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| <div class="titlepage"><div><div><h2 class="title" style="clear: both"> |
| <a name="heap.data_structures"></a><a class="link" href="data_structures.html" title="Data Structures">Data Structures</a> |
| </h2></div></div></div> |
| <div class="toc"><dl class="toc"><dt><span class="section"><a href="data_structures.html#heap.data_structures.data_structure_configuration">Data |
| Structure Configuration</a></span></dt></dl></div> |
| <p> |
| <code class="literal">boost.heap</code> provides the following data structures: |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl class="variablelist"> |
| <dt><span class="term"><code class="computeroutput"><a class="link" href="../boost/heap/priority_queue.html" title="Class template priority_queue">boost::heap::priority_queue</a></code></span></dt> |
| <dd><p> |
| The <code class="computeroutput"><a class="link" href="../boost/heap/priority_queue.html" title="Class template priority_queue">priority_queue</a></code> |
| class is a wrapper to the stl heap functions. It implements a heap as |
| container adaptor ontop of a <code class="literal">std::vector</code> and is immutable. |
| </p></dd> |
| <dt><span class="term"><code class="computeroutput"><a class="link" href="../boost/heap/d_ary_heap.html" title="Class template d_ary_heap">boost::heap::d_ary_heap</a></code></span></dt> |
| <dd> |
| <p> |
| <a href="http://en.wikipedia.org/wiki/D-ary_heap" target="_top">D-ary heaps</a> |
| are a generalization of binary heap with each non-leaf node having N |
| children. For a low arity, the height of the heap is larger, but the |
| number of comparisons to find the largest child node is bigger. D-ary |
| heaps are implemented as container adaptors based on a <code class="literal">std::vector</code>. |
| </p> |
| <p> |
| The data structure can be configured as mutable. This is achieved by |
| storing the values inside a std::list. |
| </p> |
| </dd> |
| <dt><span class="term"><code class="computeroutput"><a class="link" href="../boost/heap/binomial_heap.html" title="Class template binomial_heap">boost::heap::binomial_heap</a></code></span></dt> |
| <dd><p> |
| <a href="http://en.wikipedia.org/wiki/Binomial_heap" target="_top">Binomial heaps</a> |
| are node-base heaps, that are implemented as a set of binomial trees |
| of piecewise different order. The most important heap operations have |
| a worst-case complexity of O(log n). In contrast to d-ary heaps, binomial |
| heaps can also be merged in O(log n). |
| </p></dd> |
| <dt><span class="term"><code class="computeroutput"><a class="link" href="../boost/heap/fibonacci_heap.html" title="Class template fibonacci_heap">boost::heap::fibonacci_heap</a></code></span></dt> |
| <dd><p> |
| <a href="http://en.wikipedia.org/wiki/Fibonacci_heap" target="_top">Fibonacci heaps</a> |
| are node-base heaps, that are implemented as a forest of heap-ordered |
| trees. They provide better amortized performance than binomial heaps. |
| Except <code class="literal">pop()</code> and <code class="literal">erase()</code>, the most |
| important heap operations have constant amortized complexity. |
| </p></dd> |
| <dt><span class="term"><code class="computeroutput"><a class="link" href="../boost/heap/pairing_heap.html" title="Class template pairing_heap">boost::heap::pairing_heap</a></code></span></dt> |
| <dd> |
| <p> |
| <a href="http://en.wikipedia.org/wiki/Pairing_heap" target="_top">Pairing heaps</a> |
| are self-adjusting node-based heaps. Although design and implementation |
| are rather simple, the complexity analysis is yet unsolved. For details, |
| consult: |
| </p> |
| <p> |
| Pettie, Seth (2005), "Towards a final analysis of pairing heaps", |
| Proc. 46th Annual IEEE Symposium on Foundations of Computer Science, |
| pp. 174–183 |
| </p> |
| </dd> |
| <dt><span class="term"><code class="computeroutput"><a class="link" href="../boost/heap/skew_heap.html" title="Class template skew_heap">boost::heap::skew_heap</a></code></span></dt> |
| <dd><p> |
| <a href="http://en.wikipedia.org/wiki/Skew_heap" target="_top">Skew heaps</a> |
| are self-adjusting node-based heaps. Although there are no constraints |
| for the tree structure, all heap operations can be performed in O(log |
| n). |
| </p></dd> |
| </dl> |
| </div> |
| <div class="table"> |
| <a name="heap.data_structures.t0"></a><p class="title"><b>Table 13.1. Comparison of amortized complexity</b></p> |
| <div class="table-contents"><table class="table" summary="Comparison of amortized complexity"> |
| <colgroup> |
| <col> |
| <col> |
| <col> |
| <col> |
| <col> |
| <col> |
| <col> |
| <col> |
| <col> |
| </colgroup> |
| <thead><tr> |
| <th> |
| </th> |
| <th> |
| <p> |
| <code class="literal">top()</code> |
| </p> |
| </th> |
| <th> |
| <p> |
| <code class="literal">push()</code> |
| </p> |
| </th> |
| <th> |
| <p> |
| <code class="literal">pop()</code> |
| </p> |
| </th> |
| <th> |
| <p> |
| <code class="literal">update()</code> |
| </p> |
| </th> |
| <th> |
| <p> |
| <code class="literal">increase()</code> |
| </p> |
| </th> |
| <th> |
| <p> |
| <code class="literal">decrease()</code> |
| </p> |
| </th> |
| <th> |
| <p> |
| <code class="literal">erase()</code> |
| </p> |
| </th> |
| <th> |
| <p> |
| <code class="literal">merge_and_clear()</code> |
| </p> |
| </th> |
| </tr></thead> |
| <tbody> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/heap/priority_queue.html" title="Class template priority_queue">boost::heap::priority_queue</a></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="literal">O(1)</code> |
| </p> |
| </td> |
| <td> |
| <p> |
| O(log(N)) |
| </p> |
| </td> |
| <td> |
| <p> |
| O(log(N)) |
| </p> |
| </td> |
| <td> |
| <p> |
| n/a |
| </p> |
| </td> |
| <td> |
| <p> |
| n/a |
| </p> |
| </td> |
| <td> |
| <p> |
| n/a |
| </p> |
| </td> |
| <td> |
| <p> |
| n/a |
| </p> |
| </td> |
| <td> |
| <p> |
| O((N+M)*log(N+M)) |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/heap/d_ary_heap.html" title="Class template d_ary_heap">boost::heap::d_ary_heap</a></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="literal">O(1)</code> |
| </p> |
| </td> |
| <td> |
| <p> |
| O(log(N)) |
| </p> |
| </td> |
| <td> |
| <p> |
| O(log(N)) |
| </p> |
| </td> |
| <td> |
| <p> |
| O(log(N)) |
| </p> |
| </td> |
| <td> |
| <p> |
| O(log(N)) |
| </p> |
| </td> |
| <td> |
| <p> |
| O(log(N)) |
| </p> |
| </td> |
| <td> |
| <p> |
| O(log(N)) |
| </p> |
| </td> |
| <td> |
| <p> |
| O((N+M)*log(N+M)) |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/heap/binomial_heap.html" title="Class template binomial_heap">boost::heap::binomial_heap</a></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="literal">O(1)</code> |
| </p> |
| </td> |
| <td> |
| <p> |
| O(log(N)) |
| </p> |
| </td> |
| <td> |
| <p> |
| O(log(N)) |
| </p> |
| </td> |
| <td> |
| <p> |
| O(log(N)) |
| </p> |
| </td> |
| <td> |
| <p> |
| O(log(N)) |
| </p> |
| </td> |
| <td> |
| <p> |
| O(log(N)) |
| </p> |
| </td> |
| <td> |
| <p> |
| O(log(N)) |
| </p> |
| </td> |
| <td> |
| <p> |
| O(log(N+M)) |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/heap/fibonacci_heap.html" title="Class template fibonacci_heap">boost::heap::fibonacci_heap</a></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="literal">O(1)</code> |
| </p> |
| </td> |
| <td> |
| <p> |
| O(1) |
| </p> |
| </td> |
| <td> |
| <p> |
| O(log(N)) |
| </p> |
| </td> |
| <td> |
| <p> |
| O(log(N)) <a href="#ftn.heap.data_structures.f0" class="footnote" name="heap.data_structures.f0"><sup class="footnote">[a]</sup></a> |
| </p> |
| </td> |
| <td> |
| <p> |
| O(1) |
| </p> |
| </td> |
| <td> |
| <p> |
| O(log(N)) |
| </p> |
| </td> |
| <td> |
| <p> |
| O(log(N)) |
| </p> |
| </td> |
| <td> |
| <p> |
| O(1) |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/heap/pairing_heap.html" title="Class template pairing_heap">boost::heap::pairing_heap</a></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="literal">O(1)</code> |
| </p> |
| </td> |
| <td> |
| <p> |
| O(2**2*log(log(N))) |
| </p> |
| </td> |
| <td> |
| <p> |
| O(log(N)) |
| </p> |
| </td> |
| <td> |
| <p> |
| O(2**2*log(log(N))) |
| </p> |
| </td> |
| <td> |
| <p> |
| O(2**2*log(log(N))) |
| </p> |
| </td> |
| <td> |
| <p> |
| O(2**2*log(log(N))) |
| </p> |
| </td> |
| <td> |
| <p> |
| O(2**2*log(log(N))) |
| </p> |
| </td> |
| <td> |
| <p> |
| O(2**2*log(log(N))) |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/heap/skew_heap.html" title="Class template skew_heap">boost::heap::skew_heap</a></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="literal">O(1)</code> |
| </p> |
| </td> |
| <td> |
| <p> |
| O(log(N)) |
| </p> |
| </td> |
| <td> |
| <p> |
| O(log(N)) |
| </p> |
| </td> |
| <td> |
| <p> |
| O(log(N)) |
| </p> |
| </td> |
| <td> |
| <p> |
| O(log(N)) |
| </p> |
| </td> |
| <td> |
| <p> |
| O(log(N)) |
| </p> |
| </td> |
| <td> |
| <p> |
| O(log(N)) |
| </p> |
| </td> |
| <td> |
| <p> |
| O(log(N+M)) |
| </p> |
| </td> |
| </tr> |
| </tbody> |
| <tbody class="footnotes"><tr><td colspan="9"><div id="ftn.heap.data_structures.f0" class="footnote"><p><a href="#heap.data_structures.f0" class="para"><sup class="para">[a] </sup></a> |
| The fibonacci a <code class="literal">update_lazy()</code> method, which |
| has O(log(N)) amortized complexity as well, but does not try to |
| consolidate the internal forest |
| </p></div></td></tr></tbody> |
| </table></div> |
| </div> |
| <br class="table-break"><div class="section"> |
| <div class="titlepage"><div><div><h3 class="title"> |
| <a name="heap.data_structures.data_structure_configuration"></a><a class="link" href="data_structures.html#heap.data_structures.data_structure_configuration" title="Data Structure Configuration">Data |
| Structure Configuration</a> |
| </h3></div></div></div> |
| <p> |
| The data structures can be configured with <a href="../../../libs/parameter/doc/html/index.html" target="_top">Boost.Parameter</a>-style |
| templates. |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl class="variablelist"> |
| <dt><span class="term"><code class="computeroutput"><a class="link" href="../boost/heap/compare.html" title="Struct template compare">boost::heap::compare</a></code></span></dt> |
| <dd><p> |
| Predicate for defining the heap order, optional (defaults to <code class="literal">boost::heap::compare<std::less<T> |
| ></code>) |
| </p></dd> |
| <dt><span class="term"><code class="computeroutput"><a class="link" href="../boost/heap/allocator.html" title="Struct template allocator">boost::heap::allocator</a></code></span></dt> |
| <dd><p> |
| Allocator for internal memory management, optional (defaults to <code class="literal">boost::heap::allocator<std::allocator<T> |
| ></code>) |
| </p></dd> |
| <dt><span class="term"><code class="computeroutput"><a class="link" href="../boost/heap/stable.html" title="Struct template stable">boost::heap::stable</a></code></span></dt> |
| <dd><p> |
| Configures the heap to use a <a class="link" href="concepts.html#heap.concepts.stability" title="Stability">stable |
| heap order</a>, optional (defaults to <code class="literal">boost::heap::stable<false></code>). |
| </p></dd> |
| <dt><span class="term"><code class="computeroutput"><a class="link" href="../boost/heap/mutable_.html" title="Struct template mutable_">boost::heap::mutable_</a></code></span></dt> |
| <dd><p> |
| Configures the heap to be mutable. <code class="computeroutput"><a class="link" href="../boost/heap/d_ary_heap.html" title="Class template d_ary_heap">boost::heap::d_ary_heap</a></code> |
| and <code class="computeroutput"><a class="link" href="../boost/heap/skew_heap.html" title="Class template skew_heap">boost::heap::skew_heap</a></code> |
| have to be configured with this policy to enable the <a class="link" href="concepts.html#heap.concepts.mutability" title="Mutability">mutability |
| interface</a>. |
| </p></dd> |
| <dt><span class="term"><code class="computeroutput"><a class="link" href="../boost/heap/stability_counter_type.html" title="Struct template stability_counter_type">boost::heap::stability_counter_type</a></code></span></dt> |
| <dd><p> |
| Configures the integer type used for the stability counter, optional |
| (defaults to <code class="literal">boost::heap::stability_counter_type<boost::uintmax_t></code>). |
| For more details, consult the <a class="link" href="concepts.html#heap.concepts.stability" title="Stability">Stability</a> |
| section. |
| </p></dd> |
| <dt><span class="term"><code class="computeroutput"><a class="link" href="../boost/heap/constant_time_size.html" title="Struct template constant_time_size">boost::heap::constant_time_size</a></code></span></dt> |
| <dd><p> |
| Specifies, whether <code class="literal">size()</code> should have linear or |
| constant complexity. This argument is only available for node-based |
| heap data structures and if available, it is optional (defaults to |
| <code class="literal">boost::heap::constant_time_size<true></code>) |
| </p></dd> |
| <dt><span class="term"><code class="computeroutput"><a class="link" href="../boost/heap/arity.html" title="Struct template arity">boost::heap::arity</a></code></span></dt> |
| <dd><p> |
| Specifies the arity of a d-ary heap. For details, please consult the |
| class reference of <code class="computeroutput"><a class="link" href="../boost/heap/d_ary_heap.html" title="Class template d_ary_heap">boost::heap::d_ary_heap</a></code> |
| </p></dd> |
| <dt><span class="term"><code class="computeroutput"><a class="link" href="../boost/heap/store_parent_pointer.html" title="Struct template store_parent_pointer">boost::heap::store_parent_pointer</a></code></span></dt> |
| <dd><p> |
| Store the parent pointer in the heap nodes. This policy is only available |
| in the <code class="computeroutput"><a class="link" href="../boost/heap/skew_heap.html" title="Class template skew_heap">boost::heap::skew_heap</a></code>. |
| </p></dd> |
| </dl> |
| </div> |
| </div> |
| </div> |
| <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> |
| <td align="left"></td> |
| <td align="right"><div class="copyright-footer">Copyright © 2010, 2011 Tim Blechmann<p> |
| Distributed under the Boost Software License, Version 1.0. (See accompanying |
| file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) |
| </p> |
| </div></td> |
| </tr></table> |
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