"""Classes to represent arbitrary sets (including sets of sets). This module implements sets using dictionaries whose values areignored.  The usual operations (union, intersection, deletion, etc.)are provided as both methods and operators. Important: sets are not sequences!  While they support 'x in s','len(s)', and 'for x in s', none of those operations are unique forsequences; for example, mappings support all three as well.  Thecharacteristic operation for sequences is subscripting with smallintegers: s[i], for i in range(len(s)).  Sets don't supportsubscripting at all.  Also, sequences allow multiple occurrences andtheir elements have a definite order; sets on the other hand don'trecord multiple occurrences and don't remember the order of elementinsertion (which is why they don't support s[i]). The following classes are provided: BaseSet -- All the operations common to both mutable and immutable    sets. This is an abstract class, not meant to be directly    instantiated. Set -- Mutable sets, subclass of BaseSet; not hashable. ImmutableSet -- Immutable sets, subclass of BaseSet; hashable.    An iterable argument is mandatory to create an ImmutableSet. _TemporarilyImmutableSet -- A wrapper around a Set, hashable,    giving the same hash value as the immutable set equivalent    would have.  Do not use this class directly. Only hashable objects can be added to a Set. In particular, you cannotreally add a Set as an element to another Set; if you try, what isactually added is an ImmutableSet built from it (it compares equal tothe one you tried adding). When you ask if `x in y' where x is a Set and y is a Set orImmutableSet, x is wrapped into a _TemporarilyImmutableSet z, andwhat's tested is actually `z in y'. """ # Code history:## - Greg V. Wilson wrote the first version, using a different approach#   to the mutable/immutable problem, and inheriting from dict.## - Alex Martelli modified Greg's version to implement the current#   Set/ImmutableSet approach, and make the data an attribute.## - Guido van Rossum rewrote much of the code, made some API changes,#   and cleaned up the docstrings.## - Raymond Hettinger added a number of speedups and other#   improvements. from __future__ import generatorstry:    from itertools import ifilter, ifilterfalseexcept ImportError:    # Code to make the module run under Py2.2    def ifilter(predicate, iterable):        if predicate is None:            def predicate(x):                return x        for x in iterable:            if predicate(x):                yield x    def ifilterfalse(predicate, iterable):        if predicate is None:            def predicate(x):                return x        for x in iterable:            if not predicate(x):                yield x    try:        True, False    except NameError:        True, False = (0==0, 0!=0) __all__ = ['BaseSet', 'Set', 'ImmutableSet'] class BaseSet(object):    """Common base class for mutable and immutable sets."""     __slots__ = ['_data']     # Constructor     def __init__(self):        """This is an abstract class."""        # Don't call this from a concrete subclass!        if self.__class__ is BaseSet:            raise TypeError, ("BaseSet is an abstract class.  "                              "Use Set or ImmutableSet.")     # Standard protocols: __len__, __repr__, __str__, __iter__     def __len__(self):        """Return the number of elements of a set."""        return len(self._data)     def __repr__(self):        """Return string representation of a set.         This looks like 'Set([<list of elements>])'.        """        return self._repr()     # __str__ is the same as __repr__    __str__ = __repr__     def _repr(self, sorted=False):        elements = self._data.keys()        if sorted:            elements.sort()        return '%s(%r)' % (self.__class__.__name__, elements)     def __iter__(self):        """Return an iterator over the elements or a set.         This is the keys iterator for the underlying dict.        """        return self._data.iterkeys()     # Three-way comparison is not supported.  However, because __eq__ is    # tried before __cmp__, if Set x == Set y, x.__eq__(y) returns True and    # then cmp(x, y) returns 0 (Python doesn't actually call __cmp__ in this    # case).     def __cmp__(self, other):        raise TypeError, "can't compare sets using cmp()"     # Equality comparisons using the underlying dicts.  Mixed-type comparisons    # are allowed here, where Set == z for non-Set z always returns False,    # and Set != z always True.  This allows expressions like "x in y" to    # give the expected result when y is a sequence of mixed types, not    # raising a pointless TypeError just because y contains a Set, or x is    # a Set and y contain's a non-set ("in" invokes only __eq__).    # Subtle:  it would be nicer if __eq__ and __ne__ could return    # NotImplemented instead of True or False.  Then the other comparand    # would get a chance to determine the result, and if the other comparand    # also returned NotImplemented then it would fall back to object address    # comparison (which would always return False for __eq__ and always    # True for __ne__).  However, that doesn't work, because this type    # *also* implements __cmp__:  if, e.g., __eq__ returns NotImplemented,    # Python tries __cmp__ next, and the __cmp__ here then raises TypeError.     def __eq__(self, other):        if isinstance(other, BaseSet):            return self._data == other._data        else:            return False     def __ne__(self, other):        if isinstance(other, BaseSet):            return self._data != other._data        else:            return True     # Copying operations     def copy(self):        """Return a shallow copy of a set."""        result = self.__class__()        result._data.update(self._data)        return result     __copy__ = copy # For the copy module     def __deepcopy__(self, memo):        """Return a deep copy of a set; used by copy module."""        # This pre-creates the result and inserts it in the memo        # early, in case the deep copy recurses into another reference        # to this same set.  A set can't be an element of itself, but        # it can certainly contain an object that has a reference to        # itself.        from copy import deepcopy        result = self.__class__()        memo[id(self)] = result        data = result._data        value = True        for elt in self:            data[deepcopy(elt, memo)] = value        return result     # Standard set operations: union, intersection, both differences.    # Each has an operator version (e.g. __or__, invoked with |) and a    # method version (e.g. union).    # Subtle:  Each pair requires distinct code so that the outcome is    # correct when the type of other isn't suitable.  For example, if    # we did "union = __or__" instead, then Set().union(3) would return    # NotImplemented instead of raising TypeError (albeit that *why* it    # raises TypeError as-is is also a bit subtle).     def __or__(self, other):        """Return the union of two sets as a new set.         (I.e. all elements that are in either set.)        """        if not isinstance(other, BaseSet):            return NotImplemented        return self.union(other)     def union(self, other):        """Return the union of two sets as a new set.         (I.e. all elements that are in either set.)        """        result = self.__class__(self)        result._update(other)        return result     def __and__(self, other):        """Return the intersection of two sets as a new set.         (I.e. all elements that are in both sets.)        """        if not isinstance(other, BaseSet):            return NotImplemented        return self.intersection(other)     def intersection(self, other):        """Return the intersection of two sets as a new set.         (I.e. all elements that are in both sets.)        """        if not isinstance(other, BaseSet):            other = Set(other)        if len(self) <= len(other):            little, big = self, other        else:            little, big = other, self        common = ifilter(big._data.has_key, little)        return self.__class__(common)     def __xor__(self, other):        """Return the symmetric difference of two sets as a new set.         (I.e. all elements that are in exactly one of the sets.)        """        if not isinstance(other, BaseSet):            return NotImplemented        return self.symmetric_difference(other)     def symmetric_difference(self, other):        """Return the symmetric difference of two sets as a new set.         (I.e. all elements that are in exactly one of the sets.)        """        result = self.__class__()        data = result._data        value = True        selfdata = self._data        try:            otherdata = other._data        except AttributeError:            otherdata = Set(other)._data        for elt in ifilterfalse(otherdata.has_key, selfdata):            data[elt] = value        for elt in ifilterfalse(selfdata.has_key, otherdata):            data[elt] = value        return result     def  __sub__(self, other):        """Return the difference of two sets as a new Set.         (I.e. all elements that are in this set and not in the other.)        """        if not isinstance(other, BaseSet):            return NotImplemented        return self.difference(other)     def difference(self, other):        """Return the difference of two sets as a new Set.         (I.e. all elements that are in this set and not in the other.)        """        result = self.__class__()        data = result._data        try:            otherdata = other._data        except AttributeError:            otherdata = Set(other)._data        value = True        for elt in ifilterfalse(otherdata.has_key, self):            data[elt] = value        return result     # Membership test     def __contains__(self, element):        """Report whether an element is a member of a set.         (Called in response to the expression `element in self'.)        """        try:            return element in self._data        except TypeError:            transform = getattr(element, "__as_temporarily_immutable__", None)            if transform is None:                raise # re-raise the TypeError exception we caught            return transform() in self._data     # Subset and superset test     def issubset(self, other):        """Report whether another set contains this set."""        self._binary_sanity_check(other)        if len(self) > len(other):  # Fast check for obvious cases            return False        for elt in ifilterfalse(other._data.has_key, self):            return False        return True     def issuperset(self, other):        """Report whether this set contains another set."""        self._binary_sanity_check(other)        if len(self) < len(other):  # Fast check for obvious cases            return False        for elt in ifilterfalse(self._data.has_key, other):            return False        return True     # Inequality comparisons using the is-subset relation.    __le__ = issubset    __ge__ = issuperset     def __lt__(self, other):        self._binary_sanity_check(other)        return len(self) < len(other) and self.issubset(other)     def __gt__(self, other):        self._binary_sanity_check(other)        return len(self) > len(other) and self.issuperset(other)     # Assorted helpers     def _binary_sanity_check(self, other):        # Check that the other argument to a binary operation is also        # a set, raising a TypeError otherwise.        if not isinstance(other, BaseSet):            raise TypeError, "Binary operation only permitted between sets"     def _compute_hash(self):        # Calculate hash code for a set by xor'ing the hash codes of        # the elements.  This ensures that the hash code does not depend        # on the order in which elements are added to the set.  This is        # not called __hash__ because a BaseSet should not be hashable;        # only an ImmutableSet is hashable.        result = 0        for elt in self:            result ^= hash(elt)        return result     def _update(self, iterable):        # The main loop for update() and the subclass __init__() methods.        data = self._data         # Use the fast update() method when a dictionary is available.        if isinstance(iterable, BaseSet):            data.update(iterable._data)            return         value = True         if type(iterable) in (list, tuple, xrange):            # Optimized: we know that __iter__() and next() can't            # raise TypeError, so we can move 'try:' out of the loop.            it = iter(iterable)            while True:                try:                    for element in it:                        data[element] = value                    return                except TypeError:                    transform = getattr(element, "__as_immutable__", None)                    if transform is None:                        raise # re-raise the TypeError exception we caught                    data[transform()] = value        else:            # Safe: only catch TypeError where intended            for element in iterable:                try:                    data[element] = value                except TypeError:                    transform = getattr(element, "__as_immutable__", None)                    if transform is None:                        raise # re-raise the TypeError exception we caught                    data[transform()] = value  class ImmutableSet(BaseSet):    """Immutable set class."""     __slots__ = ['_hashcode']     # BaseSet + hashing     def __init__(self, iterable=None):        """Construct an immutable set from an optional iterable."""        self._hashcode = None        self._data = {}        if iterable is not None:            self._update(iterable)     def __hash__(self):        if self._hashcode is None:            self._hashcode = self._compute_hash()        return self._hashcode     def __getstate__(self):        return self._data, self._hashcode     def __setstate__(self, state):        self._data, self._hashcode = state class Set(BaseSet):    """ Mutable set class."""     __slots__ = []     # BaseSet + operations requiring mutability; no hashing     def __init__(self, iterable=None):        """Construct a set from an optional iterable."""        self._data = {}        if iterable is not None:            self._update(iterable)     def __getstate__(self):        # getstate's results are ignored if it is not        return self._data,     def __setstate__(self, data):        self._data, = data     def __hash__(self):        """A Set cannot be hashed."""        # We inherit object.__hash__, so we must deny this explicitly        raise TypeError, "Can't hash a Set, only an ImmutableSet."     # In-place union, intersection, differences.    # Subtle:  The xyz_update() functions deliberately return None,    # as do all mutating operations on built-in container types.    # The __xyz__ spellings have to return self, though.     def __ior__(self, other):        """Update a set with the union of itself and another."""        self._binary_sanity_check(other)        self._data.update(other._data)        return self     def union_update(self, other):        """Update a set with the union of itself and another."""        self._update(other)     def __iand__(self, other):        """Update a set with the intersection of itself and another."""        self._binary_sanity_check(other)        self._data = (self & other)._data        return self     def intersection_update(self, other):        """Update a set with the intersection of itself and another."""        if isinstance(other, BaseSet):            self &= other        else:            self._data = (self.intersection(other))._data     def __ixor__(self, other):        """Update a set with the symmetric difference of itself and another."""        self._binary_sanity_check(other)        self.symmetric_difference_update(other)        return self     def symmetric_difference_update(self, other):        """Update a set with the symmetric difference of itself and another."""        data = self._data        value = True        if not isinstance(other, BaseSet):            other = Set(other)        if self is other:            self.clear()        for elt in other:            if elt in data:                del data[elt]            else:                data[elt] = value     def __isub__(self, other):        """Remove all elements of another set from this set."""        self._binary_sanity_check(other)        self.difference_update(other)        return self     def difference_update(self, other):        """Remove all elements of another set from this set."""        data = self._data        if not isinstance(other, BaseSet):

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