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1 | <html> |
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4 | <title>Sets and Maps</title> | |
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24 | </div> | |
25 | <div class="section boost_icl_concepts_sets_and_maps" lang="en"> | |
26 | <div class="titlepage"><div><div><h3 class="title"> | |
27 | <a name="boost_icl.concepts.sets_and_maps"></a><a class="link" href="sets_and_maps.html" title="Sets and Maps">Sets and Maps</a> | |
28 | </h3></div></div></div> | |
29 | <a name="boost_icl.concepts.sets_and_maps.a_set_concept"></a><h6> | |
30 | <a name="id1076180"></a> | |
31 | <a class="link" href="sets_and_maps.html#boost_icl.concepts.sets_and_maps.a_set_concept">A Set Concept</a> | |
32 | </h6> | |
33 | <p> | |
34 | On the fundamental aspect all <code class="computeroutput"><a class="link" href="../../boost/icl/interval_base_set.html" title="Class template interval_base_set">interval_sets</a></code> | |
35 | are models of a concept <code class="computeroutput"><span class="identifier">Set</span></code>. | |
36 | The <code class="computeroutput"><span class="identifier">Set</span></code> concept of the Interval | |
37 | Template Library refers to the mathematical notion of a set. | |
38 | </p> | |
39 | <div class="informaltable"><table class="table"> | |
40 | <colgroup> | |
41 | <col> | |
42 | <col> | |
43 | <col> | |
44 | </colgroup> | |
45 | <thead><tr> | |
46 | <th> | |
47 | <p> | |
48 | Function | |
49 | </p> | |
50 | </th> | |
51 | <th> | |
52 | <p> | |
53 | Variant | |
54 | </p> | |
55 | </th> | |
56 | <th> | |
57 | <p> | |
58 | implemented as | |
59 | </p> | |
60 | </th> | |
61 | </tr></thead> | |
62 | <tbody> | |
63 | <tr> | |
64 | <td> | |
65 | <p> | |
66 | empty set | |
67 | </p> | |
68 | </td> | |
69 | <td> | |
70 | <p> | |
71 | </p> | |
72 | </td> | |
73 | <td> | |
74 | <p> | |
75 | <code class="computeroutput"><span class="identifier">Set</span><span class="special">::</span><span class="identifier">Set</span><span class="special">()</span></code> | |
76 | </p> | |
77 | </td> | |
78 | </tr> | |
79 | <tr> | |
80 | <td> | |
81 | <p> | |
82 | subset relation | |
83 | </p> | |
84 | </td> | |
85 | <td> | |
86 | <p> | |
87 | </p> | |
88 | </td> | |
89 | <td> | |
90 | <p> | |
91 | <code class="computeroutput"><span class="keyword">bool</span> <span class="identifier">Set</span><span class="special">::</span><span class="identifier">within</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Set</span><span class="special">&</span> | |
92 | <span class="identifier">s1</span><span class="special">,</span> | |
93 | <span class="keyword">const</span> <span class="identifier">Set</span><span class="special">&</span> <span class="identifier">s2</span><span class="special">)</span><span class="keyword">const</span></code> | |
94 | </p> | |
95 | </td> | |
96 | </tr> | |
97 | <tr> | |
98 | <td> | |
99 | <p> | |
100 | equality | |
101 | </p> | |
102 | </td> | |
103 | <td> | |
104 | <p> | |
105 | </p> | |
106 | </td> | |
107 | <td> | |
108 | <p> | |
109 | <code class="computeroutput"><span class="keyword">bool</span> <span class="identifier">is_element_equal</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Set</span><span class="special">&</span> | |
110 | <span class="identifier">s1</span><span class="special">,</span> | |
111 | <span class="keyword">const</span> <span class="identifier">Set</span><span class="special">&</span> <span class="identifier">s2</span><span class="special">)</span></code> | |
112 | </p> | |
113 | </td> | |
114 | </tr> | |
115 | <tr> | |
116 | <td> | |
117 | <p> | |
118 | set union | |
119 | </p> | |
120 | </td> | |
121 | <td> | |
122 | <p> | |
123 | inplace | |
124 | </p> | |
125 | </td> | |
126 | <td> | |
127 | <p> | |
128 | <code class="computeroutput"><span class="identifier">Set</span><span class="special">&</span> | |
129 | <span class="keyword">operator</span> <span class="special">+=</span> | |
130 | <span class="special">(</span><span class="identifier">Set</span><span class="special">&</span> <span class="identifier">s1</span><span class="special">,</span> <span class="keyword">const</span> | |
131 | <span class="identifier">Set</span><span class="special">&</span> | |
132 | <span class="identifier">s2</span><span class="special">)</span></code> | |
133 | </p> | |
134 | </td> | |
135 | </tr> | |
136 | <tr> | |
137 | <td> | |
138 | <p> | |
139 | </p> | |
140 | </td> | |
141 | <td> | |
142 | <p> | |
143 | </p> | |
144 | </td> | |
145 | <td> | |
146 | <p> | |
147 | <code class="computeroutput"><span class="identifier">Set</span> <span class="keyword">operator</span> | |
148 | <span class="special">+</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">Set</span><span class="special">&</span> <span class="identifier">s1</span><span class="special">,</span> <span class="keyword">const</span> | |
149 | <span class="identifier">Set</span><span class="special">&</span> | |
150 | <span class="identifier">s2</span><span class="special">)</span></code> | |
151 | </p> | |
152 | </td> | |
153 | </tr> | |
154 | <tr> | |
155 | <td> | |
156 | <p> | |
157 | set difference | |
158 | </p> | |
159 | </td> | |
160 | <td> | |
161 | <p> | |
162 | inplace | |
163 | </p> | |
164 | </td> | |
165 | <td> | |
166 | <p> | |
167 | <code class="computeroutput"><span class="identifier">Set</span><span class="special">&</span> | |
168 | <span class="keyword">operator</span> <span class="special">-=</span> | |
169 | <span class="special">(</span><span class="identifier">Set</span><span class="special">&</span> <span class="identifier">s1</span><span class="special">,</span> <span class="keyword">const</span> | |
170 | <span class="identifier">Set</span><span class="special">&</span> | |
171 | <span class="identifier">s2</span><span class="special">)</span></code> | |
172 | </p> | |
173 | </td> | |
174 | </tr> | |
175 | <tr> | |
176 | <td> | |
177 | <p> | |
178 | </p> | |
179 | </td> | |
180 | <td> | |
181 | <p> | |
182 | </p> | |
183 | </td> | |
184 | <td> | |
185 | <p> | |
186 | <code class="computeroutput"><span class="identifier">Set</span> <span class="keyword">operator</span> | |
187 | <span class="special">-</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">Set</span><span class="special">&</span> <span class="identifier">s1</span><span class="special">,</span> <span class="keyword">const</span> | |
188 | <span class="identifier">Set</span><span class="special">&</span> | |
189 | <span class="identifier">s2</span><span class="special">)</span></code> | |
190 | </p> | |
191 | </td> | |
192 | </tr> | |
193 | <tr> | |
194 | <td> | |
195 | <p> | |
196 | set intersection | |
197 | </p> | |
198 | </td> | |
199 | <td> | |
200 | <p> | |
201 | inplace | |
202 | </p> | |
203 | </td> | |
204 | <td> | |
205 | <p> | |
206 | <code class="computeroutput"><span class="identifier">Set</span><span class="special">&</span> | |
207 | <span class="keyword">operator</span> <span class="special">&=</span> | |
208 | <span class="special">(</span><span class="identifier">Set</span><span class="special">&</span> <span class="identifier">s1</span><span class="special">,</span> <span class="keyword">const</span> | |
209 | <span class="identifier">Set</span><span class="special">&</span> | |
210 | <span class="identifier">s2</span><span class="special">)</span></code> | |
211 | </p> | |
212 | </td> | |
213 | </tr> | |
214 | <tr> | |
215 | <td> | |
216 | <p> | |
217 | </p> | |
218 | </td> | |
219 | <td> | |
220 | <p> | |
221 | </p> | |
222 | </td> | |
223 | <td> | |
224 | <p> | |
225 | <code class="computeroutput"><span class="identifier">Set</span> <span class="keyword">operator</span> | |
226 | <span class="special">&</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">Set</span><span class="special">&</span> <span class="identifier">s1</span><span class="special">,</span> <span class="keyword">const</span> | |
227 | <span class="identifier">Set</span><span class="special">&</span> | |
228 | <span class="identifier">s2</span><span class="special">)</span></code> | |
229 | </p> | |
230 | </td> | |
231 | </tr> | |
232 | </tbody> | |
233 | </table></div> | |
234 | <p> | |
235 | Equality on <code class="computeroutput"><span class="identifier">Sets</span></code> is not implemented | |
236 | as <code class="computeroutput"><span class="keyword">operator</span> <span class="special">==</span></code>, | |
237 | because <code class="computeroutput"><span class="keyword">operator</span> <span class="special">==</span></code> | |
238 | is used for the stronger lexicographical equality on segments, that takes | |
239 | the segmentation of elements into account. | |
240 | </p> | |
241 | <p> | |
242 | Being models of concept <code class="computeroutput"><span class="identifier">Set</span></code>, | |
243 | <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> | |
244 | </a> and all <code class="computeroutput"><a class="link" href="../../boost/icl/interval_base_set.html" title="Class template interval_base_set">interval_sets</a></code> | |
245 | implement these operations and obey the associated laws on <code class="computeroutput"><span class="identifier">Sets</span></code>. See e.g. <a href="http://en.wikipedia.org/wiki/Algebra_of_sets" target="_top">an | |
246 | algebra of sets here</a>. | |
247 | </p> | |
248 | <a name="boost_icl.concepts.sets_and_maps.making_intervals_complete"></a><h6> | |
249 | <a name="id1077070"></a> | |
250 | <a class="link" href="sets_and_maps.html#boost_icl.concepts.sets_and_maps.making_intervals_complete">Making | |
251 | intervals complete</a> | |
252 | </h6> | |
253 | <p> | |
254 | An <code class="computeroutput"><a class="link" href="../../boost/icl/interval.html" title="Struct template interval">interval</a></code> is considered | |
255 | to be a set of elements as well. With respect to the <code class="computeroutput"><span class="identifier">Set</span></code> | |
256 | concept presented above <code class="computeroutput"><a class="link" href="../../boost/icl/interval.html" title="Struct template interval">interval</a></code> | |
257 | implements the concept only partially. The reason for that is that addition | |
258 | and subtraction can not be defined on <code class="computeroutput"><a class="link" href="../../boost/icl/interval.html" title="Struct template interval">intervals</a></code>. | |
259 | Two intervals <code class="computeroutput"><span class="special">[</span><span class="number">1</span><span class="special">,</span><span class="number">2</span><span class="special">]</span></code> | |
260 | and <code class="computeroutput"><span class="special">[</span><span class="number">4</span><span class="special">,</span><span class="number">5</span><span class="special">]</span></code> | |
261 | are not addable to a <span class="emphasis"><em><span class="bold"><strong>single</strong></span></em></span> | |
262 | new <code class="computeroutput"><a class="link" href="../../boost/icl/interval.html" title="Struct template interval">interval</a></code>. In other | |
263 | words <code class="computeroutput"><a class="link" href="../../boost/icl/interval.html" title="Struct template interval">intervals</a></code> are incomplete | |
264 | w.r.t. union and difference. <code class="computeroutput"><a class="link" href="../../boost/icl/interval_set.html" title="Class template interval_set">Interval_sets</a></code> | |
265 | can be defined as the <span class="emphasis"><em><span class="bold"><strong>completion</strong></span></em></span> | |
266 | of intervals for the union and difference operations. | |
267 | </p> | |
268 | <p> | |
269 | When we claim that addition or subtraction can not be defined on intervals, | |
270 | we are not considering things like e.g. interval arithmetics, where these | |
271 | operations can be defined, but with a different semantics. | |
272 | </p> | |
273 | <a name="boost_icl.concepts.sets_and_maps.a_map_concept"></a><h6> | |
274 | <a name="id1077199"></a> | |
275 | <a class="link" href="sets_and_maps.html#boost_icl.concepts.sets_and_maps.a_map_concept">A Map Concept</a> | |
276 | </h6> | |
277 | <p> | |
278 | On the fundamental aspect <code class="computeroutput"><a class="link" href="../../boost/icl/map.html" title="Class template map">icl::map</a></code> | |
279 | and all <code class="computeroutput"><a class="link" href="../../boost/icl/interval_base_map.html" title="Class template interval_base_map">interval_maps</a></code> | |
280 | are models of a concept <code class="computeroutput"><span class="identifier">Map</span></code>. | |
281 | Since a <code class="computeroutput"><span class="identifier">map</span></code> is a <code class="computeroutput"><span class="identifier">set</span> <span class="identifier">of</span> <span class="identifier">pairs</span></code>, we try to design the <code class="computeroutput"><span class="identifier">Map</span></code> concept in accordance to the <code class="computeroutput"><span class="identifier">Set</span></code> concept above. | |
282 | </p> | |
283 | <div class="informaltable"><table class="table"> | |
284 | <colgroup> | |
285 | <col> | |
286 | <col> | |
287 | <col> | |
288 | </colgroup> | |
289 | <thead><tr> | |
290 | <th> | |
291 | <p> | |
292 | Function | |
293 | </p> | |
294 | </th> | |
295 | <th> | |
296 | <p> | |
297 | Variant | |
298 | </p> | |
299 | </th> | |
300 | <th> | |
301 | <p> | |
302 | implemented as | |
303 | </p> | |
304 | </th> | |
305 | </tr></thead> | |
306 | <tbody> | |
307 | <tr> | |
308 | <td> | |
309 | <p> | |
310 | empty map | |
311 | </p> | |
312 | </td> | |
313 | <td> | |
314 | <p> | |
315 | </p> | |
316 | </td> | |
317 | <td> | |
318 | <p> | |
319 | <code class="computeroutput"><span class="identifier">Map</span><span class="special">::</span><span class="identifier">Map</span><span class="special">()</span></code> | |
320 | </p> | |
321 | </td> | |
322 | </tr> | |
323 | <tr> | |
324 | <td> | |
325 | <p> | |
326 | subset relation | |
327 | </p> | |
328 | </td> | |
329 | <td> | |
330 | <p> | |
331 | </p> | |
332 | </td> | |
333 | <td> | |
334 | <p> | |
335 | <code class="computeroutput"><span class="keyword">bool</span> <span class="identifier">within</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Map</span><span class="special">&</span> | |
336 | <span class="identifier">s2</span><span class="special">,</span> | |
337 | <span class="keyword">const</span> <span class="identifier">Map</span><span class="special">&</span> <span class="identifier">s2</span><span class="special">)</span><span class="keyword">const</span></code> | |
338 | </p> | |
339 | </td> | |
340 | </tr> | |
341 | <tr> | |
342 | <td> | |
343 | <p> | |
344 | equality | |
345 | </p> | |
346 | </td> | |
347 | <td> | |
348 | <p> | |
349 | </p> | |
350 | </td> | |
351 | <td> | |
352 | <p> | |
353 | <code class="computeroutput"><span class="keyword">bool</span> <span class="identifier">is_element_equal</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Map</span><span class="special">&</span> | |
354 | <span class="identifier">s1</span><span class="special">,</span> | |
355 | <span class="keyword">const</span> <span class="identifier">Map</span><span class="special">&</span> <span class="identifier">s2</span><span class="special">)</span></code> | |
356 | </p> | |
357 | </td> | |
358 | </tr> | |
359 | <tr> | |
360 | <td> | |
361 | <p> | |
362 | map union | |
363 | </p> | |
364 | </td> | |
365 | <td> | |
366 | <p> | |
367 | inplace | |
368 | </p> | |
369 | </td> | |
370 | <td> | |
371 | <p> | |
372 | <code class="computeroutput"><span class="identifier">Map</span><span class="special">&</span> | |
373 | <span class="keyword">operator</span> <span class="special">+=</span> | |
374 | <span class="special">(</span><span class="identifier">Map</span><span class="special">&</span> <span class="identifier">s1</span><span class="special">,</span> <span class="keyword">const</span> | |
375 | <span class="identifier">Map</span><span class="special">&</span> | |
376 | <span class="identifier">s2</span><span class="special">)</span></code> | |
377 | </p> | |
378 | </td> | |
379 | </tr> | |
380 | <tr> | |
381 | <td> | |
382 | <p> | |
383 | </p> | |
384 | </td> | |
385 | <td> | |
386 | <p> | |
387 | </p> | |
388 | </td> | |
389 | <td> | |
390 | <p> | |
391 | <code class="computeroutput"><span class="identifier">Map</span> <span class="keyword">operator</span> | |
392 | <span class="special">+</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">Map</span><span class="special">&</span> <span class="identifier">s1</span><span class="special">,</span> <span class="keyword">const</span> | |
393 | <span class="identifier">Map</span><span class="special">&</span> | |
394 | <span class="identifier">s2</span><span class="special">)</span></code> | |
395 | </p> | |
396 | </td> | |
397 | </tr> | |
398 | <tr> | |
399 | <td> | |
400 | <p> | |
401 | map difference | |
402 | </p> | |
403 | </td> | |
404 | <td> | |
405 | <p> | |
406 | inplace | |
407 | </p> | |
408 | </td> | |
409 | <td> | |
410 | <p> | |
411 | <code class="computeroutput"><span class="identifier">Map</span><span class="special">&</span> | |
412 | <span class="keyword">operator</span> <span class="special">-=</span> | |
413 | <span class="special">(</span><span class="identifier">Map</span><span class="special">&</span> <span class="identifier">s1</span><span class="special">,</span> <span class="keyword">const</span> | |
414 | <span class="identifier">Map</span><span class="special">&</span> | |
415 | <span class="identifier">s2</span><span class="special">)</span></code> | |
416 | </p> | |
417 | </td> | |
418 | </tr> | |
419 | <tr> | |
420 | <td> | |
421 | <p> | |
422 | </p> | |
423 | </td> | |
424 | <td> | |
425 | <p> | |
426 | </p> | |
427 | </td> | |
428 | <td> | |
429 | <p> | |
430 | <code class="computeroutput"><span class="identifier">Map</span> <span class="keyword">operator</span> | |
431 | <span class="special">-</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">Map</span><span class="special">&</span> <span class="identifier">s1</span><span class="special">,</span> <span class="keyword">const</span> | |
432 | <span class="identifier">Map</span><span class="special">&</span> | |
433 | <span class="identifier">s2</span><span class="special">)</span></code> | |
434 | </p> | |
435 | </td> | |
436 | </tr> | |
437 | <tr> | |
438 | <td> | |
439 | <p> | |
440 | map intersection | |
441 | </p> | |
442 | </td> | |
443 | <td> | |
444 | <p> | |
445 | inplace | |
446 | </p> | |
447 | </td> | |
448 | <td> | |
449 | <p> | |
450 | <code class="computeroutput"><span class="identifier">Map</span><span class="special">&</span> | |
451 | <span class="keyword">operator</span> <span class="special">&=</span> | |
452 | <span class="special">(</span><span class="identifier">Map</span><span class="special">&</span> <span class="identifier">s1</span><span class="special">,</span> <span class="keyword">const</span> | |
453 | <span class="identifier">Map</span><span class="special">&</span> | |
454 | <span class="identifier">s2</span><span class="special">)</span></code> | |
455 | </p> | |
456 | </td> | |
457 | </tr> | |
458 | <tr> | |
459 | <td> | |
460 | <p> | |
461 | </p> | |
462 | </td> | |
463 | <td> | |
464 | <p> | |
465 | </p> | |
466 | </td> | |
467 | <td> | |
468 | <p> | |
469 | <code class="computeroutput"><span class="identifier">Map</span> <span class="keyword">operator</span> | |
470 | <span class="special">&</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">Map</span><span class="special">&</span> <span class="identifier">s1</span><span class="special">,</span> <span class="keyword">const</span> | |
471 | <span class="identifier">Map</span><span class="special">&</span> | |
472 | <span class="identifier">s2</span><span class="special">)</span></code> | |
473 | </p> | |
474 | </td> | |
475 | </tr> | |
476 | </tbody> | |
477 | </table></div> | |
478 | <p> | |
479 | As one can see, on the abstract kernel the signatures of the icl's <code class="computeroutput"><span class="identifier">Set</span></code> and <code class="computeroutput"><span class="identifier">Map</span></code> | |
480 | concepts are identical, except for the typename. While signatures are identical | |
481 | The sets of valid laws are different, which will be described in more detail | |
482 | in the sections on the <a class="link" href="../semantics/sets.html" title="Sets">semantics | |
483 | of icl Sets</a> and <a class="link" href="../semantics/maps.html" title="Maps">Maps</a>. | |
484 | These semantic differences are mainly based on the implementation of the | |
485 | pivotal member functions <code class="computeroutput"><span class="identifier">add</span></code> | |
486 | and <code class="computeroutput"><span class="identifier">subtract</span></code> for elements | |
487 | and intervals that again serve for implementing <code class="computeroutput"><span class="keyword">operator</span> | |
488 | <span class="special">+=</span></code> and <code class="computeroutput"><span class="keyword">operator</span> | |
489 | <span class="special">-=</span></code>. | |
490 | </p> | |
491 | </div> | |
492 | <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> | |
493 | <td align="left"></td> | |
494 | <td align="right"><div class="copyright-footer">Copyright © 2007 -2010 Joachim Faulhaber<br>Copyright © 1999 -2006 Cortex Software GmbH<p> | |
495 | Distributed under the Boost Software License, Version 1.0. (See accompanying | |
496 | 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>) | |
497 | </p> | |
498 | </div></td> | |
499 | </tr></table> | |
500 | <hr> | |
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