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diff --git a/gcc-4.4.3/libstdc++-v3/doc/html/ext/pb_ds/trie_based_containers.html b/gcc-4.4.3/libstdc++-v3/doc/html/ext/pb_ds/trie_based_containers.html new file mode 100644 index 000000000..72bdd0697 --- /dev/null +++ b/gcc-4.4.3/libstdc++-v3/doc/html/ext/pb_ds/trie_based_containers.html @@ -0,0 +1,241 @@ +<!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> |