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    <h1>Concepts</h1>

    <h2><a name="concepts_find_and_range_iterators" id=
    "concepts_find_and_range_iterators">Point and Range Methods and
    Iterators</a></h2>

    <p>A point-type iterator is an iterator that refers to a
    specific element, <i>e.g.</i> as returned through an
    associative-container's <tt>find</tt> method; a range-type
    iterator is an iterator that is used to go over a sequence of
    elements, <i>e.g.</i>, as returned by a container's
    <tt>find</tt> method. A point-type method is a method that
    returns a point-type iterator; a range-type method is a method
    that returns a range-type iterator.</p>

    <p>For most containers, these types are synonymous; for
    self-organizing containers, such as hash-based containers or
    priority queues, these are inherently different (in any
    implementation, including that of the STL), but in
    <tt>pb_ds</tt> this is made explicit - they are distinct
    types.</p>

 
    <h2><a name="invalidation_guarantees" id=
    "invalidation_guarantees">Invalidation Guarantees</a></h2>

    <p>If one manipulates a container object, then iterators
    previously obtained from it can be invalidated. In some cases a
    previously-obtained iterator cannot be de-referenced; in other
    cases, the iterator's next or previous element might have
    changed unpredictably. This corresponds exactly to the question
    whether a point-type or range-type iterator (see previous
    concept) is valid or not. In <tt>pb_ds</tt> one can query a
    container (in compile time) what are its invalidation
    guarantees.</p>

     <h2><a name="prm_sec" id="prm_sec">Primary and Secondary Keys
    and Associative Containers</a></h2>

    <p>In <tt>pb_ds</tt> there are no associative containers which
    allow multiple values with equivalent keys (such as the STL's
    <tt>std::multimap</tt>, for example). Instead, one maps the
    unique part of a key - the primary key, into an
    associative-container of the (originally) non-unique parts of
    the key - the secondary key. A primary associative-container is
    an associative container of primary keys; a secondary
    associative-container is an associative container of secondary
    keys.</p>

 
    <h2><a name="concepts_null_policies" id=
    "concepts_null_policies">Null Policy Classes</a></h2>

    <p>Associative containers are typically parametrized by
    various policies. For example, a hash-based associative
    container is parametrized by a hash-functor, transforming each
    key into an non-negative numerical type. Each such value is
    then further mapped into a position within the table. The
    mapping of a key into a position within the table is therefore
    a two-step process.</p>

    <p>In some cases, instantiations are <i>redundant</i>. For
    example, when the keys are integers, it is possible to use a
    <i>redundant</i> hash policy, which transforms each key into
    its value.</p>

    <p>In some other cases, these policies are <i>irrelevant</i>.
    For example, a hash-based associative container might transform
    keys into positions within a table by a different method than
    the two-step method described above. In such a case, the hash
    functor is simply irrelevant.</p>

    <p><tt>pb_ds</tt> uses special pre-defined "null policies"
    classes for these cases. Some null policies in <tt>pb_ds</tt>
    are:</p>

    <ol>
      <li><a href=
      "null_mapped_type.html"><tt>null_mapped_type</tt></a></li>

      <li><a href=
      "null_tree_node_update.html"><tt>null_tree_node_update</tt></a></li>

      <li><a href=
      "null_trie_node_update.html"><tt>null_trie_node_update</tt></a></li>

      <li><a href=
      "null_hash_fn.html"><tt>null_hash_fn</tt></a></li>

      <li><a href=
      "null_probe_fn.html"><tt>null_probe_fn</tt></a></li>
    </ol>

    <p>A "set" in <tt>pb_ds</tt>, for example, is an associative
    container with its <tt>Data_Parameter</tt> instantiated by
    <a href="null_mapped_type.html"><tt>null_mapped_type</tt></a>.
    <a href=
    "tree_based_containers.html#invariants">Design::Tree-Based
    Containers::Node Invariants</a> explains another case where a
    null policy is needed.</p>
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