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diff --git a/libstdc++-v3/doc/html/ext/pb_ds/tree_based_containers.html b/libstdc++-v3/doc/html/ext/pb_ds/tree_based_containers.html new file mode 100644 index 000000000..63c7c7482 --- /dev/null +++ b/libstdc++-v3/doc/html/ext/pb_ds/tree_based_containers.html @@ -0,0 +1,358 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" + "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.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>Tree-Based Containers</title> + <meta http-equiv="Content-Type" content= + "text/html; charset=us-ascii" /> + </head> + +<body> + <div id="page"> + <h1>Tree Design</h1> + + <h2><a name="overview" id="overview">Overview</a></h2> + + <p>The tree-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="rb_tree_tag.html">rb_tree_tag</a>, + <b>template</b>< + <b>typename</b> Const_Node_Iterator, + <b>typename</b> Node_Iterator, + <b>typename</b> Cmp_Fn_, + <b>typename</b> Allocator_> + <b>class</b> Node_Update = <a href= +"null_tree_node_update.html">null_tree_node_update</a>, + <b>typename</b> Allocator = std::allocator<<b>char</b>> > +<b>class</b> <a href= +"tree.html">tree</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.</li> + + <li><tt>Cmp_Fn</tt> is a key comparison functor</li> + + <li><tt>Tag</tt> specifies which underlying data structure + to use.</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= + "rb_tree_tag.html"><tt>rb_tree_tag</tt></a>, <a href= + "splay_tree_tag.html"><tt>splay_tree_tag</tt></a>, or + <a href="ov_tree_tag.html"><tt>ov_tree_tag</tt></a>, + specifies an underlying red-black tree, splay tree, or + ordered-vector tree, respectively; any other tag is illegal. + Note that containers based on the former two contain more types + and methods than the latter (<i>e.g.</i>, + <tt>reverse_iterator</tt> and <tt>rbegin</tt>), and different + exception and invalidation guarantees.</p> + + <h2><a name="invariants" id="invariants">Node + Invariants</a></h2> + + <p>Consider the two trees in Figures <a href= + "#node_invariants">Some node invariants</a> A and B. The first + is a tree of floats; the second is a tree of pairs, each + signifying a geometric line interval. Each element in a tree is refered to as a node of the tree. Of course, each of + these trees can support the usual queries: the first can easily + search for <tt>0.4</tt>; the second can easily search for + <tt>std::make_pair(10, 41)</tt>.</p> + + <p>Each of these trees can efficiently support other queries. + The first can efficiently determine that the 2rd key in the + tree is <tt>0.3</tt>; the second can efficiently determine + whether any of its intervals overlaps + <tt>std::make_pair(29,42)</tt> (useful in geometric + applications or distributed file systems with leases, for + example). (See <a href= + "http://gcc.gnu.org/viewcvs/*checkout*/trunk/libstdc%2B%2B-v3/testsuite/ext/pb_ds/example/tree_order_statistics.cc"><tt>tree_order_statistics.cc</tt></a> + and <a href= + "http://gcc.gnu.org/viewcvs/*checkout*/trunk/libstdc%2B%2B-v3/testsuite/ext/pb_ds/example/tree_intervals.cc"><tt>tree_intervals.cc</tt></a> + for examples.) It should be noted that an <tt>std::set</tt> can + only solve these types of problems with linear complexity.</p> + + <p>In order to do so, each tree stores some <i>metadata</i> in + each node, and maintains node invariants <a href= + "references.html#clrs2001">clrs2001</a>]. The first stores in + each node the size of the sub-tree rooted at the node; the + second stores at each node the maximal endpoint of the + intervals at the sub-tree rooted at the node.</p> + + <h6 class="c1"><a name="node_invariants" id= + "node_invariants"><img src="node_invariants.png" alt= + "no image" /></a></h6> + + <h6 class="c1">Some node invariants.</h6> + + <p>Supporting such trees is difficult for a number of + reasons:</p> + + <ol> + <li>There must be a way to specify what a node's metadata + should be (if any).</li> + + <li>Various operations can invalidate node invariants. + <i>E.g.</i>, Figure <a href= + "#node_invariant_invalidations">Invalidation of node + invariants</a> shows how a right rotation, performed on A, + results in B, with nodes <i>x</i> and <i>y</i> having + corrupted invariants (the grayed nodes in C); Figure <a href= + "#node_invariant_invalidations">Invalidation of node + invariants</a> shows how an insert, performed on D, results + in E, with nodes <i>x</i> and <i>y</i> having corrupted + invariants (the grayed nodes in F). It is not feasible to + know outside the tree the effect of an operation on the nodes + of the tree.</li> + + <li>The search paths of standard associative containers are + defined by comparisons between keys, and not through + metadata.</li> + + <li>It is not feasible to know in advance which methods trees + can support. Besides the usual <tt>find</tt> method, the + first tree can support a <tt>find_by_order</tt> method, while + the second can support an <tt>overlaps</tt> method.</li> + </ol> + + <h6 class="c1"><a name="node_invariant_invalidations" id= + "node_invariant_invalidations"><img src= + "node_invariant_invalidations.png" alt="no image" /></a></h6> + + <h6 class="c1">Invalidation of node invariants.</h6> + + <p>These problems are solved by a combination of two means: + node iterators, and template-template node updater + parameters.</p> + + <h3><a name="node_it" id="node_it">Node Iterators</a></h3> + + <p>Each tree-based container defines two additional iterator + types, <a href= + "tree_const_node_iterator.html"><tt>const_node_iterator</tt></a> + and <a href= + "tree_node_iterator.html"><tt>node_iterator</tt></a>. + These iterators allow descending from a node to one of its + children. Node iterator allow search paths different than those + determined by the comparison functor. <a href= + "tree.html">tree</a> + supports the methods:</p> + <pre> + <a href="tree_const_node_iterator.html"><tt>const_node_iterator</tt></a> + node_begin() <b>const</b>; + + <a href="tree_node_iterator.html"><tt>node_iterator</tt></a> + node_begin(); + + <a href="tree_const_node_iterator.html"><tt>const_node_iterator</tt></a> + node_end() <b>const</b>; + + <a href="tree_node_iterator.html"><tt>node_iterator</tt></a> + node_end(); +</pre> + + <p>The first pairs return node iterators corresponding to the + root node of the tree; the latter pair returns node iterators + corresponding to a just-after-leaf node.</p> + + <h3><a name="node_up" id="node_up">Node Updater + (Template-Template) Parameters</a></h3> + + <p>The tree-based containers are parametrized by a + <tt>Node_Update</tt> template-template parameter. A tree-based + container instantiates <tt>Node_Update</tt> to some + <tt>node_update</tt> class, and publicly + subclasses <tt>node_update</tt>. Figure + <a href="#tree_node_update_cd">A tree and its update + policy</a> shows this scheme, as well as some predefined + policies (which are explained below).</p> + + <h6 class="c1"><a name="tree_node_update_cd" id= + "tree_node_update_cd"><img src= + "tree_node_update_policy_cd.png" alt="no image" /></a></h6> + + <h6 class="c1">A tree and its update policy.</h6> + + <p><tt>node_update</tt> (an instantiation of + <tt>Node_Update</tt>) must define <tt>metadata_type</tt> as + the type of metadata it requires. For order statistics, + <i>e.g.</i>, <tt>metadata_type</tt> might be <tt>size_t</tt>. + The tree defines within each node a <tt>metadata_type</tt> + object.</p> + + <p><tt>node_update</tt> must also define the following method + for restoring node invariants:</p> + <pre> + void + operator()(<a href= +"tree_node_iterator.html"><tt>node_iterator</tt></a> nd_it, <a href= +"tree_const_node_iterator.html"><tt>const_node_iterator</tt></a> end_nd_it) +</pre> + + <p>In this method, <tt>nd_it</tt> is a <a href= + "tree_node_iterator.html"><tt>node_iterator</tt></a> + corresponding to a node whose A) all descendants have valid + invariants, and B) its own invariants might be violated; + <tt>end_nd_it</tt> is a <a href= + "tree_const_node_iterator.html"><tt>const_node_iterator</tt></a> + corresponding to a just-after-leaf node. This method should + correct the node invariants of the node pointed to by + <tt>nd_it</tt>. For example, say node <i>x</i> in Figure + <a href="#restoring_node_invariants">Restoring node + invariants</a>-A has an invalid invariant, but its' children, + <i>y</i> and <i>z</i> have valid invariants. After the + invocation, all three nodes should have valid invariants, as in + Figure <a href="#restoring_node_invariants">Restoring node + invariants</a>-B.</p> + + <h6 class="c1"><a name="restoring_node_invariants" id= + "restoring_node_invariants"><img src= + "restoring_node_invariants.png" alt="no image" /></a></h6> + + <h6 class="c1">Invalidation of node invariants.</h6> + + <p>When a tree operation might invalidate some node invariant, + it invokes this method in its <tt>node_update</tt> base to + restore the invariant. For example, Figure <a href= + "#update_seq_diagram">Insert update sequence diagram</a> shows + an <tt>insert</tt> operation (point A); the tree performs some + operations, and calls the update functor three times (points B, + C, and D). (It is well known that any <tt>insert</tt>, + <tt>erase</tt>, <tt>split</tt> or <tt>join</tt>, can restore + all node invariants by a small number of node invariant updates + [<a href="references.html#clrs2001">clrs2001</a>].)</p> + + <h6 class="c1"><a name="update_seq_diagram" id= + "update_seq_diagram"><img src="update_seq_diagram.png" alt= + "no image" /></a></h6> + + <h6 class="c1">Insert update sequence diagram.</h6> + + <p>To complete the description of the scheme, three questions + need to be answered:</p> + + <ol> + <li>How can a tree which supports order statistics define a + method such as <tt>find_by_order</tt>?</li> + + <li>How can the node updater base access methods of the + tree?</li> + + <li>How can the following cyclic dependency be resolved? + <tt>node_update</tt> is a base class of the tree, yet it + uses node iterators defined in the tree (its child).</li> + </ol> + + <p>The first two questions are answered by the fact that + <tt>node_update</tt> (an instantiation of + <tt>Node_Update</tt>) is a <tt><b>public</b></tt> base class + of the tree. Consequently:</p> + + <ol> + <li>Any public methods of <tt>node_update</tt> are + automatically methods of the tree [<a href= + "references.html#alexandrescu01modern">alexandrescu01modern</a>]. + Thus an order-statistics node updater, <a href= + "tree_order_statistics_node_update.html"><tt>tree_order_statistics_node_update</tt></a> + defines the <tt>find_by_order</tt> method; any tree + instantiated by this policy consequently supports this method + as well.</li> + + <li>In C++, if a base class declares a method as + <tt><b>virtual</b></tt>, it is <tt><b>virtual</b></tt> in its + subclasses. If <tt>node_update</tt> needs to access one of + the tree's methods, say the member function <tt>end</tt>, it simply + declares that method as <tt><b>virtual</b></tt> + abstract.</li> + </ol> + + <p>The cyclic dependency is solved through template-template + parameters. <tt>Node_Update</tt> is parametrized by the tree's node iterators, its comparison + functor, and its allocator type. Thus, + instantiations of <tt>Node_Update</tt> have all information required.</p> + + <p class="c1"><tt>pb_ds</tt> assumes that constructing a metadata object and modifying it + are exception free. Suppose that during some method, say + <tt>insert</tt>, a metadata-related operation + (<i>e.g.</i>, changing the value of a metadata) throws an + exception. Ack! Rolling back the method is unusually complex.</p> + + <p>In <a href= + "concepts.html#concepts_null_policies">Interface::Concepts::Null + Policy Classes</a> a distinction was made between <i>redundant + policies</i> and <i>null policies</i>. Node invariants show a + case where null policies are required.</p> + + <p>Assume a regular tree is required, one which need not + support order statistics or interval overlap queries. + Seemingly, in this case a redundant policy - a policy which + doesn't affect nodes' contents would suffice. This, would lead + to the following drawbacks:</p> + + <ol> + <li>Each node would carry a useless metadata object, wasting + space.</li> + + <li>The tree cannot know if its <tt>Node_Update</tt> policy + actually modifies a node's metadata (this is halting + reducible). In Figure <a href= + "#rationale_null_node_update">Useless update path</a> , + assume the shaded node is inserted. The tree would have to + traverse the useless path shown to the root, applying + redundant updates all the way.</li> + </ol> + + <h6 class="c1"><a name="rationale_null_node_update" id= + "rationale_null_node_update"><img src= + "rationale_null_node_update.png" alt="no image" /></a></h6> + + <h6 class="c1">Useless update path.</h6> + + <p>A null policy class, <a href= + "null_tree_node_update.html"><tt>null_tree_node_update</tt></a> + solves both these problems. The tree detects that node + invariants are irrelevant, and defines all accordingly.</p> + + <h2><a name="add_methods" id="add_methods">Additional + Methods</a></h2> + + <p>Tree-based containers support split and join methods. + It is possible to split a tree so that it passes + all nodes with keys larger than a given key to a different + tree. These methods have the following advantages over the + alternative of externally inserting to the destination + tree and erasing from the source tree:</p> + + <ol> + <li>These methods are efficient - red-black trees are split + and joined in poly-logarithmic complexity; ordered-vector + trees are split and joined at linear complexity. The + alternatives have super-linear complexity.</li> + + <li>Aside from orders of growth, these operations perform + few allocations and de-allocations. For red-black trees, allocations are not performed, + and the methods are exception-free. </li> + </ol> + </div> +</body> +</html> |