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diff --git a/gcc-4.4.3/libstdc++-v3/doc/html/ext/pb_ds/tree_based_containers.html b/gcc-4.4.3/libstdc++-v3/doc/html/ext/pb_ds/tree_based_containers.html deleted file mode 100644 index 63c7c7482..000000000 --- a/gcc-4.4.3/libstdc++-v3/doc/html/ext/pb_ds/tree_based_containers.html +++ /dev/null @@ -1,358 +0,0 @@ -<!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> |