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  25 <div class="section boost_icl_function_reference_equivalences_and_orderings" lang="en">
  26 <div class="titlepage"><div><div><h3 class="title">
  27 <a name="boost_icl.function_reference.equivalences_and_orderings"></a><a class="link" href="equivalences_and_orderings.html" title="Equivalences and Orderings">Equivalences
  28       and Orderings</a>
  29 </h3></div></div></div>
  30 <div class="toc"><dl>
  31 <dt><span class="section"><a href="equivalences_and_orderings.html#boost_icl.function_reference.equivalences_and_orderings.synopsis">Synopsis</a></span></dt>
  32 <dt><span class="section"><a href="equivalences_and_orderings.html#boost_icl.function_reference.equivalences_and_orderings.less_on_intervals">Less
  33         on Intervals</a></span></dt>
  34 <dt><span class="section"><a href="equivalences_and_orderings.html#boost_icl.function_reference.equivalences_and_orderings.lexicographical_ordering">Lexicographical
  35         Ordering</a></span></dt>
  36 <dt><span class="section"><a href="equivalences_and_orderings.html#boost_icl.function_reference.equivalences_and_orderings.sequential_element_ordering">Sequential
  37         Element Ordering</a></span></dt>
  38 <dt><span class="section"><a href="equivalences_and_orderings.html#boost_icl.function_reference.equivalences_and_orderings.distinct_equality">Distinct
  39         Equality</a></span></dt>
  40 </dl></div>
  41 <div class="section boost_icl_function_reference_equivalences_and_orderings_synopsis" lang="en">
  42 <div class="titlepage"><div><div><h4 class="title">
  43 <a name="boost_icl.function_reference.equivalences_and_orderings.synopsis"></a><a class="link" href="equivalences_and_orderings.html#boost_icl.function_reference.equivalences_and_orderings.synopsis" title="Synopsis">Synopsis</a>
  44 </h4></div></div></div>
  45 <div class="informaltable"><table class="table">
  46 <colgroup>
  47 <col>
  48 <col>
  49 <col>
  50 <col>
  51 <col>
  52 <col>
  53 </colgroup>
  54 <thead><tr>
  55 <th>
  56                 <p>
  57                   <span class="emphasis"><em><span class="bold"><strong>Equivalences and Orderings</strong></span></em></span>
  58                 </p>
  59                 </th>
  60 <th>
  61                 <p>
  62                   intervals
  63                 </p>
  64                 </th>
  65 <th>
  66                 <p>
  67                   interval<br> sets
  68                 </p>
  69                 </th>
  70 <th>
  71                 <p>
  72                   interval<br> maps
  73                 </p>
  74                 </th>
  75 <th>
  76                 <p>
  77                   element<br> sets
  78                 </p>
  79                 </th>
  80 <th>
  81                 <p>
  82                   element<br> maps
  83                 </p>
  84                 </th>
  85 </tr></thead>
  86 <tbody>
  87 <tr>
  88 <td>
  89                 <p>
  90                   <span class="emphasis"><em>Segment Ordering</em></span>
  91                 </p>
  92                 </td>
  93 <td>
  94                 <p>
  95                 </p>
  96                 </td>
  97 <td>
  98                 <p>
  99                 </p>
 100                 </td>
 101 <td>
 102                 <p>
 103                 </p>
 104                 </td>
 105 <td>
 106                 <p>
 107                 </p>
 108                 </td>
 109 <td>
 110                 <p>
 111                 </p>
 112                 </td>
 113 </tr>
 114 <tr>
 115 <td>
 116                 <p>
 117                   <code class="computeroutput"><span class="keyword">bool</span> <span class="keyword">operator</span>
 118                   <span class="special">==</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span>
 119                   <span class="identifier">T</span><span class="special">&amp;)</span></code>
 120                 </p>
 121                 </td>
 122 <td>
 123                 <p>
 124                   1
 125                 </p>
 126                 </td>
 127 <td>
 128                 <p>
 129                   1
 130                 </p>
 131                 </td>
 132 <td>
 133                 <p>
 134                   1
 135                 </p>
 136                 </td>
 137 <td>
 138                 <p>
 139                   1
 140                 </p>
 141                 </td>
 142 <td>
 143                 <p>
 144                   1
 145                 </p>
 146                 </td>
 147 </tr>
 148 <tr>
 149 <td>
 150                 <p>
 151                   <code class="computeroutput"><span class="keyword">bool</span> <span class="keyword">operator</span>
 152                   <span class="special">!=</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span>
 153                   <span class="identifier">T</span><span class="special">&amp;)</span></code>
 154                 </p>
 155                 </td>
 156 <td>
 157                 <p>
 158                   1
 159                 </p>
 160                 </td>
 161 <td>
 162                 <p>
 163                   1
 164                 </p>
 165                 </td>
 166 <td>
 167                 <p>
 168                   1
 169                 </p>
 170                 </td>
 171 <td>
 172                 <p>
 173                   1
 174                 </p>
 175                 </td>
 176 <td>
 177                 <p>
 178                   1
 179                 </p>
 180                 </td>
 181 </tr>
 182 <tr>
 183 <td>
 184                 <p>
 185                   <code class="computeroutput"><span class="keyword">bool</span> <span class="keyword">operator</span>
 186                   <span class="special">&lt;</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span>
 187                   <span class="identifier">T</span><span class="special">&amp;)</span></code>
 188                 </p>
 189                 </td>
 190 <td>
 191                 <p>
 192                   1
 193                 </p>
 194                 </td>
 195 <td>
 196                 <p>
 197                   1
 198                 </p>
 199                 </td>
 200 <td>
 201                 <p>
 202                   1
 203                 </p>
 204                 </td>
 205 <td>
 206                 <p>
 207                   1
 208                 </p>
 209                 </td>
 210 <td>
 211                 <p>
 212                   1
 213                 </p>
 214                 </td>
 215 </tr>
 216 <tr>
 217 <td>
 218                 <p>
 219                   <code class="computeroutput"><span class="keyword">bool</span> <span class="keyword">operator</span>
 220                   <span class="special">&gt;</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span>
 221                   <span class="identifier">T</span><span class="special">&amp;)</span></code>
 222                 </p>
 223                 </td>
 224 <td>
 225                 <p>
 226                   1
 227                 </p>
 228                 </td>
 229 <td>
 230                 <p>
 231                   1
 232                 </p>
 233                 </td>
 234 <td>
 235                 <p>
 236                   1
 237                 </p>
 238                 </td>
 239 <td>
 240                 <p>
 241                   1
 242                 </p>
 243                 </td>
 244 <td>
 245                 <p>
 246                   1
 247                 </p>
 248                 </td>
 249 </tr>
 250 <tr>
 251 <td>
 252                 <p>
 253                   <code class="computeroutput"><span class="keyword">bool</span> <span class="keyword">operator</span>
 254                   <span class="special">&lt;=</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span>
 255                   <span class="identifier">T</span><span class="special">&amp;)</span></code>
 256                 </p>
 257                 </td>
 258 <td>
 259                 <p>
 260                   1
 261                 </p>
 262                 </td>
 263 <td>
 264                 <p>
 265                   1
 266                 </p>
 267                 </td>
 268 <td>
 269                 <p>
 270                   1
 271                 </p>
 272                 </td>
 273 <td>
 274                 <p>
 275                   1
 276                 </p>
 277                 </td>
 278 <td>
 279                 <p>
 280                   1
 281                 </p>
 282                 </td>
 283 </tr>
 284 <tr>
 285 <td>
 286                 <p>
 287                   <code class="computeroutput"><span class="keyword">bool</span> <span class="keyword">operator</span>
 288                   <span class="special">&gt;=</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span>
 289                   <span class="identifier">T</span><span class="special">&amp;)</span></code>
 290                 </p>
 291                 </td>
 292 <td>
 293                 <p>
 294                   1
 295                 </p>
 296                 </td>
 297 <td>
 298                 <p>
 299                   1
 300                 </p>
 301                 </td>
 302 <td>
 303                 <p>
 304                   1
 305                 </p>
 306                 </td>
 307 <td>
 308                 <p>
 309                   1
 310                 </p>
 311                 </td>
 312 <td>
 313                 <p>
 314                   1
 315                 </p>
 316                 </td>
 317 </tr>
 318 <tr>
 319 <td>
 320                 <p>
 321                   <span class="emphasis"><em>Element Ordering</em></span>
 322                 </p>
 323                 </td>
 324 <td>
 325                 <p>
 326                 </p>
 327                 </td>
 328 <td>
 329                 <p>
 330                 </p>
 331                 </td>
 332 <td>
 333                 <p>
 334                 </p>
 335                 </td>
 336 <td>
 337                 <p>
 338                 </p>
 339                 </td>
 340 <td>
 341                 <p>
 342                 </p>
 343                 </td>
 344 </tr>
 345 <tr>
 346 <td>
 347                 <p>
 348                   <code class="computeroutput"><span class="keyword">bool</span> <span class="identifier">is_element_equal</span><span class="special">(</span><span class="keyword">const</span>
 349                   <span class="identifier">T</span><span class="special">&amp;,</span>
 350                   <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span></code>
 351                 </p>
 352                 </td>
 353 <td>
 354                 <p>
 355                 </p>
 356                 </td>
 357 <td>
 358                 <p>
 359                   <a class="link" href="../interface/function_synopsis.html#interval_set_types"><span class="bold"><strong>S</strong></span></a>
 360                 </p>
 361                 </td>
 362 <td>
 363                 <p>
 364                   <a class="link" href="../interface/function_synopsis.html#interval_map_types"><span class="bold"><strong>M</strong></span></a>
 365                 </p>
 366                 </td>
 367 <td>
 368                 <p>
 369                   1
 370                 </p>
 371                 </td>
 372 <td>
 373                 <p>
 374                   1
 375                 </p>
 376                 </td>
 377 </tr>
 378 <tr>
 379 <td>
 380                 <p>
 381                   <code class="computeroutput"><span class="keyword">bool</span> <span class="identifier">is_element_less</span><span class="special">(</span><span class="keyword">const</span>
 382                   <span class="identifier">T</span><span class="special">&amp;,</span>
 383                   <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span></code>
 384                 </p>
 385                 </td>
 386 <td>
 387                 <p>
 388                 </p>
 389                 </td>
 390 <td>
 391                 <p>
 392                   <a class="link" href="../interface/function_synopsis.html#interval_set_types"><span class="bold"><strong>S</strong></span></a>
 393                 </p>
 394                 </td>
 395 <td>
 396                 <p>
 397                   <a class="link" href="../interface/function_synopsis.html#interval_map_types"><span class="bold"><strong>M</strong></span></a>
 398                 </p>
 399                 </td>
 400 <td>
 401                 <p>
 402                   1
 403                 </p>
 404                 </td>
 405 <td>
 406                 <p>
 407                   1
 408                 </p>
 409                 </td>
 410 </tr>
 411 <tr>
 412 <td>
 413                 <p>
 414                   <code class="computeroutput"><span class="keyword">bool</span> <span class="identifier">is_element_greater</span><span class="special">(</span><span class="keyword">const</span>
 415                   <span class="identifier">T</span><span class="special">&amp;,</span>
 416                   <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span></code>
 417                 </p>
 418                 </td>
 419 <td>
 420                 <p>
 421                 </p>
 422                 </td>
 423 <td>
 424                 <p>
 425                   <a class="link" href="../interface/function_synopsis.html#interval_set_types"><span class="bold"><strong>S</strong></span></a>
 426                 </p>
 427                 </td>
 428 <td>
 429                 <p>
 430                   <a class="link" href="../interface/function_synopsis.html#interval_map_types"><span class="bold"><strong>M</strong></span></a>
 431                 </p>
 432                 </td>
 433 <td>
 434                 <p>
 435                   1
 436                 </p>
 437                 </td>
 438 <td>
 439                 <p>
 440                   1
 441                 </p>
 442                 </td>
 443 </tr>
 444 <tr>
 445 <td>
 446                 <p>
 447                   <span class="emphasis"><em>Distinct Equality</em></span>
 448                 </p>
 449                 </td>
 450 <td>
 451                 <p>
 452                 </p>
 453                 </td>
 454 <td>
 455                 <p>
 456                 </p>
 457                 </td>
 458 <td>
 459                 <p>
 460                 </p>
 461                 </td>
 462 <td>
 463                 <p>
 464                 </p>
 465                 </td>
 466 <td>
 467                 <p>
 468                 </p>
 469                 </td>
 470 </tr>
 471 <tr>
 472 <td>
 473                 <p>
 474                   <code class="computeroutput"><span class="keyword">bool</span> <span class="identifier">is_distinct_equal</span><span class="special">(</span><span class="keyword">const</span>
 475                   <span class="identifier">T</span><span class="special">&amp;,</span>
 476                   <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span></code>
 477                 </p>
 478                 </td>
 479 <td>
 480                 <p>
 481                 </p>
 482                 </td>
 483 <td>
 484                 <p>
 485                 </p>
 486                 </td>
 487 <td>
 488                 <p>
 489                   <a class="link" href="../interface/function_synopsis.html#interval_map_types"><span class="bold"><strong>M</strong></span></a>
 490                 </p>
 491                 </td>
 492 <td>
 493                 <p>
 494                 </p>
 495                 </td>
 496 <td>
 497                 <p>
 498                   1
 499                 </p>
 500                 </td>
 501 </tr>
 502 </tbody>
 503 </table></div>
 504 </div>
 505 <div class="section boost_icl_function_reference_equivalences_and_orderings_less_on_intervals" lang="en">
 506 <div class="titlepage"><div><div><h4 class="title">
 507 <a name="boost_icl.function_reference.equivalences_and_orderings.less_on_intervals"></a><a class="link" href="equivalences_and_orderings.html#boost_icl.function_reference.equivalences_and_orderings.less_on_intervals" title="Less on Intervals">Less
 508         on Intervals</a>
 509 </h4></div></div></div>
 510 <div class="informaltable"><table class="table">
 511 <colgroup>
 512 <col>
 513 <col>
 514 <col>
 515 </colgroup>
 516 <thead><tr>
 517 <th>
 518                 <p>
 519                 </p>
 520                 </th>
 521 <th>
 522                 <p>
 523                   Types
 524                 </p>
 525                 </th>
 526 <th>
 527                 <p>
 528                 </p>
 529                 </th>
 530 </tr></thead>
 531 <tbody><tr>
 532 <td>
 533                 <p>
 534                   <code class="computeroutput"><span class="identifier">x</span> <span class="special">&lt;</span>
 535                   <span class="identifier">y</span></code>
 536                 </p>
 537                 </td>
 538 <td>
 539                 <p>
 540                   <a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a>
 541                 </p>
 542                 </td>
 543 <td>
 544                 <p>
 545                   <code class="computeroutput"><span class="identifier">x</span></code> begins before
 546                   <code class="computeroutput"><span class="identifier">y</span></code> or, for equal
 547                   beginnings <code class="computeroutput"><span class="identifier">x</span></code> ends
 548                   before <code class="computeroutput"><span class="identifier">y</span></code>
 549                 </p>
 550                 </td>
 551 </tr></tbody>
 552 </table></div>
 553 </div>
 554 <div class="section boost_icl_function_reference_equivalences_and_orderings_lexicographical_ordering" lang="en">
 555 <div class="titlepage"><div><div><h4 class="title">
 556 <a name="boost_icl.function_reference.equivalences_and_orderings.lexicographical_ordering"></a><a class="link" href="equivalences_and_orderings.html#boost_icl.function_reference.equivalences_and_orderings.lexicographical_ordering" title="Lexicographical Ordering">Lexicographical
 557         Ordering</a>
 558 </h4></div></div></div>
 559 <p>
 560           All common equality and compare operators are defined for all objects of
 561           the <span class="bold"><strong>icl</strong></span>. For all <span class="bold"><strong>icl</strong></span>
 562           containers equality and compare operators implement lexicographical equality
 563           and lexicographical comparison, that depends on the equality of template
 564           parameter <code class="computeroutput"><span class="identifier">Compare</span></code>. This
 565           includes the less ordering on intervals, that can be perceived as the sequence
 566           of elements between their lower and upper bound. This generalized lexicogrphical
 567           comparison in intervals can also be specified this way:
 568         </p>
 569 <div class="informaltable"><table class="table">
 570 <colgroup>
 571 <col>
 572 <col>
 573 <col>
 574 </colgroup>
 575 <thead><tr></tr></thead>
 576 <tbody>
 577 <tr>
 578 <td>
 579                 <p>
 580                   <code class="computeroutput"><span class="identifier">x</span> <span class="special">&lt;</span>
 581                   <span class="identifier">y</span></code>
 582                 </p>
 583                 </td>
 584 <td>
 585                 <p>
 586                   <code class="computeroutput"><span class="special">:=</span></code>
 587                 </p>
 588                 </td>
 589 <td>
 590                 <p>
 591                   <code class="computeroutput"><span class="identifier">x</span></code> begins before
 592                   <code class="computeroutput"><span class="identifier">y</span></code> or, for equal
 593                   beginnings <code class="computeroutput"><span class="identifier">x</span></code> ends
 594                   before <code class="computeroutput"><span class="identifier">y</span></code>.
 595                 </p>
 596                 </td>
 597 </tr>
 598 <tr>
 599 <td>
 600                 <p>
 601                 </p>
 602                 </td>
 603 <td>
 604                 <p>
 605                 </p>
 606                 </td>
 607 <td>
 608                 <p>
 609                   The other operators can be deduced in the usual way
 610                 </p>
 611                 </td>
 612 </tr>
 613 <tr>
 614 <td>
 615                 <p>
 616                   <code class="computeroutput"><span class="identifier">x</span> <span class="special">&gt;</span>
 617                   <span class="identifier">y</span></code>
 618                 </p>
 619                 </td>
 620 <td>
 621                 <p>
 622                   <code class="computeroutput"><span class="special">:=</span></code>
 623                 </p>
 624                 </td>
 625 <td>
 626                 <p>
 627                   <code class="computeroutput"><span class="identifier">y</span> <span class="special">&lt;</span>
 628                   <span class="identifier">x</span></code>
 629                 </p>
 630                 </td>
 631 </tr>
 632 <tr>
 633 <td>
 634                 <p>
 635                   <code class="computeroutput"><span class="identifier">x</span> <span class="special">&lt;=</span>
 636                   <span class="identifier">y</span></code>
 637                 </p>
 638                 </td>
 639 <td>
 640                 <p>
 641                   <code class="computeroutput"><span class="special">:=</span></code>
 642                 </p>
 643                 </td>
 644 <td>
 645                 <p>
 646                   <code class="computeroutput"><span class="special">!(</span><span class="identifier">y</span>
 647                   <span class="special">&lt;</span> <span class="identifier">x</span><span class="special">)</span></code>
 648                 </p>
 649                 </td>
 650 </tr>
 651 <tr>
 652 <td>
 653                 <p>
 654                   <code class="computeroutput"><span class="identifier">x</span> <span class="special">&gt;=</span>
 655                   <span class="identifier">y</span></code>
 656                 </p>
 657                 </td>
 658 <td>
 659                 <p>
 660                   <code class="computeroutput"><span class="special">:=</span></code>
 661                 </p>
 662                 </td>
 663 <td>
 664                 <p>
 665                   <code class="computeroutput"><span class="special">!(</span><span class="identifier">x</span>
 666                   <span class="special">&lt;</span> <span class="identifier">y</span><span class="special">)</span></code>
 667                 </p>
 668                 </td>
 669 </tr>
 670 <tr>
 671 <td>
 672                 <p>
 673                   <code class="computeroutput"><span class="identifier">x</span> <span class="special">==</span>
 674                   <span class="identifier">y</span></code>
 675                 </p>
 676                 </td>
 677 <td>
 678                 <p>
 679                   <code class="computeroutput"><span class="special">:=</span></code>
 680                 </p>
 681                 </td>
 682 <td>
 683                 <p>
 684                   <code class="computeroutput"><span class="special">!(</span><span class="identifier">x</span>
 685                   <span class="special">&lt;</span> <span class="identifier">y</span><span class="special">)</span> <span class="special">&amp;&amp;</span>
 686                   <span class="special">!(</span><span class="identifier">y</span>
 687                   <span class="special">&lt;</span> <span class="identifier">x</span><span class="special">)</span></code> induced equivalence
 688                 </p>
 689                 </td>
 690 </tr>
 691 <tr>
 692 <td>
 693                 <p>
 694                   <code class="computeroutput"><span class="identifier">x</span> <span class="special">!=</span>
 695                   <span class="identifier">y</span></code>
 696                 </p>
 697                 </td>
 698 <td>
 699                 <p>
 700                   <code class="computeroutput"><span class="special">:=</span></code>
 701                 </p>
 702                 </td>
 703 <td>
 704                 <p>
 705                   <code class="computeroutput"><span class="special">!(</span><span class="identifier">x</span>
 706                   <span class="special">==</span> <span class="identifier">y</span><span class="special">)</span></code>
 707                 </p>
 708                 </td>
 709 </tr>
 710 </tbody>
 711 </table></div>
 712 <p>
 713           Equality and compare operators are defined for all <span class="bold"><strong>icl</strong></span>
 714           objects but there are no overloads between different types.
 715         </p>
 716 <p>
 717           Containers of different segmentation are different, even if their elements
 718           are the same:
 719 </p>
 720 <pre class="programlisting"><span class="identifier">split_interval_set</span><span class="special">&lt;</span><span class="identifier">time</span><span class="special">&gt;</span> <span class="identifier">w1</span><span class="special">,</span> <span class="identifier">w2</span><span class="special">;</span> <span class="comment">//Pseudocode
 721 </span><span class="identifier">w1</span> <span class="special">=</span> <span class="special">{[</span><span class="identifier">Mon</span>       <span class="special">..</span>       <span class="identifier">Sun</span><span class="special">)};</span> <span class="comment">//split_interval_set containing a week
 722 </span><span class="identifier">w2</span> <span class="special">=</span> <span class="special">{[</span><span class="identifier">Mon</span> <span class="special">..</span> <span class="identifier">Fri</span><span class="special">)[</span><span class="identifier">Sat</span> <span class="special">..</span> <span class="identifier">Sun</span><span class="special">)};</span> <span class="comment">//Same week split in work and week end parts.
 723 </span><span class="identifier">w1</span> <span class="special">==</span> <span class="identifier">w2</span><span class="special">;</span>                        <span class="comment">//false: Different segmentation
 724 </span><span class="identifier">is_element_equal</span><span class="special">(</span><span class="identifier">w1</span><span class="special">,</span><span class="identifier">w2</span><span class="special">);</span>         <span class="comment">//true:  Same elements contained
 725 </span></pre>
 726 <p>
 727         </p>
 728 <p>
 729           <span class="bold"><strong>Complexity</strong></span> is <span class="emphasis"><em><span class="bold"><strong>linear</strong></span></em></span>
 730           in the <code class="computeroutput"><span class="identifier">iterative_size</span></code> of
 731           the shorter container to compare.
 732         </p>
 733 </div>
 734 <div class="section boost_icl_function_reference_equivalences_and_orderings_sequential_element_ordering" lang="en">
 735 <div class="titlepage"><div><div><h4 class="title">
 736 <a name="boost_icl.function_reference.equivalences_and_orderings.sequential_element_ordering"></a><a class="link" href="equivalences_and_orderings.html#boost_icl.function_reference.equivalences_and_orderings.sequential_element_ordering" title="Sequential Element Ordering">Sequential
 737         Element Ordering</a>
 738 </h4></div></div></div>
 739 <p>
 740           The <span class="emphasis"><em><span class="bold"><strong>Sequential Element Ordering</strong></span></em></span>
 741           abstracts from the way in which elements of interval containers are clustered
 742           into intervals: it's <span class="emphasis"><em><span class="bold"><strong>segmentation</strong></span></em></span>.
 743         </p>
 744 <p>
 745           So these equality and compare operations can be applied within interval
 746           container types. The admissible type combinations are summarized in the
 747           next overload table.
 748         </p>
 749 <p>
 750
 751 </p>
 752 <pre class="programlisting"><span class="comment">// overload tables for
 753 </span><span class="keyword">bool</span> <span class="identifier">is_element_equal</span>  <span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span>
 754 <span class="keyword">bool</span> <span class="identifier">is_element_less</span>   <span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span>
 755 <span class="keyword">bool</span> <span class="identifier">is_element_greater</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span>
 756
 757 <span class="identifier">element</span> <span class="identifier">containers</span><span class="special">:</span>     <span class="identifier">interval</span> <span class="identifier">containers</span><span class="special">:</span>
 758 <span class="identifier">T</span><span class="special">\</span><span class="identifier">P</span><span class="special">|</span> <span class="identifier">s</span> <span class="identifier">m</span>                <span class="identifier">T</span><span class="special">\</span><span class="identifier">P</span><span class="special">|</span> <span class="identifier">S1</span> <span class="identifier">S2</span> <span class="identifier">S3</span> <span class="identifier">M1</span> <span class="identifier">M3</span>
 759 <span class="special">---+----</span>                <span class="special">---+---------------</span>
 760 <span class="identifier">s</span>  <span class="special">|</span> <span class="number">1</span>                  <span class="identifier">S1</span> <span class="special">|</span> <span class="number">1</span>  <span class="number">1</span>  <span class="number">1</span>
 761 <span class="identifier">m</span>  <span class="special">|</span>   <span class="number">1</span>                <span class="identifier">S2</span> <span class="special">|</span> <span class="number">1</span>  <span class="number">1</span>  <span class="number">1</span>
 762                         <span class="identifier">S3</span> <span class="special">|</span> <span class="number">1</span>  <span class="number">1</span>  <span class="number">1</span>
 763                         <span class="identifier">M1</span> <span class="special">|</span>          <span class="number">1</span>  <span class="number">1</span>
 764                         <span class="identifier">M3</span> <span class="special">|</span>          <span class="number">1</span>  <span class="number">1</span>
 765 </pre>
 766 <p>
 767         </p>
 768 <p>
 769           For element containers lexicographical equality and sequential element
 770           equality are identical.
 771         </p>
 772 <p>
 773           The <span class="bold"><strong>complexity</strong></span> of sequential element comparison
 774           functions is <span class="emphasis"><em><span class="bold"><strong>linear</strong></span></em></span>
 775           in the <code class="computeroutput"><span class="identifier">iterative_size</span></code> of
 776           the larger container.
 777         </p>
 778 </div>
 779 <div class="section boost_icl_function_reference_equivalences_and_orderings_distinct_equality" lang="en">
 780 <div class="titlepage"><div><div><h4 class="title">
 781 <a name="boost_icl.function_reference.equivalences_and_orderings.distinct_equality"></a><a class="link" href="equivalences_and_orderings.html#boost_icl.function_reference.equivalences_and_orderings.distinct_equality" title="Distinct Equality">Distinct
 782         Equality</a>
 783 </h4></div></div></div>
 784 <p>
 785           <span class="emphasis"><em><span class="bold"><strong>Distinct Equality</strong></span></em></span>
 786           is an equality predicate that is available for <code class="computeroutput"><a class="link" href="../../boost/icl/map.html" title="Class template map">icl::maps</a></code>
 787           and <code class="computeroutput"><a class="link" href="../../boost/icl/interval_map.html" title="Class template interval_map">interval_maps</a></code>.
 788           It yields true, if two maps are sequential element equal except for value
 789           pairs whose associated values are identity elements.
 790         </p>
 791 <p>
 792           <span class="bold"><strong>Complexity</strong></span> is linear in the <code class="computeroutput"><span class="identifier">iterative_size</span></code> of the larger container
 793           to compare.
 794         </p>
 795 </div>
 796 <p>
 797         <span class="emphasis"><em><span class="bold"><strong>See also . . .</strong></span></em></span>
 798       </p>
 799 <div class="informaltable"><table class="table">
 800 <colgroup><col></colgroup>
 801 <thead><tr></tr></thead>
 802 <tbody><tr><td>
 803               <p>
 804                 <a class="link" href="../semantics.html#boost_icl.semantics.orderings_and_equivalences" title="Orderings and Equivalences"><span class="emphasis"><em><span class="bold"><strong>Semantics</strong></span></em></span></a>
 805               </p>
 806               </td></tr></tbody>
 807 </table></div>
 808 <p>
 809         <span class="emphasis"><em><span class="bold"><strong>Back to section . . .</strong></span></em></span>
 810       </p>
 811 <div class="informaltable"><table class="table">
 812 <colgroup><col></colgroup>
 813 <thead><tr></tr></thead>
 814 <tbody>
 815 <tr><td>
 816               <p>
 817                 <a class="link" href="../interface/function_synopsis.html#function_synopsis_table"><span class="emphasis"><em><span class="bold"><strong>Function
 818                 Synopsis</strong></span></em></span></a>
 819               </p>
 820               </td></tr>
 821 <tr><td>
 822               <p>
 823                 <a class="link" href="../interface.html" title="Interface"><span class="emphasis"><em><span class="bold"><strong>Interface</strong></span></em></span></a>
 824               </p>
 825               </td></tr>
 826 </tbody>
 827 </table></div>
 828 </div>
 829 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 830 <td align="left"></td>
 831 <td align="right"><div class="copyright-footer">Copyright &#169; 2007 -2010 Joachim Faulhaber<br>Copyright &#169; 1999 -2006 Cortex Software GmbH<p>
 832         Distributed under the Boost Software License, Version 1.0. (See accompanying
 833         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>)
 834       </p>
 835 </div></td>
 836 </tr></table>
 837 <hr>
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