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+ <title>Trie-Based Containers</title>
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+ <div id="page">
+ <h1>Trie Design</h1>
+
+ <h2><a name="overview" id="overview">Overview</a></h2>
+
+ <p>The trie-based container has the following declaration:</p>
+ <pre>
+<b>template</b><
+ <b>typename</b> Key,
+ <b>typename</b> Mapped,
+ <b>typename</b> Cmp_Fn = std::less<Key>,
+ <b>typename</b> Tag = <a href="pat_trie_tag.html">pat_trie_tag</a>,
+ <b>template</b><
+ <b>typename</b> Const_Node_Iterator,
+ <b>typename</b> Node_Iterator,
+ <b>typename</b> E_Access_Traits_,
+ <b>typename</b> Allocator_>
+ <b>class</b> Node_Update = <a href=
+"null_trie_node_update.html">null_trie_node_update</a>,
+ <b>typename</b> Allocator = std::allocator<<b>char</b>> >
+<b>class</b> <a href=
+"trie.html">trie</a>;
+</pre>
+
+ <p>The parameters have the following meaning:</p>
+
+ <ol>
+ <li><tt>Key</tt> is the key type.</li>
+
+ <li><tt>Mapped</tt> is the mapped-policy, and is explained in
+ <a href="tutorial.html#assoc_ms">Tutorial::Associative
+ Containers::Associative Containers Others than Maps</a>.</li>
+
+ <li><tt>E_Access_Traits</tt> is described in <a href=
+ "#e_access_traits">Element-Access Traits</a>.</li>
+
+ <li><tt>Tag</tt> specifies which underlying data structure
+ to use, and is described shortly.</li>
+
+ <li><tt>Node_Update</tt> is a policy for updating node
+ invariants. This is described in <a href="#invariants">Node
+ Invariants</a>.</li>
+
+ <li><tt>Allocator</tt> is an allocator
+ type.</li>
+ </ol>
+
+ <p>The <tt>Tag</tt> parameter specifies which underlying
+ data structure to use. Instantiating it by <a href=
+ "pat_trie_tag.html">pat_trie_tag</a>, specifies an
+ underlying PATRICIA trie (explained shortly); any other tag is
+ currently illegal.</p>
+ <hr />
+
+ <p>Following is a description of a (PATRICIA) trie
+ (<tt>pb_ds</tt> follows specifically [<a href=
+ "references.html#okasaki98mereable">okasaki98mereable</a>] and
+ [<a href=
+ "references.html#filliatre2000ptset">filliatre2000ptset</a>]).</p>
+
+ <p>A (PATRICIA) trie is similar to a tree, but with the
+ following differences:</p>
+
+ <ol>
+ <li>It explicitly views keys as a sequence of elements.
+ <i>E.g.</i>, a trie can view a string as a sequence of
+ characters; a trie can view a number as a sequence of
+ bits.</li>
+
+ <li>It is not (necessarily) binary. Each node has fan-out <i>n
+ + 1</i>, where <i>n</i> is the number of distinct
+ elements.</li>
+
+ <li>It stores values only at leaf nodes.</li>
+
+ <li>Internal nodes have the properties that A) each has at
+ least two children, and B) each shares the same prefix with
+ any of its descendant.</li>
+ </ol>
+
+ <p><a href="#e_access_traits">Element-Access Traits</a> shows
+ an example of such a trie.</p>
+
+ <p>A (PATRICIA) trie has some useful properties:</p>
+
+ <ol>
+ <li>It can be configured to use large node fan-out, giving it
+ very efficient find performance (albeit at insertion
+ complexity and size).</li>
+
+ <li>It works well for common-prefix keys.</li>
+
+ <li>It can support efficiently queries such as which keys
+ match a certain prefix. This is sometimes useful in
+ file systems and routers.</li>
+ </ol>
+
+ <p>(We would like to thank Matt Austern for the suggestion to
+ include tries.)</p>
+
+ <h2><a name="e_access_traits" id=
+ "e_access_traits">Element-Access Traits</a></h2>
+
+ <p>A trie inherently views its keys as sequences of elements.
+ For example, a trie can view a string as a sequence of
+ characters. A trie needs to map each of <i>n</i> elements to a
+ number in <i>{0, n - 1}</i>. For example, a trie can map a
+ character <tt>c</tt> to
+ <tt>static_cast<size_t>(c)</tt>.</p>
+
+ <p>Seemingly, then, a trie can assume that its keys support
+ (const) iterators, and that the <tt>value_type</tt> of this
+ iterator can be cast to a <tt>size_t</tt>. There are several
+ reasons, though, to decouple the mechanism by which the trie
+ accesses its keys' elements from the trie:</p>
+
+ <ol>
+ <li>In some cases, the numerical value of an element is
+ inappropriate. Consider a trie storing DNA strings. It is
+ logical to use a trie with a fan-out of <i>5 = 1 + |{'A', 'C',
+ 'G', 'T'}|</i>. This requires mapping 'T' to 3, though.</li>
+
+ <li>In some cases the keys' iterators are different than what
+ is needed. For example, a trie can be used to search for
+ common <u>suffixes</u>, by using strings'
+ <tt>reverse_iterator</tt>. As another example, a trie mapping
+ UNICODE strings would have a huge fan-out if each node would
+ branch on a UNICODE character; instead, one can define an
+ iterator iterating over 8-bit (or less) groups.</li>
+ </ol>
+
+ <p><a href=
+ "trie.html">trie</a> is,
+ consequently, parametrized by <tt>E_Access_Traits</tt> -
+ traits which instruct how to access sequences' elements.
+ <a href=
+ "string_trie_e_access_traits.html"><tt>string_trie_e_access_traits</tt></a>
+ is a traits class for strings. Each such traits define some
+ types, <i>e.g.</i>,</p>
+ <pre>
+<b>typename</b> E_Access_Traits::const_iterator
+</pre>
+
+ <p>is a const iterator iterating over a key's elements. The
+ traits class must also define methods for obtaining an iterator
+ to the first and last element of a key.</p>
+
+ <p>Figure <a href="#pat_trie">A PATRICIA trie</a> shows a
+ (PATRICIA) trie resulting from inserting the words: "I wish
+ that I could ever see a poem lovely as a trie" (which,
+ unfortunately, does not rhyme).</p>
+
+ <p>The leaf nodes contain values; each internal node contains
+ two <tt><b>typename</b> E_Access_Traits::const_iterator</tt>
+ objects, indicating the maximal common prefix of all keys in
+ the sub-tree. For example, the shaded internal node roots a
+ sub-tree with leafs "a" and "as". The maximal common prefix is
+ "a". The internal node contains, consequently, to const
+ iterators, one pointing to <tt>'a'</tt>, and the other to
+ <tt>'s'</tt>.</p>
+
+ <h6 class="c1"><a name="pat_trie" id="pat_trie"><img src=
+ "pat_trie.png" alt="no image" /></a></h6>
+
+ <h6 class="c1">A PATRICIA trie.</h6>
+
+ <h2><a name="invariants" id="invariants">Node
+ Invariants</a></h2>
+
+ <p>Trie-based containers support node invariants, as do
+ tree-based containers (see <a href=
+ "tree_based_containers.html#invariants">Tree-Based
+ Containers::Node Invariants</a>). There are two minor
+ differences, though, which, unfortunately, thwart sharing them
+ sharing the same node-updating policies:</p>
+
+ <ol>
+ <li>A trie's <tt>Node_Update</tt> template-template
+ parameter is parametrized by <tt>E_Access_Traits</tt>, while
+ a tree's <tt>Node_Update</tt> template-template parameter is
+ parametrized by <tt>Cmp_Fn</tt>.</li>
+
+ <li>Tree-based containers store values in all nodes, while
+ trie-based containers (at least in this implementation) store
+ values in leafs.</li>
+ </ol>
+
+ <p>Figure <a href="#trie_node_update_cd">A trie and its update
+ policy</a> shows the scheme, as well as some predefined
+ policies (which are explained below).</p>
+
+ <h6 class="c1"><a name="trie_node_update_cd" id=
+ "trie_node_update_cd"><img src=
+ "trie_node_update_policy_cd.png" alt="no image" /></a></h6>
+
+ <h6 class="c1">A trie and its update policy.</h6>
+
+ <p><tt>pb_ds</tt> offers the following pre-defined trie node
+ updating policies:</p>
+
+ <ol>
+ <li><a href=
+ "trie_order_statistics_node_update.html"><tt>trie_order_statistics_node_update</tt></a>
+ supports order statistics.</li>
+
+ <li><a href=
+ "trie_prefix_search_node_update.html"><tt>trie_prefix_search_node_update</tt></a>
+ supports searching for ranges that match a given prefix. See
+ <a href=
+ "http://gcc.gnu.org/viewcvs/*checkout*/trunk/libstdc%2B%2B-v3/testsuite/ext/pb_ds/example/trie_prefix_search.cc"><tt>trie_prefix_search.cc</tt></a>.</li>
+
+ <li><a href=
+ "null_trie_node_update.html"><tt>null_trie_node_update</tt></a>
+ is the null node updater.</li>
+ </ol>
+
+ <h2><a name="add_methods" id="add_methods">Additional
+ Methods</a></h2>
+
+ <p>Trie-based containers support split and join methods; the
+ rationale is equal to that of tree-based containers supporting
+ these methods (see <a href=
+ "tree_based_containers.html#add_methods">Tree-Based
+ Containers::Additional Methods</a>).</p>
+ </div>
+</body>
+</html>
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