563 lines
19 KiB
Python
563 lines
19 KiB
Python
"""Classes to represent arbitrary sets (including sets of sets).
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This module implements sets using dictionaries whose values are
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ignored. The usual operations (union, intersection, deletion, etc.)
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are provided as both methods and operators.
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Important: sets are not sequences! While they support 'x in s',
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'len(s)', and 'for x in s', none of those operations are unique for
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sequences; for example, mappings support all three as well. The
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characteristic operation for sequences is subscripting with small
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integers: s[i], for i in range(len(s)). Sets don't support
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subscripting at all. Also, sequences allow multiple occurrences and
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their elements have a definite order; sets on the other hand don't
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record multiple occurrences and don't remember the order of element
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insertion (which is why they don't support s[i]).
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The following classes are provided:
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BaseSet -- All the operations common to both mutable and immutable
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sets. This is an abstract class, not meant to be directly
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instantiated.
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Set -- Mutable sets, subclass of BaseSet; not hashable.
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ImmutableSet -- Immutable sets, subclass of BaseSet; hashable.
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An iterable argument is mandatory to create an ImmutableSet.
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_TemporarilyImmutableSet -- A wrapper around a Set, hashable,
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giving the same hash value as the immutable set equivalent
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would have. Do not use this class directly.
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Only hashable objects can be added to a Set. In particular, you cannot
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really add a Set as an element to another Set; if you try, what is
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actually added is an ImmutableSet built from it (it compares equal to
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the one you tried adding).
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When you ask if `x in y' where x is a Set and y is a Set or
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ImmutableSet, x is wrapped into a _TemporarilyImmutableSet z, and
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what's tested is actually `z in y'.
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"""
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# Code history:
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#
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# - Greg V. Wilson wrote the first version, using a different approach
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# to the mutable/immutable problem, and inheriting from dict.
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#
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# - Alex Martelli modified Greg's version to implement the current
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# Set/ImmutableSet approach, and make the data an attribute.
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#
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# - Guido van Rossum rewrote much of the code, made some API changes,
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# and cleaned up the docstrings.
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#
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# - Raymond Hettinger added a number of speedups and other
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# improvements.
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# protect this import from the fixers...
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exec('from itertools import ifilterfalse as filterfalse')
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__all__ = ['BaseSet', 'Set', 'ImmutableSet']
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class BaseSet(object):
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"""Common base class for mutable and immutable sets."""
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__slots__ = ['_data']
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# Constructor
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def __init__(self):
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"""This is an abstract class."""
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# Don't call this from a concrete subclass!
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if self.__class__ is BaseSet:
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raise TypeError("BaseSet is an abstract class. "
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"Use Set or ImmutableSet.")
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# Standard protocols: __len__, __repr__, __str__, __iter__
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def __len__(self):
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"""Return the number of elements of a set."""
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return len(self._data)
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def __repr__(self):
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"""Return string representation of a set.
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This looks like 'Set([<list of elements>])'.
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"""
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return self._repr()
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# __str__ is the same as __repr__
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__str__ = __repr__
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def _repr(self, sort_them=False):
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elements = list(self._data.keys())
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if sort_them:
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elements.sort()
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return '%s(%r)' % (self.__class__.__name__, elements)
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def __iter__(self):
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"""Return an iterator over the elements or a set.
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This is the keys iterator for the underlying dict.
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"""
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# Wrapping name in () prevents fixer from "fixing" this
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return (self._data.iterkeys)()
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# Three-way comparison is not supported. However, because __eq__ is
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# tried before __cmp__, if Set x == Set y, x.__eq__(y) returns True and
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# then cmp(x, y) returns 0 (Python doesn't actually call __cmp__ in this
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# case).
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def __cmp__(self, other):
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raise TypeError("can't compare sets using cmp()")
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# Equality comparisons using the underlying dicts. Mixed-type comparisons
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# are allowed here, where Set == z for non-Set z always returns False,
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# and Set != z always True. This allows expressions like "x in y" to
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# give the expected result when y is a sequence of mixed types, not
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# raising a pointless TypeError just because y contains a Set, or x is
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# a Set and y contain's a non-set ("in" invokes only __eq__).
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# Subtle: it would be nicer if __eq__ and __ne__ could return
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# NotImplemented instead of True or False. Then the other comparand
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# would get a chance to determine the result, and if the other comparand
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# also returned NotImplemented then it would fall back to object address
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# comparison (which would always return False for __eq__ and always
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# True for __ne__). However, that doesn't work, because this type
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# *also* implements __cmp__: if, e.g., __eq__ returns NotImplemented,
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# Python tries __cmp__ next, and the __cmp__ here then raises TypeError.
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def __eq__(self, other):
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if isinstance(other, BaseSet):
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return self._data == other._data
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else:
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return False
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def __ne__(self, other):
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if isinstance(other, BaseSet):
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return self._data != other._data
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else:
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return True
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# Copying operations
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def copy(self):
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"""Return a shallow copy of a set."""
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result = self.__class__()
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result._data.update(self._data)
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return result
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__copy__ = copy # For the copy module
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def __deepcopy__(self, memo):
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"""Return a deep copy of a set; used by copy module."""
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# This pre-creates the result and inserts it in the memo
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# early, in case the deep copy recurses into another reference
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# to this same set. A set can't be an element of itself, but
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# it can certainly contain an object that has a reference to
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# itself.
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from copy import deepcopy
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result = self.__class__()
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memo[id(self)] = result
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data = result._data
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value = True
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for elt in self:
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data[deepcopy(elt, memo)] = value
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return result
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# Standard set operations: union, intersection, both differences.
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# Each has an operator version (e.g. __or__, invoked with |) and a
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# method version (e.g. union).
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# Subtle: Each pair requires distinct code so that the outcome is
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# correct when the type of other isn't suitable. For example, if
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# we did "union = __or__" instead, then Set().union(3) would return
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# NotImplemented instead of raising TypeError (albeit that *why* it
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# raises TypeError as-is is also a bit subtle).
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def __or__(self, other):
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"""Return the union of two sets as a new set.
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(I.e. all elements that are in either set.)
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"""
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if not isinstance(other, BaseSet):
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return NotImplemented
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return self.union(other)
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def union(self, other):
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"""Return the union of two sets as a new set.
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(I.e. all elements that are in either set.)
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"""
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result = self.__class__(self)
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result._update(other)
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return result
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def __and__(self, other):
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"""Return the intersection of two sets as a new set.
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(I.e. all elements that are in both sets.)
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"""
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if not isinstance(other, BaseSet):
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return NotImplemented
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return self.intersection(other)
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def intersection(self, other):
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"""Return the intersection of two sets as a new set.
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(I.e. all elements that are in both sets.)
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"""
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if not isinstance(other, BaseSet):
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other = Set(other)
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if len(self) <= len(other):
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little, big = self, other
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else:
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little, big = other, self
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common = iter(filter(big._data.has_key, little))
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return self.__class__(common)
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def __xor__(self, other):
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"""Return the symmetric difference of two sets as a new set.
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(I.e. all elements that are in exactly one of the sets.)
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"""
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if not isinstance(other, BaseSet):
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return NotImplemented
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return self.symmetric_difference(other)
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def symmetric_difference(self, other):
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"""Return the symmetric difference of two sets as a new set.
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(I.e. all elements that are in exactly one of the sets.)
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"""
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result = self.__class__()
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data = result._data
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value = True
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selfdata = self._data
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try:
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otherdata = other._data
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except AttributeError:
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otherdata = Set(other)._data
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for elt in filterfalse(otherdata.has_key, selfdata):
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data[elt] = value
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for elt in filterfalse(selfdata.has_key, otherdata):
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data[elt] = value
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return result
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def __sub__(self, other):
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"""Return the difference of two sets as a new Set.
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(I.e. all elements that are in this set and not in the other.)
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"""
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if not isinstance(other, BaseSet):
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return NotImplemented
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return self.difference(other)
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def difference(self, other):
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"""Return the difference of two sets as a new Set.
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(I.e. all elements that are in this set and not in the other.)
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"""
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result = self.__class__()
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data = result._data
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try:
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otherdata = other._data
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except AttributeError:
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otherdata = Set(other)._data
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value = True
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for elt in filterfalse(otherdata.has_key, self):
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data[elt] = value
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return result
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# Membership test
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def __contains__(self, element):
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"""Report whether an element is a member of a set.
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(Called in response to the expression `element in self'.)
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"""
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try:
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return element in self._data
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except TypeError:
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transform = getattr(element, "__as_temporarily_immutable__", None)
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if transform is None:
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raise # re-raise the TypeError exception we caught
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return transform() in self._data
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# Subset and superset test
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def issubset(self, other):
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"""Report whether another set contains this set."""
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self._binary_sanity_check(other)
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if len(self) > len(other): # Fast check for obvious cases
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return False
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for elt in filterfalse(other._data.has_key, self):
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return False
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return True
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def issuperset(self, other):
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"""Report whether this set contains another set."""
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self._binary_sanity_check(other)
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if len(self) < len(other): # Fast check for obvious cases
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return False
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for elt in filterfalse(self._data.has_key, other):
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return False
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return True
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# Inequality comparisons using the is-subset relation.
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__le__ = issubset
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__ge__ = issuperset
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def __lt__(self, other):
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self._binary_sanity_check(other)
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return len(self) < len(other) and self.issubset(other)
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def __gt__(self, other):
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self._binary_sanity_check(other)
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return len(self) > len(other) and self.issuperset(other)
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# Assorted helpers
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def _binary_sanity_check(self, other):
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# Check that the other argument to a binary operation is also
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# a set, raising a TypeError otherwise.
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if not isinstance(other, BaseSet):
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raise TypeError("Binary operation only permitted between sets")
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def _compute_hash(self):
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# Calculate hash code for a set by xor'ing the hash codes of
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# the elements. This ensures that the hash code does not depend
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# on the order in which elements are added to the set. This is
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# not called __hash__ because a BaseSet should not be hashable;
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# only an ImmutableSet is hashable.
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result = 0
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for elt in self:
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result ^= hash(elt)
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return result
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def _update(self, iterable):
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# The main loop for update() and the subclass __init__() methods.
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data = self._data
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# Use the fast update() method when a dictionary is available.
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if isinstance(iterable, BaseSet):
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data.update(iterable._data)
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return
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value = True
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if type(iterable) in (list, tuple, xrange):
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# Optimized: we know that __iter__() and next() can't
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# raise TypeError, so we can move 'try:' out of the loop.
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it = iter(iterable)
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while True:
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try:
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for element in it:
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data[element] = value
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return
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except TypeError:
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transform = getattr(element, "__as_immutable__", None)
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if transform is None:
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raise # re-raise the TypeError exception we caught
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data[transform()] = value
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else:
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# Safe: only catch TypeError where intended
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for element in iterable:
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try:
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data[element] = value
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except TypeError:
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transform = getattr(element, "__as_immutable__", None)
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if transform is None:
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raise # re-raise the TypeError exception we caught
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data[transform()] = value
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class ImmutableSet(BaseSet):
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"""Immutable set class."""
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__slots__ = ['_hashcode']
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# BaseSet + hashing
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def __init__(self, iterable=None):
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"""Construct an immutable set from an optional iterable."""
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self._hashcode = None
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self._data = {}
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if iterable is not None:
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self._update(iterable)
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def __hash__(self):
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if self._hashcode is None:
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self._hashcode = self._compute_hash()
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return self._hashcode
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def __getstate__(self):
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return self._data, self._hashcode
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def __setstate__(self, state):
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self._data, self._hashcode = state
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class Set(BaseSet):
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""" Mutable set class."""
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__slots__ = []
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# BaseSet + operations requiring mutability; no hashing
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def __init__(self, iterable=None):
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"""Construct a set from an optional iterable."""
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self._data = {}
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if iterable is not None:
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self._update(iterable)
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def __getstate__(self):
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# getstate's results are ignored if it is not
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return self._data,
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def __setstate__(self, data):
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self._data, = data
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def __hash__(self):
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"""A Set cannot be hashed."""
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# We inherit object.__hash__, so we must deny this explicitly
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raise TypeError("Can't hash a Set, only an ImmutableSet.")
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# In-place union, intersection, differences.
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# Subtle: The xyz_update() functions deliberately return None,
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# as do all mutating operations on built-in container types.
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# The __xyz__ spellings have to return self, though.
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def __ior__(self, other):
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"""Update a set with the union of itself and another."""
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self._binary_sanity_check(other)
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self._data.update(other._data)
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return self
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def union_update(self, other):
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"""Update a set with the union of itself and another."""
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self._update(other)
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def __iand__(self, other):
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"""Update a set with the intersection of itself and another."""
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self._binary_sanity_check(other)
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self._data = (self & other)._data
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return self
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def intersection_update(self, other):
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"""Update a set with the intersection of itself and another."""
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if isinstance(other, BaseSet):
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self &= other
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else:
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self._data = (self.intersection(other))._data
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def __ixor__(self, other):
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"""Update a set with the symmetric difference of itself and another."""
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self._binary_sanity_check(other)
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self.symmetric_difference_update(other)
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return self
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def symmetric_difference_update(self, other):
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"""Update a set with the symmetric difference of itself and another."""
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data = self._data
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value = True
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if not isinstance(other, BaseSet):
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other = Set(other)
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if self is other:
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self.clear()
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for elt in other:
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if elt in data:
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del data[elt]
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else:
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data[elt] = value
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def __isub__(self, other):
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"""Remove all elements of another set from this set."""
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self._binary_sanity_check(other)
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self.difference_update(other)
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return self
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def difference_update(self, other):
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"""Remove all elements of another set from this set."""
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data = self._data
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if not isinstance(other, BaseSet):
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other = Set(other)
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if self is other:
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self.clear()
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for elt in filter(data.has_key, other):
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del data[elt]
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# Python dict-like mass mutations: update, clear
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def update(self, iterable):
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"""Add all values from an iterable (such as a list or file)."""
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self._update(iterable)
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def clear(self):
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"""Remove all elements from this set."""
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self._data.clear()
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# Single-element mutations: add, remove, discard
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def add(self, element):
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"""Add an element to a set.
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This has no effect if the element is already present.
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"""
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try:
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self._data[element] = True
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except TypeError:
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transform = getattr(element, "__as_immutable__", None)
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if transform is None:
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raise # re-raise the TypeError exception we caught
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self._data[transform()] = True
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def remove(self, element):
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"""Remove an element from a set; it must be a member.
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If the element is not a member, raise a KeyError.
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"""
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try:
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del self._data[element]
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except TypeError:
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transform = getattr(element, "__as_temporarily_immutable__", None)
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if transform is None:
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raise # re-raise the TypeError exception we caught
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del self._data[transform()]
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def discard(self, element):
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"""Remove an element from a set if it is a member.
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If the element is not a member, do nothing.
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"""
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try:
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self.remove(element)
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except KeyError:
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pass
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def pop(self):
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"""Remove and return an arbitrary set element."""
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return self._data.popitem()[0]
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def __as_immutable__(self):
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# Return a copy of self as an immutable set
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return ImmutableSet(self)
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def __as_temporarily_immutable__(self):
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# Return self wrapped in a temporarily immutable set
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return _TemporarilyImmutableSet(self)
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class _TemporarilyImmutableSet(BaseSet):
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# Wrap a mutable set as if it was temporarily immutable.
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# This only supplies hashing and equality comparisons.
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def __init__(self, set):
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self._set = set
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self._data = set._data # Needed by ImmutableSet.__eq__()
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def __hash__(self):
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return self._set._compute_hash()
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# Local Variables:
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# tab-width:4
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# indent-tabs-mode:nil
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# End:
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# vim: set expandtab tabstop=4 shiftwidth=4:
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