1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Subtraction</title> 5<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> 6<meta name="generator" content="DocBook XSL Stylesheets V1.79.1"> 7<link rel="home" href="../../index.html" title="Chapter 1. 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alt="Prev"></a><a accesskey="u" href="../function_reference.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="insertion.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> 24</div> 25<div class="section"> 26<div class="titlepage"><div><div><h3 class="title"> 27<a name="boost_icl.function_reference.subtraction"></a><a class="link" href="subtraction.html" title="Subtraction">Subtraction</a> 28</h3></div></div></div> 29<div class="toc"><dl class="toc"> 30<dt><span class="section"><a href="subtraction.html#boost_icl.function_reference.subtraction.synopsis">Synopsis</a></span></dt> 31<dt><span class="section"><a href="subtraction.html#boost_icl.function_reference.subtraction.functions">Functions</a></span></dt> 32<dt><span class="section"><a href="subtraction.html#boost_icl.function_reference.subtraction.inplace_operators">Inplace 33 operators</a></span></dt> 34<dt><span class="section"><a href="subtraction.html#boost_icl.function_reference.subtraction.infix_operators">Infix 35 operators</a></span></dt> 36<dt><span class="section"><a href="subtraction.html#boost_icl.function_reference.subtraction.subtraction_on_intervals">Subtraction 37 on Intervals</a></span></dt> 38</dl></div> 39<div class="section"> 40<div class="titlepage"><div><div><h4 class="title"> 41<a name="boost_icl.function_reference.subtraction.synopsis"></a><a class="link" href="subtraction.html#boost_icl.function_reference.subtraction.synopsis" title="Synopsis">Synopsis</a> 42</h4></div></div></div> 43<div class="informaltable"><table class="table"> 44<colgroup> 45<col> 46<col> 47<col> 48<col> 49<col> 50<col> 51</colgroup> 52<thead><tr> 53<th> 54 <p> 55 Subtraction 56 </p> 57 </th> 58<th> 59 <p> 60 intervals 61 </p> 62 </th> 63<th> 64 <p> 65 interval<br> sets 66 </p> 67 </th> 68<th> 69 <p> 70 interval<br> maps 71 </p> 72 </th> 73<th> 74 <p> 75 element<br> sets 76 </p> 77 </th> 78<th> 79 <p> 80 element<br> maps 81 </p> 82 </th> 83</tr></thead> 84<tbody> 85<tr> 86<td> 87 <p> 88 <code class="computeroutput"><span class="identifier">T</span><span class="special">&</span> 89 <span class="identifier">T</span><span class="special">::</span><span class="identifier">subtract</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">P</span><span class="special">&)</span></code> 90 </p> 91 </td> 92<td> 93 </td> 94<td> 95 <p> 96 <a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a> 97 <a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a> 98 </p> 99 </td> 100<td> 101 <p> 102 <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a> 103 <a class="link" href="../interface/function_synopsis.html#interval_mapping_type"><span class="bold"><strong>p</strong></span></a> 104 </p> 105 </td> 106<td> 107 </td> 108<td> 109 <p> 110 <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a> 111 </p> 112 </td> 113</tr> 114<tr> 115<td> 116 <p> 117 <code class="computeroutput"><span class="identifier">T</span><span class="special">&</span> 118 <span class="identifier">subtract</span><span class="special">(</span><span class="identifier">T</span><span class="special">&,</span> 119 <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&)</span></code> 120 </p> 121 </td> 122<td> 123 </td> 124<td> 125 <p> 126 <a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a> 127 <a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a> 128 </p> 129 </td> 130<td> 131 <p> 132 <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a> 133 <a class="link" href="../interface/function_synopsis.html#interval_mapping_type"><span class="bold"><strong>p</strong></span></a> 134 </p> 135 </td> 136<td> 137 <p> 138 <a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a> 139 </p> 140 </td> 141<td> 142 <p> 143 <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a> 144 </p> 145 </td> 146</tr> 147<tr> 148<td> 149 <p> 150 <code class="computeroutput"><span class="identifier">T</span><span class="special">&</span> 151 <span class="keyword">operator</span> <span class="special">-=(</span><span class="identifier">T</span><span class="special">&,</span> 152 <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&)</span></code> 153 </p> 154 </td> 155<td> 156 </td> 157<td> 158 <p> 159 <a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a> 160 <a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a> 161 <a class="link" href="../interface/function_synopsis.html#interval_set_types"><span class="bold"><strong>S</strong></span></a> 162 </p> 163 </td> 164<td> 165 <p> 166 <a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a> 167 <a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a> 168 <a class="link" href="../interface/function_synopsis.html#interval_set_types"><span class="bold"><strong>S</strong></span></a> 169 <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a> 170 <a class="link" href="../interface/function_synopsis.html#interval_mapping_type"><span class="bold"><strong>p</strong></span></a> 171 <a class="link" href="../interface/function_synopsis.html#interval_map_types"><span class="bold"><strong>M</strong></span></a> 172 </p> 173 </td> 174<td> 175 <p> 176 <a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a> 177 <a class="link" href="../interface/function_synopsis.html#itl_set_type"><span class="bold"><strong>s</strong></span></a> 178 </p> 179 </td> 180<td> 181 <p> 182 <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a> 183 <a class="link" href="../interface/function_synopsis.html#itl_map_type"><span class="bold"><strong>m</strong></span></a> 184 </p> 185 </td> 186</tr> 187<tr> 188<td> 189 <p> 190 <code class="computeroutput"><span class="identifier">T</span> <span class="keyword">operator</span> 191 <span class="special">-</span> <span class="special">(</span><span class="identifier">T</span><span class="special">,</span> 192 <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&)</span></code> 193 </p> 194 </td> 195<td> 196 </td> 197<td> 198 <p> 199 <a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a> 200 <a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a> 201 <a class="link" href="../interface/function_synopsis.html#interval_set_types"><span class="bold"><strong>S</strong></span></a> 202 </p> 203 </td> 204<td> 205 <p> 206 <a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a> 207 <a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a> 208 <a class="link" href="../interface/function_synopsis.html#interval_set_types"><span class="bold"><strong>S</strong></span></a> 209 <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a> 210 <a class="link" href="../interface/function_synopsis.html#interval_mapping_type"><span class="bold"><strong>p</strong></span></a> 211 <a class="link" href="../interface/function_synopsis.html#interval_map_types"><span class="bold"><strong>M</strong></span></a> 212 </p> 213 </td> 214<td> 215 <p> 216 <a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a> 217 <a class="link" href="../interface/function_synopsis.html#itl_set_type"><span class="bold"><strong>s</strong></span></a> 218 </p> 219 </td> 220<td> 221 <p> 222 <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a> 223 <a class="link" href="../interface/function_synopsis.html#itl_map_type"><span class="bold"><strong>m</strong></span></a> 224 </p> 225 </td> 226</tr> 227<tr> 228<td> 229 <p> 230 <code class="computeroutput"><span class="identifier">T</span> <span class="identifier">left_subtract</span><span class="special">(</span><span class="identifier">T</span><span class="special">,</span> <span class="keyword">const</span> 231 <span class="identifier">T</span><span class="special">&)</span></code> 232 </p> 233 </td> 234<td> 235 <p> 236 1 237 </p> 238 </td> 239<td> 240 </td> 241<td> 242 </td> 243<td> 244 </td> 245<td> 246 </td> 247</tr> 248<tr> 249<td> 250 <p> 251 <code class="computeroutput"><span class="identifier">T</span> <span class="identifier">right_subtract</span><span class="special">(</span><span class="identifier">T</span><span class="special">,</span> <span class="keyword">const</span> 252 <span class="identifier">T</span><span class="special">&)</span></code> 253 </p> 254 </td> 255<td> 256 <p> 257 1 258 </p> 259 </td> 260<td> 261 </td> 262<td> 263 </td> 264<td> 265 </td> 266<td> 267 </td> 268</tr> 269</tbody> 270</table></div> 271<p> 272 Functions and operators that implement <span class="emphasis"><em><span class="bold"><strong>Subtraction</strong></span></em></span> 273 on <span class="bold"><strong>icl</strong></span> objects are given in the table 274 above. 275 </p> 276<div class="informaltable"><table class="table"> 277<colgroup> 278<col> 279<col> 280</colgroup> 281<thead><tr> 282<th> 283 </th> 284<th> 285 <p> 286 Description of Subtraction 287 </p> 288 </th> 289</tr></thead> 290<tbody> 291<tr> 292<td> 293 <p> 294 <code class="computeroutput"><span class="identifier">Sets</span></code> 295 </p> 296 </td> 297<td> 298 <p> 299 Subtraction on Sets implements <span class="emphasis"><em><span class="bold"><strong>set 300 difference</strong></span></em></span> 301 </p> 302 </td> 303</tr> 304<tr> 305<td> 306 <p> 307 <code class="computeroutput"><span class="identifier">Maps</span></code> 308 </p> 309 </td> 310<td> 311 <p> 312 Subtraction on Maps implements a <span class="emphasis"><em><span class="bold"><strong>map 313 difference</strong></span></em></span> function similar to <span class="emphasis"><em>set 314 difference</em></span>. If, on subtraction of an element value 315 pair <code class="computeroutput"><span class="special">(</span><span class="identifier">k</span><span class="special">,</span><span class="identifier">v</span><span class="special">)</span></code> it's key <code class="computeroutput"><span class="identifier">k</span></code> 316 is in the map already, the subtraction function is propagated 317 to the associated value. On the associated value an aggregation 318 is performed, that reverses the effect of the corresponding addition 319 function. 320 </p> 321 <p> 322 Find more on <a class="link" href="../concepts/aggrovering.html" title="Addability, Subtractability and Aggregate on Overlap"><span class="emphasis"><em>subtractability 323 of maps</em></span></a> and related <a class="link" href="../semantics/maps.html" title="Maps"><span class="emphasis"><em>semantic 324 issues</em></span></a> following the links. 325 </p> 326 </td> 327</tr> 328</tbody> 329</table></div> 330</div> 331<div class="section"> 332<div class="titlepage"><div><div><h4 class="title"> 333<a name="boost_icl.function_reference.subtraction.functions"></a><a class="link" href="subtraction.html#boost_icl.function_reference.subtraction.functions" title="Functions">Functions</a> 334</h4></div></div></div> 335<p> 336 The admissible combinations of types for subtraction functions can be summarized 337 in the <span class="emphasis"><em><span class="bold"><strong>overload table</strong></span></em></span> 338 below: 339 </p> 340<p> 341</p> 342<pre class="programlisting"><span class="comment">// overload table for T\P| e i b p </span> 343<span class="identifier">T</span><span class="special">&</span> <span class="identifier">T</span><span class="special">::</span><span class="identifier">subtract</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">P</span><span class="special">&)</span> <span class="special">---+--------</span> 344<span class="identifier">T</span><span class="special">&</span> <span class="identifier">subtract</span><span class="special">(</span><span class="identifier">T</span><span class="special">&,</span> <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&)</span> <span class="identifier">s</span> <span class="special">|</span> <span class="identifier">s</span> 345 <span class="identifier">m</span> <span class="special">|</span> <span class="identifier">m</span> 346 <span class="identifier">S</span> <span class="special">|</span> <span class="identifier">S</span> <span class="identifier">S</span> 347 <span class="identifier">M</span> <span class="special">|</span> <span class="identifier">M</span> <span class="identifier">M</span> 348</pre> 349<p> 350 </p> 351<p> 352 The next table contains complexity characteristics for <code class="computeroutput"><span class="identifier">subtract</span></code>. 353 </p> 354<div class="table"> 355<a name="boost_icl.function_reference.subtraction.functions.t0"></a><p class="title"><b>Table 1.24. Time Complexity for function subtract on icl containers</b></p> 356<div class="table-contents"><table class="table" summary="Time Complexity for function subtract on icl containers"> 357<colgroup> 358<col> 359<col> 360<col> 361<col> 362<col> 363</colgroup> 364<thead><tr> 365<th> 366 <p> 367 <code class="computeroutput"><span class="identifier">T</span><span class="special">&</span> 368 <span class="identifier">T</span><span class="special">::</span><span class="identifier">subtract</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">P</span><span class="special">&)</span></code><br> <code class="computeroutput"><span class="identifier">T</span><span class="special">&</span> <span class="identifier">subtract</span><span class="special">(</span><span class="identifier">T</span><span class="special">&,</span> <span class="keyword">const</span> 369 <span class="identifier">P</span><span class="special">&)</span></code> 370 </p> 371 </th> 372<th> 373 <p> 374 domain<br> type 375 </p> 376 </th> 377<th> 378 <p> 379 interval<br> type 380 </p> 381 </th> 382<th> 383 <p> 384 domain<br> mapping<br> type 385 </p> 386 </th> 387<th> 388 <p> 389 interval<br> mapping<br> type 390 </p> 391 </th> 392</tr></thead> 393<tbody> 394<tr> 395<td> 396 <p> 397 <a href="http://www.cplusplus.com/reference/stl/set/" target="_top"><code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">set</span></code> </a> 398 </p> 399 </td> 400<td> 401 <p> 402 <span class="emphasis"><em>O(log n)</em></span> 403 </p> 404 </td> 405<td> 406 </td> 407<td> 408 </td> 409<td> 410 </td> 411</tr> 412<tr> 413<td> 414 <p> 415 <code class="computeroutput"><a class="link" href="../../boost/icl/map.html" title="Class template map">icl::map</a></code> 416 </p> 417 </td> 418<td> 419 <p> 420 <span class="emphasis"><em>O(log n)</em></span> 421 </p> 422 </td> 423<td> 424 </td> 425<td> 426 <p> 427 <span class="emphasis"><em>O(log n)</em></span> 428 </p> 429 </td> 430<td> 431 </td> 432</tr> 433<tr> 434<td> 435 <p> 436 <code class="computeroutput"><a class="link" href="../../boost/icl/interval_set.html" title="Class template interval_set">interval_sets</a></code> 437 </p> 438 </td> 439<td> 440 <p> 441 <span class="emphasis"><em>O(log n)</em></span> 442 </p> 443 </td> 444<td> 445 <p> 446 <span class="emphasis"><em>amortized<br> O(log n)</em></span> 447 </p> 448 </td> 449<td> 450 </td> 451<td> 452 </td> 453</tr> 454<tr> 455<td> 456 <p> 457 <code class="computeroutput"><a class="link" href="../../boost/icl/interval_map.html" title="Class template interval_map">interval_maps</a></code> 458 </p> 459 </td> 460<td> 461 <p> 462 <span class="emphasis"><em>O(log n)</em></span> 463 </p> 464 </td> 465<td> 466 <p> 467 <span class="emphasis"><em>O(n)</em></span> 468 </p> 469 </td> 470<td> 471 <p> 472 <span class="emphasis"><em>O(log n)</em></span> 473 </p> 474 </td> 475<td> 476 <p> 477 <span class="emphasis"><em>O(n)</em></span> 478 </p> 479 </td> 480</tr> 481</tbody> 482</table></div> 483</div> 484<br class="table-break"> 485</div> 486<div class="section"> 487<div class="titlepage"><div><div><h4 class="title"> 488<a name="boost_icl.function_reference.subtraction.inplace_operators"></a><a class="link" href="subtraction.html#boost_icl.function_reference.subtraction.inplace_operators" title="Inplace operators">Inplace 489 operators</a> 490</h4></div></div></div> 491<p> 492 As presented in the overload tables for <code class="computeroutput"><span class="keyword">operator</span> 493 <span class="special">-=</span></code> more type combinations are provided 494 for subtraction than for addition. 495 </p> 496<p> 497</p> 498<pre class="programlisting"><span class="comment">// overload tables for element containers: interval containers: </span> 499<span class="identifier">T</span><span class="special">&</span> <span class="keyword">operator</span> <span class="special">-=</span> <span class="special">(</span><span class="identifier">T</span><span class="special">&,</span> <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&)</span> <span class="special">-=</span> <span class="special">|</span> <span class="identifier">e</span> <span class="identifier">b</span> <span class="identifier">s</span> <span class="identifier">m</span> <span class="special">-=</span> <span class="special">|</span> <span class="identifier">e</span> <span class="identifier">i</span> <span class="identifier">b</span> <span class="identifier">p</span> <span class="identifier">S</span> <span class="identifier">M</span> 500 <span class="special">---+--------</span> <span class="special">---+------------</span> 501 <span class="identifier">s</span> <span class="special">|</span> <span class="identifier">s</span> <span class="identifier">s</span> <span class="identifier">S</span> <span class="special">|</span> <span class="identifier">S</span> <span class="identifier">S</span> <span class="identifier">S</span> 502 <span class="identifier">m</span> <span class="special">|</span> <span class="identifier">m</span> <span class="identifier">m</span> <span class="identifier">m</span> <span class="identifier">m</span> <span class="identifier">M</span> <span class="special">|</span> <span class="identifier">M</span> <span class="identifier">M</span> <span class="identifier">M</span> <span class="identifier">M</span> <span class="identifier">M</span> <span class="identifier">M</span> 503</pre> 504<p> 505 </p> 506<p> 507 Subtraction provides the <span class="emphasis"><em>reverse</em></span> operation of an addition 508 for these overloads, 509 </p> 510<p> 511</p> 512<pre class="programlisting"><span class="comment">// Reverse addition -= | e b s m -= | e i b p S M </span> 513 <span class="special">---+--------</span> <span class="special">---+------------</span> 514 <span class="identifier">s</span> <span class="special">|</span> <span class="identifier">s</span> <span class="identifier">s</span> <span class="identifier">S</span> <span class="special">|</span> <span class="identifier">S</span> <span class="identifier">S</span> <span class="identifier">S</span> 515 <span class="identifier">m</span> <span class="special">|</span> <span class="identifier">m</span> <span class="identifier">m</span> <span class="identifier">M</span> <span class="special">|</span> <span class="identifier">M</span> <span class="identifier">M</span> <span class="identifier">M</span> 516</pre> 517<p> 518 </p> 519<p> 520 <span class="bold"><strong>and</strong></span> you can erase parts of <code class="computeroutput"><a class="link" href="../../boost/icl/map.html" title="Class template map">icl::maps</a></code> or <code class="computeroutput"><a class="link" href="../../boost/icl/interval_map.html" title="Class template interval_map">interval_maps</a></code> 521 using <span class="emphasis"><em>key values</em></span>, <span class="emphasis"><em>intervals</em></span> or 522 <span class="emphasis"><em>element or interval sets</em></span> using these overloads: 523 </p> 524<p> 525</p> 526<pre class="programlisting"><span class="comment">// Erasure by key objects -= | e b s m -= | e i b p S M </span> 527 <span class="special">---+--------</span> <span class="special">---+------------</span> 528 <span class="identifier">s</span> <span class="special">|</span> <span class="identifier">s</span> <span class="identifier">s</span> <span class="identifier">S</span> <span class="special">|</span> <span class="identifier">S</span> <span class="identifier">S</span> <span class="identifier">S</span> 529 <span class="identifier">m</span> <span class="special">|</span> <span class="identifier">m</span> <span class="identifier">m</span> <span class="identifier">M</span> <span class="special">|</span> <span class="identifier">M</span> <span class="identifier">M</span> <span class="identifier">M</span> 530</pre> 531<p> 532 </p> 533<p> 534 On Sets both function groups fall together as <span class="emphasis"><em><span class="bold"><strong>set 535 difference</strong></span></em></span>. 536 </p> 537<p> 538 Complexity characteristics for inplace subtraction operations are given 539 by the next tables where 540</p> 541<pre class="programlisting"><span class="identifier">n</span> <span class="special">=</span> <span class="identifier">iterative_size</span><span class="special">(</span><span class="identifier">y</span><span class="special">);</span> 542<span class="identifier">m</span> <span class="special">=</span> <span class="identifier">iterative_size</span><span class="special">(</span><span class="identifier">x</span><span class="special">);</span> <span class="comment">//if P is a container type</span> 543</pre> 544<p> 545 </p> 546<div class="table"> 547<a name="boost_icl.function_reference.subtraction.inplace_operators.t0"></a><p class="title"><b>Table 1.25. Time Complexity for inplace Subtraction on element containers</b></p> 548<div class="table-contents"><table class="table" summary="Time Complexity for inplace Subtraction on element containers"> 549<colgroup> 550<col> 551<col> 552<col> 553<col> 554<col> 555</colgroup> 556<thead><tr> 557<th> 558 <p> 559 <code class="computeroutput"><span class="identifier">T</span><span class="special">&</span> 560 <span class="keyword">operator</span> <span class="special">-=</span> 561 <span class="special">(</span><span class="identifier">T</span><span class="special">&,</span> <span class="keyword">const</span> 562 <span class="identifier">P</span><span class="special">&)</span></code> 563 </p> 564 </th> 565<th> 566 <p> 567 domain<br> type 568 </p> 569 </th> 570<th> 571 <p> 572 domain<br> mapping<br> type 573 </p> 574 </th> 575<th> 576 <p> 577 std::set 578 </p> 579 </th> 580<th> 581 <p> 582 icl::map 583 </p> 584 </th> 585</tr></thead> 586<tbody> 587<tr> 588<td> 589 <p> 590 <a href="http://www.cplusplus.com/reference/stl/set/" target="_top"><code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">set</span></code> </a> 591 </p> 592 </td> 593<td> 594 <p> 595 <span class="emphasis"><em>O(log n)</em></span> 596 </p> 597 </td> 598<td> 599 </td> 600<td> 601 <p> 602 <span class="emphasis"><em>O(m log n)</em></span> 603 </p> 604 </td> 605<td> 606 </td> 607</tr> 608<tr> 609<td> 610 <p> 611 <code class="computeroutput"><a class="link" href="../../boost/icl/map.html" title="Class template map">icl::map</a></code> 612 </p> 613 </td> 614<td> 615 <p> 616 <span class="emphasis"><em>O(log n)</em></span> 617 </p> 618 </td> 619<td> 620 <p> 621 <span class="emphasis"><em>O(log n)</em></span> 622 </p> 623 </td> 624<td> 625 <p> 626 <span class="emphasis"><em>O(m log n)</em></span> 627 </p> 628 </td> 629<td> 630 <p> 631 <span class="emphasis"><em>O(m log n)</em></span> 632 </p> 633 </td> 634</tr> 635</tbody> 636</table></div> 637</div> 638<br class="table-break"><div class="table"> 639<a name="boost_icl.function_reference.subtraction.inplace_operators.t1"></a><p class="title"><b>Table 1.26. Time Complexity for inplace Subtraction on interval containers</b></p> 640<div class="table-contents"><table class="table" summary="Time Complexity for inplace Subtraction on interval containers"> 641<colgroup> 642<col> 643<col> 644<col> 645<col> 646<col> 647<col> 648<col> 649</colgroup> 650<thead><tr> 651<th> 652 <p> 653 <code class="computeroutput"><span class="identifier">T</span><span class="special">&</span> 654 <span class="keyword">operator</span> <span class="special">-=</span> 655 <span class="special">(</span><span class="identifier">T</span><span class="special">&,</span> <span class="keyword">const</span> 656 <span class="identifier">P</span><span class="special">&)</span></code> 657 </p> 658 </th> 659<th> 660 <p> 661 domain<br> type 662 </p> 663 </th> 664<th> 665 <p> 666 interval<br> type 667 </p> 668 </th> 669<th> 670 <p> 671 domain<br> mapping<br> type 672 </p> 673 </th> 674<th> 675 <p> 676 interval<br> mapping<br> type 677 </p> 678 </th> 679<th> 680 <p> 681 interval<br> sets 682 </p> 683 </th> 684<th> 685 <p> 686 interval<br> maps 687 </p> 688 </th> 689</tr></thead> 690<tbody> 691<tr> 692<td> 693 <p> 694 interval_sets 695 </p> 696 </td> 697<td> 698 <p> 699 <span class="emphasis"><em>O(log n)</em></span> 700 </p> 701 </td> 702<td> 703 <p> 704 <span class="emphasis"><em>amortized<br> O(log n)</em></span> 705 </p> 706 </td> 707<td> 708 </td> 709<td> 710 </td> 711<td> 712 <p> 713 <span class="emphasis"><em>O(m log(n+m))</em></span> 714 </p> 715 </td> 716<td> 717 </td> 718</tr> 719<tr> 720<td> 721 <p> 722 interval_maps 723 </p> 724 </td> 725<td> 726 <p> 727 <span class="emphasis"><em>O(log n)</em></span> 728 </p> 729 </td> 730<td> 731 <p> 732 <span class="emphasis"><em>amortized<br> O(log n)</em></span> 733 </p> 734 </td> 735<td> 736 <p> 737 <span class="emphasis"><em>O(log n)</em></span> 738 </p> 739 </td> 740<td> 741 <p> 742 <span class="emphasis"><em>O(n)</em></span> 743 </p> 744 </td> 745<td> 746 <p> 747 <span class="emphasis"><em>O(m log(n+m))</em></span> 748 </p> 749 </td> 750<td> 751 <p> 752 <span class="emphasis"><em>O(m log(n+m))</em></span> 753 </p> 754 </td> 755</tr> 756</tbody> 757</table></div> 758</div> 759<br class="table-break"> 760</div> 761<div class="section"> 762<div class="titlepage"><div><div><h4 class="title"> 763<a name="boost_icl.function_reference.subtraction.infix_operators"></a><a class="link" href="subtraction.html#boost_icl.function_reference.subtraction.infix_operators" title="Infix operators">Infix 764 operators</a> 765</h4></div></div></div> 766<p> 767 The admissible overloads for the infix <span class="emphasis"><em>subtraction</em></span> 768 <code class="computeroutput"><span class="keyword">operator</span> <span class="special">-</span></code> 769 which is a non commutative operation is given by the next overload table. 770 </p> 771<p> 772</p> 773<pre class="programlisting"><span class="comment">// overload tables for - | e b s m - | e i b p S M </span> 774<span class="identifier">T</span> <span class="keyword">operator</span> <span class="special">-</span> <span class="special">(</span><span class="identifier">T</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&)</span> <span class="special">---+--------</span> <span class="special">---+------------</span> 775 <span class="identifier">s</span> <span class="special">|</span> <span class="identifier">s</span> <span class="identifier">s</span> <span class="identifier">S</span> <span class="special">|</span> <span class="identifier">S</span> <span class="identifier">S</span> <span class="identifier">S</span> 776 <span class="identifier">m</span> <span class="special">|</span> <span class="identifier">m</span> <span class="identifier">m</span> <span class="identifier">m</span> <span class="identifier">m</span> <span class="identifier">M</span> <span class="special">|</span> <span class="identifier">M</span> <span class="identifier">M</span> <span class="identifier">M</span> <span class="identifier">M</span> <span class="identifier">M</span> <span class="identifier">M</span> 777</pre> 778<p> 779 </p> 780</div> 781<div class="section"> 782<div class="titlepage"><div><div><h4 class="title"> 783<a name="boost_icl.function_reference.subtraction.subtraction_on_intervals"></a><a class="link" href="subtraction.html#boost_icl.function_reference.subtraction.subtraction_on_intervals" title="Subtraction on Intervals">Subtraction 784 on Intervals</a> 785</h4></div></div></div> 786<div class="informaltable"><table class="table"> 787<colgroup> 788<col> 789<col> 790<col> 791</colgroup> 792<thead><tr> 793<th> 794 <p> 795 <span class="emphasis"><em><span class="bold"><strong>Subtraction</strong></span></em></span> 796 </p> 797 </th> 798<th> 799 <p> 800 Types 801 </p> 802 </th> 803<th> 804 <p> 805 Description 806 </p> 807 </th> 808</tr></thead> 809<tbody> 810<tr> 811<td> 812 <p> 813 <code class="computeroutput"><span class="identifier">T</span> <span class="identifier">left_subtract</span><span class="special">(</span><span class="identifier">T</span> 814 <span class="identifier">right</span><span class="special">,</span> 815 <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">left_minuend</span><span class="special">)</span></code> 816 </p> 817 </td> 818<td> 819 <p> 820 <a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a> 821 </p> 822 </td> 823<td> 824 <p> 825 subtract <code class="computeroutput"><span class="identifier">left_minuend</span></code> 826 from the interval <code class="computeroutput"><span class="identifier">right</span></code> 827 on it's left side. 828</p> 829<pre xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="table-programlisting"><span class="identifier">right_over</span> <span class="special">=</span> <span class="identifier">left_subtract</span><span class="special">(</span><span class="identifier">right</span><span class="special">,</span> <span class="identifier">left_minuend</span><span class="special">);</span> 830<span class="special">...</span> <span class="identifier">d</span><span class="special">)</span> <span class="special">:</span> <span class="identifier">right</span> 831<span class="special">...</span> <span class="identifier">c</span><span class="special">)</span> <span class="special">:</span> <span class="identifier">left_minuend</span> 832 <span class="special">[</span><span class="identifier">c</span> <span class="identifier">d</span><span class="special">)</span> <span class="special">:</span> <span class="identifier">right_over</span> 833</pre> 834<p> 835 </p> 836 </td> 837</tr> 838<tr> 839<td> 840 <p> 841 <code class="computeroutput"><span class="identifier">T</span> <span class="identifier">right_subtract</span><span class="special">(</span><span class="identifier">T</span> 842 <span class="identifier">left</span><span class="special">,</span> 843 <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">right_minuend</span><span class="special">)</span></code> 844 </p> 845 </td> 846<td> 847 <p> 848 <a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a> 849 </p> 850 </td> 851<td> 852 <p> 853 subtract <code class="computeroutput"><span class="identifier">right_minuend</span></code> 854 from the interval <code class="computeroutput"><span class="identifier">left</span></code> 855 on it's right side. 856</p> 857<pre xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="table-programlisting"><span class="identifier">left_over</span> <span class="special">=</span> <span class="identifier">right_subtract</span><span class="special">(</span><span class="identifier">left</span><span class="special">,</span> <span class="identifier">right_minuend</span><span class="special">);</span> 858<span class="special">[</span><span class="identifier">a</span> <span class="special">...</span> <span class="special">:</span> <span class="identifier">left</span> 859 <span class="special">[</span><span class="identifier">b</span> <span class="special">...</span> <span class="special">:</span> <span class="identifier">right_minuend</span> 860<span class="special">[</span><span class="identifier">a</span> <span class="identifier">b</span><span class="special">)</span> <span class="special">:</span> <span class="identifier">left_over</span> 861</pre> 862<p> 863 </p> 864 </td> 865</tr> 866</tbody> 867</table></div> 868</div> 869<p> 870 <span class="emphasis"><em><span class="bold"><strong>See also . . .</strong></span></em></span> 871 </p> 872<div class="informaltable"><table class="table"> 873<colgroup><col></colgroup> 874<thead><tr></tr></thead> 875<tbody> 876<tr><td> 877 <p> 878 <a class="link" href="addition.html" title="Addition"><span class="emphasis"><em><span class="bold"><strong>Addition</strong></span></em></span></a> 879 </p> 880 </td></tr> 881<tr><td> 882 <p> 883 <a class="link" href="erasure.html" title="Erasure"><span class="emphasis"><em><span class="bold"><strong>Erasure</strong></span></em></span></a> 884 </p> 885 </td></tr> 886</tbody> 887</table></div> 888<p> 889 <span class="emphasis"><em><span class="bold"><strong>Back to section . . .</strong></span></em></span> 890 </p> 891<div class="informaltable"><table class="table"> 892<colgroup><col></colgroup> 893<thead><tr></tr></thead> 894<tbody> 895<tr><td> 896 <p> 897 <a class="link" href="../interface/function_synopsis.html#function_synopsis_table"><span class="emphasis"><em><span class="bold"><strong>Function 898 Synopsis</strong></span></em></span></a> 899 </p> 900 </td></tr> 901<tr><td> 902 <p> 903 <a class="link" href="../interface.html" title="Interface"><span class="emphasis"><em><span class="bold"><strong>Interface</strong></span></em></span></a> 904 </p> 905 </td></tr> 906</tbody> 907</table></div> 908</div> 909<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 910<td align="left"></td> 911<td align="right"><div class="copyright-footer">Copyright © 2007-2010 Joachim 912 Faulhaber<br>Copyright © 1999-2006 Cortex Software 913 GmbH<p> 914 Distributed under the Boost Software License, Version 1.0. (See accompanying 915 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>) 916 </p> 917</div></td> 918</tr></table> 919<hr> 920<div class="spirit-nav"> 921<a accesskey="p" href="addition.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../function_reference.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="insertion.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> 922</div> 923</body> 924</html> 925
