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| 1 """Classes to represent arbitrary sets (including sets of sets). |
| 2 |
| 3 This module implements sets using dictionaries whose values are |
| 4 ignored. The usual operations (union, intersection, deletion, etc.) |
| 5 are provided as both methods and operators. |
| 6 |
| 7 Important: sets are not sequences! While they support 'x in s', |
| 8 'len(s)', and 'for x in s', none of those operations are unique for |
| 9 sequences; for example, mappings support all three as well. The |
| 10 characteristic operation for sequences is subscripting with small |
| 11 integers: s[i], for i in range(len(s)). Sets don't support |
| 12 subscripting at all. Also, sequences allow multiple occurrences and |
| 13 their elements have a definite order; sets on the other hand don't |
| 14 record multiple occurrences and don't remember the order of element |
| 15 insertion (which is why they don't support s[i]). |
| 16 |
| 17 The following classes are provided: |
| 18 |
| 19 BaseSet -- All the operations common to both mutable and immutable |
| 20 sets. This is an abstract class, not meant to be directly |
| 21 instantiated. |
| 22 |
| 23 Set -- Mutable sets, subclass of BaseSet; not hashable. |
| 24 |
| 25 ImmutableSet -- Immutable sets, subclass of BaseSet; hashable. |
| 26 An iterable argument is mandatory to create an ImmutableSet. |
| 27 |
| 28 _TemporarilyImmutableSet -- A wrapper around a Set, hashable, |
| 29 giving the same hash value as the immutable set equivalent |
| 30 would have. Do not use this class directly. |
| 31 |
| 32 Only hashable objects can be added to a Set. In particular, you cannot |
| 33 really add a Set as an element to another Set; if you try, what is |
| 34 actually added is an ImmutableSet built from it (it compares equal to |
| 35 the one you tried adding). |
| 36 |
| 37 When you ask if `x in y' where x is a Set and y is a Set or |
| 38 ImmutableSet, x is wrapped into a _TemporarilyImmutableSet z, and |
| 39 what's tested is actually `z in y'. |
| 40 |
| 41 """ |
| 42 |
| 43 # Code history: |
| 44 # |
| 45 # - Greg V. Wilson wrote the first version, using a different approach |
| 46 # to the mutable/immutable problem, and inheriting from dict. |
| 47 # |
| 48 # - Alex Martelli modified Greg's version to implement the current |
| 49 # Set/ImmutableSet approach, and make the data an attribute. |
| 50 # |
| 51 # - Guido van Rossum rewrote much of the code, made some API changes, |
| 52 # and cleaned up the docstrings. |
| 53 # |
| 54 # - Raymond Hettinger added a number of speedups and other |
| 55 # improvements. |
| 56 |
| 57 # protect this import from the fixers... |
| 58 exec('from itertools import ifilterfalse as filterfalse') |
| 59 |
| 60 __all__ = ['BaseSet', 'Set', 'ImmutableSet'] |
| 61 |
| 62 class BaseSet(object): |
| 63 """Common base class for mutable and immutable sets.""" |
| 64 |
| 65 __slots__ = ['_data'] |
| 66 |
| 67 # Constructor |
| 68 |
| 69 def __init__(self): |
| 70 """This is an abstract class.""" |
| 71 # Don't call this from a concrete subclass! |
| 72 if self.__class__ is BaseSet: |
| 73 raise TypeError("BaseSet is an abstract class. " |
| 74 "Use Set or ImmutableSet.") |
| 75 |
| 76 # Standard protocols: __len__, __repr__, __str__, __iter__ |
| 77 |
| 78 def __len__(self): |
| 79 """Return the number of elements of a set.""" |
| 80 return len(self._data) |
| 81 |
| 82 def __repr__(self): |
| 83 """Return string representation of a set. |
| 84 |
| 85 This looks like 'Set([<list of elements>])'. |
| 86 """ |
| 87 return self._repr() |
| 88 |
| 89 # __str__ is the same as __repr__ |
| 90 __str__ = __repr__ |
| 91 |
| 92 def _repr(self, sort_them=False): |
| 93 elements = list(self._data.keys()) |
| 94 if sort_them: |
| 95 elements.sort() |
| 96 return '%s(%r)' % (self.__class__.__name__, elements) |
| 97 |
| 98 def __iter__(self): |
| 99 """Return an iterator over the elements or a set. |
| 100 |
| 101 This is the keys iterator for the underlying dict. |
| 102 """ |
| 103 # Wrapping name in () prevents fixer from "fixing" this |
| 104 return (self._data.iterkeys)() |
| 105 |
| 106 # Three-way comparison is not supported. However, because __eq__ is |
| 107 # tried before __cmp__, if Set x == Set y, x.__eq__(y) returns True and |
| 108 # then cmp(x, y) returns 0 (Python doesn't actually call __cmp__ in this |
| 109 # case). |
| 110 |
| 111 def __cmp__(self, other): |
| 112 raise TypeError("can't compare sets using cmp()") |
| 113 |
| 114 # Equality comparisons using the underlying dicts. Mixed-type comparisons |
| 115 # are allowed here, where Set == z for non-Set z always returns False, |
| 116 # and Set != z always True. This allows expressions like "x in y" to |
| 117 # give the expected result when y is a sequence of mixed types, not |
| 118 # raising a pointless TypeError just because y contains a Set, or x is |
| 119 # a Set and y contain's a non-set ("in" invokes only __eq__). |
| 120 # Subtle: it would be nicer if __eq__ and __ne__ could return |
| 121 # NotImplemented instead of True or False. Then the other comparand |
| 122 # would get a chance to determine the result, and if the other comparand |
| 123 # also returned NotImplemented then it would fall back to object address |
| 124 # comparison (which would always return False for __eq__ and always |
| 125 # True for __ne__). However, that doesn't work, because this type |
| 126 # *also* implements __cmp__: if, e.g., __eq__ returns NotImplemented, |
| 127 # Python tries __cmp__ next, and the __cmp__ here then raises TypeError. |
| 128 |
| 129 def __eq__(self, other): |
| 130 if isinstance(other, BaseSet): |
| 131 return self._data == other._data |
| 132 else: |
| 133 return False |
| 134 |
| 135 def __ne__(self, other): |
| 136 if isinstance(other, BaseSet): |
| 137 return self._data != other._data |
| 138 else: |
| 139 return True |
| 140 |
| 141 # Copying operations |
| 142 |
| 143 def copy(self): |
| 144 """Return a shallow copy of a set.""" |
| 145 result = self.__class__() |
| 146 result._data.update(self._data) |
| 147 return result |
| 148 |
| 149 __copy__ = copy # For the copy module |
| 150 |
| 151 def __deepcopy__(self, memo): |
| 152 """Return a deep copy of a set; used by copy module.""" |
| 153 # This pre-creates the result and inserts it in the memo |
| 154 # early, in case the deep copy recurses into another reference |
| 155 # to this same set. A set can't be an element of itself, but |
| 156 # it can certainly contain an object that has a reference to |
| 157 # itself. |
| 158 from copy import deepcopy |
| 159 result = self.__class__() |
| 160 memo[id(self)] = result |
| 161 data = result._data |
| 162 value = True |
| 163 for elt in self: |
| 164 data[deepcopy(elt, memo)] = value |
| 165 return result |
| 166 |
| 167 # Standard set operations: union, intersection, both differences. |
| 168 # Each has an operator version (e.g. __or__, invoked with |) and a |
| 169 # method version (e.g. union). |
| 170 # Subtle: Each pair requires distinct code so that the outcome is |
| 171 # correct when the type of other isn't suitable. For example, if |
| 172 # we did "union = __or__" instead, then Set().union(3) would return |
| 173 # NotImplemented instead of raising TypeError (albeit that *why* it |
| 174 # raises TypeError as-is is also a bit subtle). |
| 175 |
| 176 def __or__(self, other): |
| 177 """Return the union of two sets as a new set. |
| 178 |
| 179 (I.e. all elements that are in either set.) |
| 180 """ |
| 181 if not isinstance(other, BaseSet): |
| 182 return NotImplemented |
| 183 return self.union(other) |
| 184 |
| 185 def union(self, other): |
| 186 """Return the union of two sets as a new set. |
| 187 |
| 188 (I.e. all elements that are in either set.) |
| 189 """ |
| 190 result = self.__class__(self) |
| 191 result._update(other) |
| 192 return result |
| 193 |
| 194 def __and__(self, other): |
| 195 """Return the intersection of two sets as a new set. |
| 196 |
| 197 (I.e. all elements that are in both sets.) |
| 198 """ |
| 199 if not isinstance(other, BaseSet): |
| 200 return NotImplemented |
| 201 return self.intersection(other) |
| 202 |
| 203 def intersection(self, other): |
| 204 """Return the intersection of two sets as a new set. |
| 205 |
| 206 (I.e. all elements that are in both sets.) |
| 207 """ |
| 208 if not isinstance(other, BaseSet): |
| 209 other = Set(other) |
| 210 if len(self) <= len(other): |
| 211 little, big = self, other |
| 212 else: |
| 213 little, big = other, self |
| 214 common = iter(filter(big._data.has_key, little)) |
| 215 return self.__class__(common) |
| 216 |
| 217 def __xor__(self, other): |
| 218 """Return the symmetric difference of two sets as a new set. |
| 219 |
| 220 (I.e. all elements that are in exactly one of the sets.) |
| 221 """ |
| 222 if not isinstance(other, BaseSet): |
| 223 return NotImplemented |
| 224 return self.symmetric_difference(other) |
| 225 |
| 226 def symmetric_difference(self, other): |
| 227 """Return the symmetric difference of two sets as a new set. |
| 228 |
| 229 (I.e. all elements that are in exactly one of the sets.) |
| 230 """ |
| 231 result = self.__class__() |
| 232 data = result._data |
| 233 value = True |
| 234 selfdata = self._data |
| 235 try: |
| 236 otherdata = other._data |
| 237 except AttributeError: |
| 238 otherdata = Set(other)._data |
| 239 for elt in filterfalse(otherdata.has_key, selfdata): |
| 240 data[elt] = value |
| 241 for elt in filterfalse(selfdata.has_key, otherdata): |
| 242 data[elt] = value |
| 243 return result |
| 244 |
| 245 def __sub__(self, other): |
| 246 """Return the difference of two sets as a new Set. |
| 247 |
| 248 (I.e. all elements that are in this set and not in the other.) |
| 249 """ |
| 250 if not isinstance(other, BaseSet): |
| 251 return NotImplemented |
| 252 return self.difference(other) |
| 253 |
| 254 def difference(self, other): |
| 255 """Return the difference of two sets as a new Set. |
| 256 |
| 257 (I.e. all elements that are in this set and not in the other.) |
| 258 """ |
| 259 result = self.__class__() |
| 260 data = result._data |
| 261 try: |
| 262 otherdata = other._data |
| 263 except AttributeError: |
| 264 otherdata = Set(other)._data |
| 265 value = True |
| 266 for elt in filterfalse(otherdata.has_key, self): |
| 267 data[elt] = value |
| 268 return result |
| 269 |
| 270 # Membership test |
| 271 |
| 272 def __contains__(self, element): |
| 273 """Report whether an element is a member of a set. |
| 274 |
| 275 (Called in response to the expression `element in self'.) |
| 276 """ |
| 277 try: |
| 278 return element in self._data |
| 279 except TypeError: |
| 280 transform = getattr(element, "__as_temporarily_immutable__", None) |
| 281 if transform is None: |
| 282 raise # re-raise the TypeError exception we caught |
| 283 return transform() in self._data |
| 284 |
| 285 # Subset and superset test |
| 286 |
| 287 def issubset(self, other): |
| 288 """Report whether another set contains this set.""" |
| 289 self._binary_sanity_check(other) |
| 290 if len(self) > len(other): # Fast check for obvious cases |
| 291 return False |
| 292 for elt in filterfalse(other._data.has_key, self): |
| 293 return False |
| 294 return True |
| 295 |
| 296 def issuperset(self, other): |
| 297 """Report whether this set contains another set.""" |
| 298 self._binary_sanity_check(other) |
| 299 if len(self) < len(other): # Fast check for obvious cases |
| 300 return False |
| 301 for elt in filterfalse(self._data.has_key, other): |
| 302 return False |
| 303 return True |
| 304 |
| 305 # Inequality comparisons using the is-subset relation. |
| 306 __le__ = issubset |
| 307 __ge__ = issuperset |
| 308 |
| 309 def __lt__(self, other): |
| 310 self._binary_sanity_check(other) |
| 311 return len(self) < len(other) and self.issubset(other) |
| 312 |
| 313 def __gt__(self, other): |
| 314 self._binary_sanity_check(other) |
| 315 return len(self) > len(other) and self.issuperset(other) |
| 316 |
| 317 # Assorted helpers |
| 318 |
| 319 def _binary_sanity_check(self, other): |
| 320 # Check that the other argument to a binary operation is also |
| 321 # a set, raising a TypeError otherwise. |
| 322 if not isinstance(other, BaseSet): |
| 323 raise TypeError("Binary operation only permitted between sets") |
| 324 |
| 325 def _compute_hash(self): |
| 326 # Calculate hash code for a set by xor'ing the hash codes of |
| 327 # the elements. This ensures that the hash code does not depend |
| 328 # on the order in which elements are added to the set. This is |
| 329 # not called __hash__ because a BaseSet should not be hashable; |
| 330 # only an ImmutableSet is hashable. |
| 331 result = 0 |
| 332 for elt in self: |
| 333 result ^= hash(elt) |
| 334 return result |
| 335 |
| 336 def _update(self, iterable): |
| 337 # The main loop for update() and the subclass __init__() methods. |
| 338 data = self._data |
| 339 |
| 340 # Use the fast update() method when a dictionary is available. |
| 341 if isinstance(iterable, BaseSet): |
| 342 data.update(iterable._data) |
| 343 return |
| 344 |
| 345 value = True |
| 346 |
| 347 if type(iterable) in (list, tuple, xrange): |
| 348 # Optimized: we know that __iter__() and next() can't |
| 349 # raise TypeError, so we can move 'try:' out of the loop. |
| 350 it = iter(iterable) |
| 351 while True: |
| 352 try: |
| 353 for element in it: |
| 354 data[element] = value |
| 355 return |
| 356 except TypeError: |
| 357 transform = getattr(element, "__as_immutable__", None) |
| 358 if transform is None: |
| 359 raise # re-raise the TypeError exception we caught |
| 360 data[transform()] = value |
| 361 else: |
| 362 # Safe: only catch TypeError where intended |
| 363 for element in iterable: |
| 364 try: |
| 365 data[element] = value |
| 366 except TypeError: |
| 367 transform = getattr(element, "__as_immutable__", None) |
| 368 if transform is None: |
| 369 raise # re-raise the TypeError exception we caught |
| 370 data[transform()] = value |
| 371 |
| 372 |
| 373 class ImmutableSet(BaseSet): |
| 374 """Immutable set class.""" |
| 375 |
| 376 __slots__ = ['_hashcode'] |
| 377 |
| 378 # BaseSet + hashing |
| 379 |
| 380 def __init__(self, iterable=None): |
| 381 """Construct an immutable set from an optional iterable.""" |
| 382 self._hashcode = None |
| 383 self._data = {} |
| 384 if iterable is not None: |
| 385 self._update(iterable) |
| 386 |
| 387 def __hash__(self): |
| 388 if self._hashcode is None: |
| 389 self._hashcode = self._compute_hash() |
| 390 return self._hashcode |
| 391 |
| 392 def __getstate__(self): |
| 393 return self._data, self._hashcode |
| 394 |
| 395 def __setstate__(self, state): |
| 396 self._data, self._hashcode = state |
| 397 |
| 398 class Set(BaseSet): |
| 399 """ Mutable set class.""" |
| 400 |
| 401 __slots__ = [] |
| 402 |
| 403 # BaseSet + operations requiring mutability; no hashing |
| 404 |
| 405 def __init__(self, iterable=None): |
| 406 """Construct a set from an optional iterable.""" |
| 407 self._data = {} |
| 408 if iterable is not None: |
| 409 self._update(iterable) |
| 410 |
| 411 def __getstate__(self): |
| 412 # getstate's results are ignored if it is not |
| 413 return self._data, |
| 414 |
| 415 def __setstate__(self, data): |
| 416 self._data, = data |
| 417 |
| 418 def __hash__(self): |
| 419 """A Set cannot be hashed.""" |
| 420 # We inherit object.__hash__, so we must deny this explicitly |
| 421 raise TypeError("Can't hash a Set, only an ImmutableSet.") |
| 422 |
| 423 # In-place union, intersection, differences. |
| 424 # Subtle: The xyz_update() functions deliberately return None, |
| 425 # as do all mutating operations on built-in container types. |
| 426 # The __xyz__ spellings have to return self, though. |
| 427 |
| 428 def __ior__(self, other): |
| 429 """Update a set with the union of itself and another.""" |
| 430 self._binary_sanity_check(other) |
| 431 self._data.update(other._data) |
| 432 return self |
| 433 |
| 434 def union_update(self, other): |
| 435 """Update a set with the union of itself and another.""" |
| 436 self._update(other) |
| 437 |
| 438 def __iand__(self, other): |
| 439 """Update a set with the intersection of itself and another.""" |
| 440 self._binary_sanity_check(other) |
| 441 self._data = (self & other)._data |
| 442 return self |
| 443 |
| 444 def intersection_update(self, other): |
| 445 """Update a set with the intersection of itself and another.""" |
| 446 if isinstance(other, BaseSet): |
| 447 self &= other |
| 448 else: |
| 449 self._data = (self.intersection(other))._data |
| 450 |
| 451 def __ixor__(self, other): |
| 452 """Update a set with the symmetric difference of itself and another.""" |
| 453 self._binary_sanity_check(other) |
| 454 self.symmetric_difference_update(other) |
| 455 return self |
| 456 |
| 457 def symmetric_difference_update(self, other): |
| 458 """Update a set with the symmetric difference of itself and another.""" |
| 459 data = self._data |
| 460 value = True |
| 461 if not isinstance(other, BaseSet): |
| 462 other = Set(other) |
| 463 if self is other: |
| 464 self.clear() |
| 465 for elt in other: |
| 466 if elt in data: |
| 467 del data[elt] |
| 468 else: |
| 469 data[elt] = value |
| 470 |
| 471 def __isub__(self, other): |
| 472 """Remove all elements of another set from this set.""" |
| 473 self._binary_sanity_check(other) |
| 474 self.difference_update(other) |
| 475 return self |
| 476 |
| 477 def difference_update(self, other): |
| 478 """Remove all elements of another set from this set.""" |
| 479 data = self._data |
| 480 if not isinstance(other, BaseSet): |
| 481 other = Set(other) |
| 482 if self is other: |
| 483 self.clear() |
| 484 for elt in filter(data.has_key, other): |
| 485 del data[elt] |
| 486 |
| 487 # Python dict-like mass mutations: update, clear |
| 488 |
| 489 def update(self, iterable): |
| 490 """Add all values from an iterable (such as a list or file).""" |
| 491 self._update(iterable) |
| 492 |
| 493 def clear(self): |
| 494 """Remove all elements from this set.""" |
| 495 self._data.clear() |
| 496 |
| 497 # Single-element mutations: add, remove, discard |
| 498 |
| 499 def add(self, element): |
| 500 """Add an element to a set. |
| 501 |
| 502 This has no effect if the element is already present. |
| 503 """ |
| 504 try: |
| 505 self._data[element] = True |
| 506 except TypeError: |
| 507 transform = getattr(element, "__as_immutable__", None) |
| 508 if transform is None: |
| 509 raise # re-raise the TypeError exception we caught |
| 510 self._data[transform()] = True |
| 511 |
| 512 def remove(self, element): |
| 513 """Remove an element from a set; it must be a member. |
| 514 |
| 515 If the element is not a member, raise a KeyError. |
| 516 """ |
| 517 try: |
| 518 del self._data[element] |
| 519 except TypeError: |
| 520 transform = getattr(element, "__as_temporarily_immutable__", None) |
| 521 if transform is None: |
| 522 raise # re-raise the TypeError exception we caught |
| 523 del self._data[transform()] |
| 524 |
| 525 def discard(self, element): |
| 526 """Remove an element from a set if it is a member. |
| 527 |
| 528 If the element is not a member, do nothing. |
| 529 """ |
| 530 try: |
| 531 self.remove(element) |
| 532 except KeyError: |
| 533 pass |
| 534 |
| 535 def pop(self): |
| 536 """Remove and return an arbitrary set element.""" |
| 537 return self._data.popitem()[0] |
| 538 |
| 539 def __as_immutable__(self): |
| 540 # Return a copy of self as an immutable set |
| 541 return ImmutableSet(self) |
| 542 |
| 543 def __as_temporarily_immutable__(self): |
| 544 # Return self wrapped in a temporarily immutable set |
| 545 return _TemporarilyImmutableSet(self) |
| 546 |
| 547 |
| 548 class _TemporarilyImmutableSet(BaseSet): |
| 549 # Wrap a mutable set as if it was temporarily immutable. |
| 550 # This only supplies hashing and equality comparisons. |
| 551 |
| 552 def __init__(self, set): |
| 553 self._set = set |
| 554 self._data = set._data # Needed by ImmutableSet.__eq__() |
| 555 |
| 556 def __hash__(self): |
| 557 return self._set._compute_hash() |
| 558 |
| 559 # Local Variables: |
| 560 # tab-width:4 |
| 561 # indent-tabs-mode:nil |
| 562 # End: |
| 563 # vim: set expandtab tabstop=4 shiftwidth=4: |
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