic_assoc_cntnr.html"><tt>basic_assoc_cntnr</tt></a>.
<a href = "tree_assoc_cntnr.html"><tt>tree_assoc_cntnr</tt></a>
 encapsulates a tree-based container, and is parameterized by which underlying data-structure to use (<i>e.g.</i>, a red-black tree);
<a href = "basic_assoc_cntnr.html"><tt>basic_assoc_cntnr</tt></a>.
is specialized to the capabilities of the underlying structure.
<a href = "tree_assoc_cntnr.html"><tt>tree_assoc_cntnr</tt></a> contains some additional methods over
<a href = "basic_assoc_cntnr.html"><tt>basic_assoc_cntnr</tt></a>,
<i>e.g.</i>, split and join methods.
	</li>
		<li>
<a href = "lu_assoc_cntnr.html"><tt>lu_assoc_cntnr</tt></a>
subclasses
<a href = "basic_assoc_cntnr.html"><tt>basic_assoc_cntnr</tt></a>,
and encapsulates a list with update policies.
	</li>
</ol>

<p>
	The hierarchy is composed naturally, such that each container inherits
all types and methods from its base. <a href = "#ds_traits">Data-Structure Tags and Traits</a> discusses how to query which types and methods each container supports.
</p>


<h2><a name = "ds_traits">Data-Structure Tags and Traits</a></h2>

<p>
	<tt>pb_assoc</tt> contains a tag and traits mechanism similar to that of the STL's iterators.
</p>

<p>
	<tt>pb_assoc</tt> contains a tag hierarchy corresponding to the hierarchy
in Figure
<a href = "#cd">Class hierarchy</a>.
The tag hierarchy is shown in Figure
<a href = "#ds_tag_cd">Data-structure tag class hierarchy</a>.
</p>

<h6 align = "center">
<a name = "cd">
<img src = "ds_tag_cd.jpg" width = "70%" alt = "no image">
</h6>
</a>
<h6 align = "center">
Data-structure tag class hierarchy.
</h6>

<p>
	<a href = "basic_assoc_cntnr.html"><tt>basic_assoc_cntnr</tt></a> publicly defines
<tt>ds_category</tt> as one of the classes in Figure
.
Given any container <tt>Cntnr</tt>, the tag of the underlying data-structure can be found via <tt><b>typename</b> Cntnr::ds_category</tt>.
</p>

<p>
	Additionally, a traits mechanism can be used to query a container type for its attributes. Given any container <tt>Cntnr</tt>, then
<tt><a href = "ds_traits.html">ds_traits</a>&lt;Cntnr&gt;</tt>
is a traits class identifying the properties of the container.
</p>

<p>
	To find if a container can throw when a key is erased (which is true for vector-based trees, for example), one can use
</p>
<a href = "ds_traits.html"><tt>ds_traits</tt></a><tt>&lt;Cntnr&gt;::erase_can_throw</tt>,
for example.

<p>
	Some of the definitions in
<a href = "ds_traits.html"><tt>ds_traits</tt></a>
are dependent on other definitions. <i>E.g.</i>, if
<a href = "ds_traits.html"><tt>ds_traits</tt></a><tt>&lt;Cntnr&gt;::split_join</tt>
is <tt><b>true</b></tt> (which is the case for containers based on trees),
then
<a href = "ds_traits.html"><tt>ds_traits</tt></a><tt>&lt;Cntnr&gt;::split_join_can_throw</tt>
indicates whether splits or joins can throw exceptions (which is true for vector-based trees); otherwise
<a href = "ds_traits.html"><tt>ds_traits</tt></a><tt>&lt;Cntnr&gt;::split_join_can_throw</tt>
will yield a compilation error. (This is somewhat similar to a compile-time
version of the COM model
[<a href = "references.html#mscom">mscom</a>]).


<h2><a name = "find_range">Find-Type and Range-Type Methods and Iterators</a></h2>

<p>
	<tt>pb_assoc</tt> differentiates between two types of methods: find-type methods, and range-type methods. For example, <tt>find</tt> is a find-type method, since a container object searches for an element with a given key; <tt>insert</tt> is a find-type method, since, by STL convention, a container object returns an iterator corresponding to an element with a given key; <tt>begin</tt> and <tt>end</tt> are range-type methods, since they are not used to find a specific element, but rather to go over all elements in a container object.
</p>

<p>
	Correspondingly, containers in <tt>pb_assoc</tt> define two families of iterators. <tt>const_find_iterator</tt> and <tt>find_iterator</tt> are the iterator types returned by find-type methods; <tt>const_iterator</tt> and <tt>iterator</tt> are the iterator types returned by range-type methods.
</p>

<p>
	The relationship between these iterator types varies between container types. In a tree-based container, for example, <tt>const_find_iterator</tt> and <tt>const_iterator</tt> are synonymous, and <tt>find_iterator</tt> and <tt>iterator</tt> are synonymous; in a hash-based container, for example, this is not the case. Futhermore, find-type iterators in a hash-based container lack movement operators, such as
	<tt><b>operator++</b></tt>.
	All containers, however, maintain the invariants shown in Figure

.
</p>


<p>
	This distinction between find-type and range-type iterators and methods, while complicating the interface, has several advantages:
</p>

<h3>Iterators in unordered container types</h3>

<p>
 Given an unordered container type, <i>e.g.</i>, a hash-based container, it makes no sense to move an iterator returned by a find-type method.
Let <tt>cntnr</tt> be an associative-container object, and
consider:
</p>

<pre>
std::for_each(m.find(1), m.find(5), foo);
</pre>

<p>
which applies <tt>foo</tt> to all elements in <tt>m</tt>
between <tt>1</tt> and <tt>5</tt>.
</p>

<p>If <tt>cntnr</tt> is a
tree-based container object, then an in-order walk will apply <tt>foo</tt>
to the relevant elements, <i>e.g.</i>, as in Figure
<a href = "#range_it_in_hts">Range iteration in different data-structures</a>
-A. If <tt>m</tt> is a
hash-based container, then the order of elements between any two
elements is undefined (and probably time-varying); there is no
guarantee that the elements traversed will coincide with the
<i>logical</i> elements between 1 and 5, <i>e.g.</i>, as in
Figure <a href = "#range_it_in_hts">Range iteration in different data-structures</a>-B.
</p>

<p>
The application of a
range function <i>e.g.</i>, <tt>for_each</tt>, to a
pair of hash-based container's iterators is possibly sensical only
if the iterators are those returned by <tt>begin</tt> and <tt>end</tt>,
respectively. Therefore, the iterator returned by
<tt>m</tt>'s <tt>find</tt> method should be immovable.
</p>

<p>
    Another point also indicates that hash-based containers'
find-type iterators and range-type iterators should be distinct.
Consider Figure
<a href = "#find_its_in_hash_tables">
Find-type iterators in hash tables</a>-A.
An
(immovable) find-type iterator, designed only to access an
element, requires at most a single pointer to the element's link.
Conversely, an iterator designed for range operations
requires some more information <i>e.g.</i>, the bucket number),
since a cross-list traversal might be necessary. Alternatively,
the lists might be linked, forming a monolithic total-element
list, as in Figure
<a href = "#find_its_in_hash_tables">
Find-type iterators in hash tables</a>-B (this seems
similar to the Dinkumware design
[<a href = "references.html#dinkumware_stl">dinkumware_stl</a>]). This,
however, complicates the hash-table's operations.

<h6 align = "center">
<a name = "range_it_in_hts">
<img src = "find_iterators_range_ops_1.jpg" width = "70%" alt = "no image">
</a>
</h6>
<h6 align = "center">
Range iteration in different data-structures.
</h6>


<h6 align = "center">
<a name = "find_its_in_hash_tables">
<img src = "find_iterators_range_ops_2.jpg" width = "70%" alt = "no image">
</a>
</h6>
<h6 align = "center">
Find-type iterators in hash tables.
</h6>

<p>
	As a consequence of this design,
</p>

<pre>
std::for_each(m.find(1), m.find(5), foo);
</pre>

<p>
	will compile for tree-based containers, but will not compile
for hash-tables or other types. The returned type of <tt>find</tt>
is a find-type iterator. For tree-based containers, this is synonymous
with a range-type iterator, and therefore supports <tt><b>operator</b>++</tt>;
for other types of containers, a find-type iterator lacks <tt><b>operator</b>++</tt>.
</p>

<h3>Invalidation Guarantees</h3>

<p>
	Consider the following snippet:
</p>

<pre>
it = c.find(3);

c.erase(5);
</pre>

<p>
	Following the call to <tt>erase</tt>, what is the validity
of <tt>it</tt>: can it be dereferenced? can it be incremented?
</p>

<p>
	The answer depends on the underlying data-structure of the container.
Figure
<a href = "#invalidation_guarantee_erase">Effect of erase in different underlying data-structures</a>
shows three cases: A1 and A2 show a red-black tree;
B1 and B2 show an ordered-vector tree; C1 and C2
show a collision-chaining hash table.
</p>

<h6 align = "center">
<a name = "invalidation_guarantee_erase">
<img src = "invalidation_guarantee_erase.jpg" width = "70%" alt = "no image">
</h6>
</a>
<h6 align = "center">
Effect of erase in different underlying data-structures.
</h6>


<ol>
	<li>
		`Erasing 5 from A1 yields A2. Clearly, an iterator to 3
	can be dereferenced and incremented.
	</li>
	<li>
		Erasing 5 from B1 yields B2. Clearly, an iterator to 3 is
	not valid at all.
	</li>
	<li>
		Erasing 5 from C1 yields C2. Here the situation is more complicated.
On the one hand, incrementing <tt>it</tt> can be undefined. On the other
hand, there is no problem in dereferencing <tt>it</tt>. In
classic STL, it is not possible to express whether <tt>it</tt>
is valid or not.
	</li>
</ol>

<p>
	Thus again, the iterator concept seems overloaded. Distinguishing
between find and range types allows fine-grained invalidation guarantees.
<a href = #invalidation_guarantee_cd">Invalidation guarantees class hierarchy</a>
shows tags corresponding to different types of invalidation guarantees.
</p>

<h6 align = "center">
<a name = "invalidation_guarantee_cd">
<img src = "invalidation_guarantee_cd.jpg" width = "70%" alt = "no image">
</h6>
</a>
<h6 align = "center">
Invalidation guarantees class hierarchy.
</h6>

<ol>
	<li> <a href = "basic_invalidation_guarantee.html"><tt>basic_invalidation_guarantee</tt></a> corresponds to a basic guarantee that a find-type iterator, a found pointer, or a found reference, remains valid as long as the container object is not modified.
	</li>
	<li> <a href = "find_invalidation_guarantee.html"><tt>find_invalidation_guarantee</tt></a> corresponds to a guarantee that a find-type iterator, a found pointer, or a found reference, remains valid even if the containter object is modified.
	</li>
	<li> <a href = "range_invalidation_guarantee.html"><tt>range_invalidation_guarantee</tt></a> corresponds to a guarantee that a range-type iterator remains valid even if the containter object is modified.
	</li>
</ol>


<p>
	To find the invalidation guarantee of a container, one can use
</p>
<pre>
<b>typename</b> <a href = "ds_traits.html">ds_traits</a>&lt;Cntnr&gt;::invalidation_guarantee
</pre>

<p>
	which is one of the classes in Figure
<a href = #invalidation_guarantee_cd">Invalidation guarantees class hierarchy</a>.
</p>


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