Lib/sets.py

   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 from __future__ import generators
  58 try:
  59     from itertools import ifilter, ifilterfalse
  60 except ImportError:
  61     # Code to make the module run under Py2.2
  62     def ifilter(predicate, iterable):
  63         if predicate is None:
  64             def predicate(x):
  65                 return x
  66         for x in iterable:
  67             if predicate(x):
  68                 yield x
  69     def ifilterfalse(predicate, iterable):
  70         if predicate is None:
  71             def predicate(x):
  72                 return x
  73         for x in iterable:
  74             if not predicate(x):
  75                 yield x
  76     try:
  77         True, False
  78     except NameError:
  79         True, False = (0==0, 0!=0)
  80
  81 __all__ = ['BaseSet', 'Set', 'ImmutableSet']
  82
  83 class BaseSet(object):
  84     """Common base class for mutable and immutable sets."""
  85
  86     __slots__ = ['_data']
  87
  88     # Constructor
  89
  90     def __init__(self):
  91         """This is an abstract class."""
  92         # Don't call this from a concrete subclass!
  93         if self.__class__ is BaseSet:
  94             raise TypeError, ("BaseSet is an abstract class.  "
  95                               "Use Set or ImmutableSet.")
  96
  97     # Standard protocols: __len__, __repr__, __str__, __iter__
  98
  99     def __len__(self):
 100         """Return the number of elements of a set."""
 101         return len(self._data)
 102
 103     def __repr__(self):
 104         """Return string representation of a set.
 105
 106         This looks like 'Set([<list of elements>])'.
 107         """
 108         return self._repr()
 109
 110     # __str__ is the same as __repr__
 111     __str__ = __repr__
 112
 113     def _repr(self, sorted=False):
 114         elements = self._data.keys()
 115         if sorted:
 116             elements.sort()
 117         return '%s(%r)' % (self.__class__.__name__, elements)
 118
 119     def __iter__(self):
 120         """Return an iterator over the elements or a set.
 121
 122         This is the keys iterator for the underlying dict.
 123         """
 124         return self._data.iterkeys()
 125
 126     # Three-way comparison is not supported.  However, because __eq__ is
 127     # tried before __cmp__, if Set x == Set y, x.__eq__(y) returns True and
 128     # then cmp(x, y) returns 0 (Python doesn't actually call __cmp__ in this
 129     # case).
 130
 131     def __cmp__(self, other):
 132         raise TypeError, "can't compare sets using cmp()"
 133
 134     # Equality comparisons using the underlying dicts.  Mixed-type comparisons
 135     # are allowed here, where Set == z for non-Set z always returns False,
 136     # and Set != z always True.  This allows expressions like "x in y" to
 137     # give the expected result when y is a sequence of mixed types, not
 138     # raising a pointless TypeError just because y contains a Set, or x is
 139     # a Set and y contain's a non-set ("in" invokes only __eq__).
 140     # Subtle:  it would be nicer if __eq__ and __ne__ could return
 141     # NotImplemented instead of True or False.  Then the other comparand
 142     # would get a chance to determine the result, and if the other comparand
 143     # also returned NotImplemented then it would fall back to object address
 144     # comparison (which would always return False for __eq__ and always
 145     # True for __ne__).  However, that doesn't work, because this type
 146     # *also* implements __cmp__:  if, e.g., __eq__ returns NotImplemented,
 147     # Python tries __cmp__ next, and the __cmp__ here then raises TypeError.
 148
 149     def __eq__(self, other):
 150         if isinstance(other, BaseSet):
 151             return self._data == other._data
 152         else:
 153             return False
 154
 155     def __ne__(self, other):
 156         if isinstance(other, BaseSet):
 157             return self._data != other._data
 158         else:
 159             return True
 160
 161     # Copying operations
 162
 163     def copy(self):
 164         """Return a shallow copy of a set."""
 165         result = self.__class__()
 166         result._data.update(self._data)
 167         return result
 168
 169     __copy__ = copy # For the copy module
 170
 171     def __deepcopy__(self, memo):
 172         """Return a deep copy of a set; used by copy module."""
 173         # This pre-creates the result and inserts it in the memo
 174         # early, in case the deep copy recurses into another reference
 175         # to this same set.  A set can't be an element of itself, but
 176         # it can certainly contain an object that has a reference to
 177         # itself.
 178         from copy import deepcopy
 179         result = self.__class__()
 180         memo[id(self)] = result
 181         data = result._data
 182         value = True
 183         for elt in self:
 184             data[deepcopy(elt, memo)] = value
 185         return result
 186
 187     # Standard set operations: union, intersection, both differences.
 188     # Each has an operator version (e.g. __or__, invoked with |) and a
 189     # method version (e.g. union).
 190     # Subtle:  Each pair requires distinct code so that the outcome is
 191     # correct when the type of other isn't suitable.  For example, if
 192     # we did "union = __or__" instead, then Set().union(3) would return
 193     # NotImplemented instead of raising TypeError (albeit that *why* it
 194     # raises TypeError as-is is also a bit subtle).
 195
 196     def __or__(self, other):
 197         """Return the union of two sets as a new set.
 198
 199         (I.e. all elements that are in either set.)
 200         """
 201         if not isinstance(other, BaseSet):
 202             return NotImplemented
 203         return self.union(other)
 204
 205     def union(self, other):
 206         """Return the union of two sets as a new set.
 207
 208         (I.e. all elements that are in either set.)
 209         """
 210         result = self.__class__(self)
 211         result._update(other)
 212         return result
 213
 214     def __and__(self, other):
 215         """Return the intersection of two sets as a new set.
 216
 217         (I.e. all elements that are in both sets.)
 218         """
 219         if not isinstance(other, BaseSet):
 220             return NotImplemented
 221         return self.intersection(other)
 222
 223     def intersection(self, other):
 224         """Return the intersection of two sets as a new set.
 225
 226         (I.e. all elements that are in both sets.)
 227         """
 228         if not isinstance(other, BaseSet):
 229             other = Set(other)
 230         if len(self) <= len(other):
 231             little, big = self, other
 232         else:
 233             little, big = other, self
 234         common = ifilter(big._data.has_key, little)
 235         return self.__class__(common)
 236
 237     def __xor__(self, other):
 238         """Return the symmetric difference of two sets as a new set.
 239
 240         (I.e. all elements that are in exactly one of the sets.)
 241         """
 242         if not isinstance(other, BaseSet):
 243             return NotImplemented
 244         return self.symmetric_difference(other)
 245
 246     def symmetric_difference(self, other):
 247         """Return the symmetric difference of two sets as a new set.
 248
 249         (I.e. all elements that are in exactly one of the sets.)
 250         """
 251         result = self.__class__()
 252         data = result._data
 253         value = True
 254         selfdata = self._data
 255         try:
 256             otherdata = other._data
 257         except AttributeError:
 258             otherdata = Set(other)._data
 259         for elt in ifilterfalse(otherdata.has_key, selfdata):
 260             data[elt] = value
 261         for elt in ifilterfalse(selfdata.has_key, otherdata):
 262             data[elt] = value
 263         return result
 264
 265     def  __sub__(self, other):
 266         """Return the difference of two sets as a new Set.
 267
 268         (I.e. all elements that are in this set and not in the other.)
 269         """
 270         if not isinstance(other, BaseSet):
 271             return NotImplemented
 272         return self.difference(other)
 273
 274     def difference(self, other):
 275         """Return the difference of two sets as a new Set.
 276
 277         (I.e. all elements that are in this set and not in the other.)
 278         """
 279         result = self.__class__()
 280         data = result._data
 281         try:
 282             otherdata = other._data
 283         except AttributeError:
 284             otherdata = Set(other)._data
 285         value = True
 286         for elt in ifilterfalse(otherdata.has_key, self):
 287             data[elt] = value
 288         return result
 289
 290     # Membership test
 291
 292     def __contains__(self, element):
 293         """Report whether an element is a member of a set.
 294
 295         (Called in response to the expression `element in self'.)
 296         """
 297         try:
 298             return element in self._data
 299         except TypeError:
 300             transform = getattr(element, "__as_temporarily_immutable__", None)
 301             if transform is None:
 302                 raise # re-raise the TypeError exception we caught
 303             return transform() in self._data
 304
 305     # Subset and superset test
 306
 307     def issubset(self, other):
 308         """Report whether another set contains this set."""
 309         self._binary_sanity_check(other)
 310         if len(self) > len(other):  # Fast check for obvious cases
 311             return False
 312         for elt in ifilterfalse(other._data.has_key, self):
 313             return False
 314         return True
 315
 316     def issuperset(self, other):
 317         """Report whether this set contains another set."""
 318         self._binary_sanity_check(other)
 319         if len(self) < len(other):  # Fast check for obvious cases
 320             return False
 321         for elt in ifilterfalse(self._data.has_key, other):
 322             return False
 323         return True
 324
 325     # Inequality comparisons using the is-subset relation.
 326     __le__ = issubset
 327     __ge__ = issuperset
 328
 329     def __lt__(self, other):
 330         self._binary_sanity_check(other)
 331         return len(self) < len(other) and self.issubset(other)
 332
 333     def __gt__(self, other):
 334         self._binary_sanity_check(other)
 335         return len(self) > len(other) and self.issuperset(other)
 336
 337     # Assorted helpers
 338
 339     def _binary_sanity_check(self, other):
 340         # Check that the other argument to a binary operation is also
 341         # a set, raising a TypeError otherwise.
 342         if not isinstance(other, BaseSet):
 343             raise TypeError, "Binary operation only permitted between sets"
 344
 345     def _compute_hash(self):
 346         # Calculate hash code for a set by xor'ing the hash codes of
 347         # the elements.  This ensures that the hash code does not depend
 348         # on the order in which elements are added to the set.  This is
 349         # not called __hash__ because a BaseSet should not be hashable;
 350         # only an ImmutableSet is hashable.
 351         result = 0
 352         for elt in self:
 353             result ^= hash(elt)
 354         return result
 355
 356     def _update(self, iterable):
 357         # The main loop for update() and the subclass __init__() methods.
 358         data = self._data
 359
 360         # Use the fast update() method when a dictionary is available.
 361         if isinstance(iterable, BaseSet):
 362             data.update(iterable._data)
 363             return
 364
 365         value = True
 366
 367         if type(iterable) in (list, tuple, xrange):
 368             # Optimized: we know that __iter__() and next() can't
 369             # raise TypeError, so we can move 'try:' out of the loop.
 370             it = iter(iterable)
 371             while True:
 372                 try:
 373                     for element in it:
 374                         data[element] = value
 375                     return
 376                 except TypeError:
 377                     transform = getattr(element, "__as_immutable__", None)
 378                     if transform is None:
 379                         raise # re-raise the TypeError exception we caught
 380                     data[transform()] = value
 381         else:
 382             # Safe: only catch TypeError where intended
 383             for element in iterable:
 384                 try:
 385                     data[element] = value
 386                 except TypeError:
 387                     transform = getattr(element, "__as_immutable__", None)
 388                     if transform is None:
 389                         raise # re-raise the TypeError exception we caught
 390                     data[transform()] = value
 391
 392
 393 class ImmutableSet(BaseSet):
 394     """Immutable set class."""
 395
 396     __slots__ = ['_hashcode']
 397
 398     # BaseSet + hashing
 399
 400     def __init__(self, iterable=None):
 401         """Construct an immutable set from an optional iterable."""
 402         self._hashcode = None
 403         self._data = {}
 404         if iterable is not None:
 405             self._update(iterable)
 406
 407     def __hash__(self):
 408         if self._hashcode is None:
 409             self._hashcode = self._compute_hash()
 410         return self._hashcode
 411
 412     def __getstate__(self):
 413         return self._data, self._hashcode
 414
 415     def __setstate__(self, state):
 416         self._data, self._hashcode = state
 417
 418 class Set(BaseSet):
 419     """ Mutable set class."""
 420
 421     __slots__ = []
 422
 423     # BaseSet + operations requiring mutability; no hashing
 424
 425     def __init__(self, iterable=None):
 426         """Construct a set from an optional iterable."""
 427         self._data = {}
 428         if iterable is not None:
 429             self._update(iterable)
 430
 431     def __getstate__(self):
 432         # getstate's results are ignored if it is not
 433         return self._data,
 434
 435     def __setstate__(self, data):
 436         self._data, = data
 437
 438     def __hash__(self):
 439         """A Set cannot be hashed."""
 440         # We inherit object.__hash__, so we must deny this explicitly
 441         raise TypeError, "Can't hash a Set, only an ImmutableSet."
 442
 443     # In-place union, intersection, differences.
 444     # Subtle:  The xyz_update() functions deliberately return None,
 445     # as do all mutating operations on built-in container types.
 446     # The __xyz__ spellings have to return self, though.
 447
 448     def __ior__(self, other):
 449         """Update a set with the union of itself and another."""
 450         self._binary_sanity_check(other)
 451         self._data.update(other._data)
 452         return self
 453
 454     def union_update(self, other):
 455         """Update a set with the union of itself and another."""
 456         self._update(other)
 457
 458     def __iand__(self, other):
 459         """Update a set with the intersection of itself and another."""
 460         self._binary_sanity_check(other)
 461         self._data = (self & other)._data
 462         return self
 463
 464     def intersection_update(self, other):
 465         """Update a set with the intersection of itself and another."""
 466         if isinstance(other, BaseSet):
 467             self &= other
 468         else:
 469             self._data = (self.intersection(other))._data
 470
 471     def __ixor__(self, other):
 472         """Update a set with the symmetric difference of itself and another."""
 473         self._binary_sanity_check(other)
 474         self.symmetric_difference_update(other)
 475         return self
 476
 477     def symmetric_difference_update(self, other):
 478         """Update a set with the symmetric difference of itself and another."""
 479         data = self._data
 480         value = True
 481         if not isinstance(other, BaseSet):
 482             other = Set(other)
 483         if self is other:
 484             self.clear()
 485         for elt in other:
 486             if elt in data:
 487                 del data[elt]
 488             else:
 489                 data[elt] = value
 490
 491     def __isub__(self, other):
 492         """Remove all elements of another set from this set."""
 493         self._binary_sanity_check(other)
 494         self.difference_update(other)
 495         return self
 496
 497     def difference_update(self, other):
 498         """Remove all elements of another set from this set."""
 499         data = self._data
 500         if not isinstance(other, BaseSet):
 501             other = Set(other)
 502         if self is other:
 503             self.clear()
 504         for elt in ifilter(data.has_key, other):
 505             del data[elt]
 506
 507     # Python dict-like mass mutations: update, clear
 508
 509     def update(self, iterable):
 510         """Add all values from an iterable (such as a list or file)."""
 511         self._update(iterable)
 512
 513     def clear(self):
 514         """Remove all elements from this set."""
 515         self._data.clear()
 516
 517     # Single-element mutations: add, remove, discard
 518
 519     def add(self, element):
 520         """Add an element to a set.
 521
 522         This has no effect if the element is already present.
 523         """
 524         try:
 525             self._data[element] = True
 526         except TypeError:
 527             transform = getattr(element, "__as_immutable__", None)
 528             if transform is None:
 529                 raise # re-raise the TypeError exception we caught
 530             self._data[transform()] = True
 531
 532     def remove(self, element):
 533         """Remove an element from a set; it must be a member.
 534
 535         If the element is not a member, raise a KeyError.
 536         """
 537         try:
 538             del self._data[element]
 539         except TypeError:
 540             transform = getattr(element, "__as_temporarily_immutable__", None)
 541             if transform is None:
 542                 raise # re-raise the TypeError exception we caught
 543             del self._data[transform()]
 544
 545     def discard(self, element):
 546         """Remove an element from a set if it is a member.
 547
 548         If the element is not a member, do nothing.
 549         """
 550         try:
 551             self.remove(element)
 552         except KeyError:
 553             pass
 554
 555     def pop(self):
 556         """Remove and return an arbitrary set element."""
 557         return self._data.popitem()[0]
 558
 559     def __as_immutable__(self):
 560         # Return a copy of self as an immutable set
 561         return ImmutableSet(self)
 562
 563     def __as_temporarily_immutable__(self):
 564         # Return self wrapped in a temporarily immutable set
 565         return _TemporarilyImmutableSet(self)
 566
 567
 568 class _TemporarilyImmutableSet(BaseSet):
 569     # Wrap a mutable set as if it was temporarily immutable.
 570     # This only supplies hashing and equality comparisons.
 571
 572     def __init__(self, set):
 573         self._set = set
 574         self._data = set._data  # Needed by ImmutableSet.__eq__()
 575
 576     def __hash__(self):
 577         return self._set._compute_hash()