1<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> 2<html> 3<head> 4<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 5<title>Data Structures</title> 6<link rel="stylesheet" href="../../../doc/src/boostbook.css" type="text/css"> 7<meta name="generator" content="DocBook XSL Stylesheets V1.79.1"> 8<link rel="home" href="../index.html" title="The Boost C++ Libraries BoostBook Documentation Subset"> 9<link rel="up" href="../heap.html" title="Chapter 17. Boost.Heap"> 10<link rel="prev" href="concepts.html" title="Concepts & Interface"> 11<link rel="next" href="reference.html" title="Reference"> 12</head> 13<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> 14<table cellpadding="2" width="100%"><tr> 15<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../boost.png"></td> 16<td align="center"><a href="../../../index.html">Home</a></td> 17<td align="center"><a href="../../../libs/libraries.htm">Libraries</a></td> 18<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> 19<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> 20<td align="center"><a href="../../../more/index.htm">More</a></td> 21</tr></table> 22<hr> 23<div class="spirit-nav"> 24<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> 25</div> 26<div class="section"> 27<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 28<a name="heap.data_structures"></a><a class="link" href="data_structures.html" title="Data Structures">Data Structures</a> 29</h2></div></div></div> 30<div class="toc"><dl class="toc"><dt><span class="section"><a href="data_structures.html#heap.data_structures.data_structure_configuration">Data 31 Structure Configuration</a></span></dt></dl></div> 32<p> 33 <code class="literal">boost.heap</code> provides the following data structures: 34 </p> 35<div class="variablelist"> 36<p class="title"><b></b></p> 37<dl class="variablelist"> 38<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> 39<dd><p> 40 The <code class="computeroutput"><a class="link" href="../boost/heap/priority_queue.html" title="Class template priority_queue">priority_queue</a></code> 41 class is a wrapper to the stl heap functions. It implements a heap as 42 container adaptor ontop of a <code class="literal">std::vector</code> and is immutable. 43 </p></dd> 44<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> 45<dd> 46<p> 47 <a href="http://en.wikipedia.org/wiki/D-ary_heap" target="_top">D-ary heaps</a> 48 are a generalization of binary heap with each non-leaf node having N 49 children. For a low arity, the height of the heap is larger, but the 50 number of comparisons to find the largest child node is bigger. D-ary 51 heaps are implemented as container adaptors based on a <code class="literal">std::vector</code>. 52 </p> 53<p> 54 The data structure can be configured as mutable. This is achieved by 55 storing the values inside a std::list. 56 </p> 57</dd> 58<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> 59<dd><p> 60 <a href="http://en.wikipedia.org/wiki/Binomial_heap" target="_top">Binomial heaps</a> 61 are node-base heaps, that are implemented as a set of binomial trees 62 of piecewise different order. The most important heap operations have 63 a worst-case complexity of O(log n). In contrast to d-ary heaps, binomial 64 heaps can also be merged in O(log n). 65 </p></dd> 66<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> 67<dd><p> 68 <a href="http://en.wikipedia.org/wiki/Fibonacci_heap" target="_top">Fibonacci heaps</a> 69 are node-base heaps, that are implemented as a forest of heap-ordered 70 trees. They provide better amortized performance than binomial heaps. 71 Except <code class="literal">pop()</code> and <code class="literal">erase()</code>, the most 72 important heap operations have constant amortized complexity. 73 </p></dd> 74<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> 75<dd> 76<p> 77 <a href="http://en.wikipedia.org/wiki/Pairing_heap" target="_top">Pairing heaps</a> 78 are self-adjusting node-based heaps. Although design and implementation 79 are rather simple, the complexity analysis is yet unsolved. For details, 80 consult: 81 </p> 82<p> 83 Pettie, Seth (2005), "Towards a final analysis of pairing heaps", 84 Proc. 46th Annual IEEE Symposium on Foundations of Computer Science, 85 pp. 174–183 86 </p> 87</dd> 88<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> 89<dd><p> 90 <a href="http://en.wikipedia.org/wiki/Skew_heap" target="_top">Skew heaps</a> 91 are self-adjusting node-based heaps. Although there are no constraints 92 for the tree structure, all heap operations can be performed in O(log 93 n). 94 </p></dd> 95</dl> 96</div> 97<div class="table"> 98<a name="heap.data_structures.t0"></a><p class="title"><b>Table 17.1. Comparison of amortized complexity</b></p> 99<div class="table-contents"><table class="table" summary="Comparison of amortized complexity"> 100<colgroup> 101<col> 102<col> 103<col> 104<col> 105<col> 106<col> 107<col> 108<col> 109<col> 110</colgroup> 111<thead><tr> 112<th> 113 </th> 114<th> 115 <p> 116 <code class="literal">top()</code> 117 </p> 118 </th> 119<th> 120 <p> 121 <code class="literal">push()</code> 122 </p> 123 </th> 124<th> 125 <p> 126 <code class="literal">pop()</code> 127 </p> 128 </th> 129<th> 130 <p> 131 <code class="literal">update()</code> 132 </p> 133 </th> 134<th> 135 <p> 136 <code class="literal">increase()</code> 137 </p> 138 </th> 139<th> 140 <p> 141 <code class="literal">decrease()</code> 142 </p> 143 </th> 144<th> 145 <p> 146 <code class="literal">erase()</code> 147 </p> 148 </th> 149<th> 150 <p> 151 <code class="literal">merge_and_clear()</code> 152 </p> 153 </th> 154</tr></thead> 155<tbody> 156<tr> 157<td> 158 <p> 159 <code class="computeroutput"><a class="link" href="../boost/heap/priority_queue.html" title="Class template priority_queue">boost::heap::priority_queue</a></code> 160 </p> 161 </td> 162<td> 163 <p> 164 <code class="literal">O(1)</code> 165 </p> 166 </td> 167<td> 168 <p> 169 O(log(N)) 170 </p> 171 </td> 172<td> 173 <p> 174 O(log(N)) 175 </p> 176 </td> 177<td> 178 <p> 179 n/a 180 </p> 181 </td> 182<td> 183 <p> 184 n/a 185 </p> 186 </td> 187<td> 188 <p> 189 n/a 190 </p> 191 </td> 192<td> 193 <p> 194 n/a 195 </p> 196 </td> 197<td> 198 <p> 199 O((N+M)*log(N+M)) 200 </p> 201 </td> 202</tr> 203<tr> 204<td> 205 <p> 206 <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> 207 </p> 208 </td> 209<td> 210 <p> 211 <code class="literal">O(1)</code> 212 </p> 213 </td> 214<td> 215 <p> 216 O(log(N)) 217 </p> 218 </td> 219<td> 220 <p> 221 O(log(N)) 222 </p> 223 </td> 224<td> 225 <p> 226 O(log(N)) 227 </p> 228 </td> 229<td> 230 <p> 231 O(log(N)) 232 </p> 233 </td> 234<td> 235 <p> 236 O(log(N)) 237 </p> 238 </td> 239<td> 240 <p> 241 O(log(N)) 242 </p> 243 </td> 244<td> 245 <p> 246 O((N+M)*log(N+M)) 247 </p> 248 </td> 249</tr> 250<tr> 251<td> 252 <p> 253 <code class="computeroutput"><a class="link" href="../boost/heap/binomial_heap.html" title="Class template binomial_heap">boost::heap::binomial_heap</a></code> 254 </p> 255 </td> 256<td> 257 <p> 258 <code class="literal">O(1)</code> 259 </p> 260 </td> 261<td> 262 <p> 263 O(log(N)) 264 </p> 265 </td> 266<td> 267 <p> 268 O(log(N)) 269 </p> 270 </td> 271<td> 272 <p> 273 O(log(N)) 274 </p> 275 </td> 276<td> 277 <p> 278 O(log(N)) 279 </p> 280 </td> 281<td> 282 <p> 283 O(log(N)) 284 </p> 285 </td> 286<td> 287 <p> 288 O(log(N)) 289 </p> 290 </td> 291<td> 292 <p> 293 O(log(N+M)) 294 </p> 295 </td> 296</tr> 297<tr> 298<td> 299 <p> 300 <code class="computeroutput"><a class="link" href="../boost/heap/fibonacci_heap.html" title="Class template fibonacci_heap">boost::heap::fibonacci_heap</a></code> 301 </p> 302 </td> 303<td> 304 <p> 305 <code class="literal">O(1)</code> 306 </p> 307 </td> 308<td> 309 <p> 310 O(1) 311 </p> 312 </td> 313<td> 314 <p> 315 O(log(N)) 316 </p> 317 </td> 318<td> 319 <p> 320 O(log(N)) <a href="#ftn.heap.data_structures.f0" class="footnote" name="heap.data_structures.f0"><sup class="footnote">[a]</sup></a> 321 </p> 322 </td> 323<td> 324 <p> 325 O(1) 326 </p> 327 </td> 328<td> 329 <p> 330 O(log(N)) 331 </p> 332 </td> 333<td> 334 <p> 335 O(log(N)) 336 </p> 337 </td> 338<td> 339 <p> 340 O(1) 341 </p> 342 </td> 343</tr> 344<tr> 345<td> 346 <p> 347 <code class="computeroutput"><a class="link" href="../boost/heap/pairing_heap.html" title="Class template pairing_heap">boost::heap::pairing_heap</a></code> 348 </p> 349 </td> 350<td> 351 <p> 352 <code class="literal">O(1)</code> 353 </p> 354 </td> 355<td> 356 <p> 357 O(2**2*log(log(N))) 358 </p> 359 </td> 360<td> 361 <p> 362 O(log(N)) 363 </p> 364 </td> 365<td> 366 <p> 367 O(2**2*log(log(N))) 368 </p> 369 </td> 370<td> 371 <p> 372 O(2**2*log(log(N))) 373 </p> 374 </td> 375<td> 376 <p> 377 O(2**2*log(log(N))) 378 </p> 379 </td> 380<td> 381 <p> 382 O(2**2*log(log(N))) 383 </p> 384 </td> 385<td> 386 <p> 387 O(2**2*log(log(N))) 388 </p> 389 </td> 390</tr> 391<tr> 392<td> 393 <p> 394 <code class="computeroutput"><a class="link" href="../boost/heap/skew_heap.html" title="Class template skew_heap">boost::heap::skew_heap</a></code> 395 </p> 396 </td> 397<td> 398 <p> 399 <code class="literal">O(1)</code> 400 </p> 401 </td> 402<td> 403 <p> 404 O(log(N)) 405 </p> 406 </td> 407<td> 408 <p> 409 O(log(N)) 410 </p> 411 </td> 412<td> 413 <p> 414 O(log(N)) 415 </p> 416 </td> 417<td> 418 <p> 419 O(log(N)) 420 </p> 421 </td> 422<td> 423 <p> 424 O(log(N)) 425 </p> 426 </td> 427<td> 428 <p> 429 O(log(N)) 430 </p> 431 </td> 432<td> 433 <p> 434 O(log(N+M)) 435 </p> 436 </td> 437</tr> 438</tbody> 439<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> 440 The fibonacci a <code class="literal">update_lazy()</code> method, which 441 has O(log(N)) amortized complexity as well, but does not try to 442 consolidate the internal forest 443 </p></div></td></tr></tbody> 444</table></div> 445</div> 446<br class="table-break"><div class="section"> 447<div class="titlepage"><div><div><h3 class="title"> 448<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 449 Structure Configuration</a> 450</h3></div></div></div> 451<p> 452 The data structures can be configured with <a href="../../../libs/parameter/doc/html/index.html" target="_top">Boost.Parameter</a>-style 453 templates. 454 </p> 455<div class="variablelist"> 456<p class="title"><b></b></p> 457<dl class="variablelist"> 458<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> 459<dd><p> 460 Predicate for defining the heap order, optional (defaults to <code class="literal">boost::heap::compare<std::less<T> 461 ></code>) 462 </p></dd> 463<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> 464<dd><p> 465 Allocator for internal memory management, optional (defaults to <code class="literal">boost::heap::allocator<std::allocator<T> 466 ></code>) 467 </p></dd> 468<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> 469<dd><p> 470 Configures the heap to use a <a class="link" href="concepts.html#heap.concepts.stability" title="Stability">stable 471 heap order</a>, optional (defaults to <code class="literal">boost::heap::stable<false></code>). 472 </p></dd> 473<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> 474<dd><p> 475 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> 476 and <code class="computeroutput"><a class="link" href="../boost/heap/skew_heap.html" title="Class template skew_heap">boost::heap::skew_heap</a></code> 477 have to be configured with this policy to enable the <a class="link" href="concepts.html#heap.concepts.mutability" title="Mutability">mutability 478 interface</a>. 479 </p></dd> 480<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> 481<dd><p> 482 Configures the integer type used for the stability counter, optional 483 (defaults to <code class="literal">boost::heap::stability_counter_type<boost::uintmax_t></code>). 484 For more details, consult the <a class="link" href="concepts.html#heap.concepts.stability" title="Stability">Stability</a> 485 section. 486 </p></dd> 487<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> 488<dd><p> 489 Specifies, whether <code class="literal">size()</code> should have linear or 490 constant complexity. This argument is only available for node-based 491 heap data structures and if available, it is optional (defaults to 492 <code class="literal">boost::heap::constant_time_size<true></code>) 493 </p></dd> 494<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> 495<dd><p> 496 Specifies the arity of a d-ary heap. For details, please consult the 497 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> 498 </p></dd> 499<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> 500<dd><p> 501 Store the parent pointer in the heap nodes. This policy is only available 502 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>. 503 </p></dd> 504</dl> 505</div> 506</div> 507</div> 508<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 509<td align="left"></td> 510<td align="right"><div class="copyright-footer">Copyright © 2010, 2011 Tim Blechmann<p> 511 Distributed under the Boost Software License, Version 1.0. (See accompanying 512 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>) 513 </p> 514</div></td> 515</tr></table> 516<hr> 517<div class="spirit-nav"> 518<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> 519</div> 520</body> 521</html> 522
