<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en"> <head> <meta name="generator" content= "HTML Tidy for Linux/x86 (vers 12 April 2005), see www.w3.org" /> <title>Trie-Based Containers</title> <meta http-equiv="Content-Type" content= "text/html; charset=us-ascii" /> </head> <body> <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>