boost/doc/html/heap/data_structures.html
2021-10-05 21:37:46 +02:00

522 lines
19 KiB
HTML
Raw Permalink Blame History

This file contains invisible Unicode characters

This file contains invisible Unicode characters that are indistinguishable to humans but may be processed differently by a computer. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Data Structures</title>
<link rel="stylesheet" href="../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../index.html" title="The Boost C++ Libraries BoostBook Documentation Subset">
<link rel="up" href="../heap.html" title="Chapter 17. Boost.Heap">
<link rel="prev" href="concepts.html" title="Concepts &amp; Interface">
<link rel="next" href="reference.html" title="Reference">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../boost.png"></td>
<td align="center"><a href="../../../index.html">Home</a></td>
<td align="center"><a href="../../../libs/libraries.htm">Libraries</a></td>
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
<td align="center"><a href="../../../more/index.htm">More</a></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="concepts.html"><img src="../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../heap.html"><img src="../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="reference.html"><img src="../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<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. 174183
</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 17.1. 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&lt;std::less&lt;T&gt;
&gt;</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&lt;std::allocator&lt;T&gt;
&gt;</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&lt;false&gt;</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&lt;boost::uintmax_t&gt;</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&lt;true&gt;</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>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="concepts.html"><img src="../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../heap.html"><img src="../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="reference.html"><img src="../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>