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+
+:mod:`sets` --- Unordered collections of unique elements
+========================================================
+
+.. module:: sets
+ :synopsis: Implementation of sets of unique elements.
+.. moduleauthor:: Greg V. Wilson <gvwilson@nevex.com>
+.. moduleauthor:: Alex Martelli <aleax@aleax.it>
+.. moduleauthor:: Guido van Rossum <guido@python.org>
+.. sectionauthor:: Raymond D. Hettinger <python@rcn.com>
+
+
+.. versionadded:: 2.3
+
+.. deprecated:: 2.6
+ The built-in ``set``/``frozenset`` types replace this module.
+
+The :mod:`sets` module provides classes for constructing and manipulating
+unordered collections of unique elements. Common uses include membership
+testing, removing duplicates from a sequence, and computing standard math
+operations on sets such as intersection, union, difference, and symmetric
+difference.
+
+Like other collections, sets support ``x in set``, ``len(set)``, and ``for x in
+set``. Being an unordered collection, sets do not record element position or
+order of insertion. Accordingly, sets do not support indexing, slicing, or
+other sequence-like behavior.
+
+Most set applications use the :class:`Set` class which provides every set method
+except for :meth:`__hash__`. For advanced applications requiring a hash method,
+the :class:`ImmutableSet` class adds a :meth:`__hash__` method but omits methods
+which alter the contents of the set. Both :class:`Set` and :class:`ImmutableSet`
+derive from :class:`BaseSet`, an abstract class useful for determining whether
+something is a set: ``isinstance(obj, BaseSet)``.
+
+The set classes are implemented using dictionaries. Accordingly, the
+requirements for set elements are the same as those for dictionary keys; namely,
+that the element defines both :meth:`__eq__` and :meth:`__hash__`. As a result,
+sets cannot contain mutable elements such as lists or dictionaries. However,
+they can contain immutable collections such as tuples or instances of
+:class:`ImmutableSet`. For convenience in implementing sets of sets, inner sets
+are automatically converted to immutable form, for example,
+``Set([Set(['dog'])])`` is transformed to ``Set([ImmutableSet(['dog'])])``.
+
+
+.. class:: Set([iterable])
+
+ Constructs a new empty :class:`Set` object. If the optional *iterable*
+ parameter is supplied, updates the set with elements obtained from iteration.
+ All of the elements in *iterable* should be immutable or be transformable to an
+ immutable using the protocol described in section :ref:`immutable-transforms`.
+
+
+.. class:: ImmutableSet([iterable])
+
+ Constructs a new empty :class:`ImmutableSet` object. If the optional *iterable*
+ parameter is supplied, updates the set with elements obtained from iteration.
+ All of the elements in *iterable* should be immutable or be transformable to an
+ immutable using the protocol described in section :ref:`immutable-transforms`.
+
+ Because :class:`ImmutableSet` objects provide a :meth:`__hash__` method, they
+ can be used as set elements or as dictionary keys. :class:`ImmutableSet`
+ objects do not have methods for adding or removing elements, so all of the
+ elements must be known when the constructor is called.
+
+
+.. _set-objects:
+
+Set Objects
+-----------
+
+Instances of :class:`Set` and :class:`ImmutableSet` both provide the following
+operations:
+
++-------------------------------+------------+---------------------------------+
+| Operation | Equivalent | Result |
++===============================+============+=================================+
+| ``len(s)`` | | cardinality of set *s* |
++-------------------------------+------------+---------------------------------+
+| ``x in s`` | | test *x* for membership in *s* |
++-------------------------------+------------+---------------------------------+
+| ``x not in s`` | | test *x* for non-membership in |
+| | | *s* |
++-------------------------------+------------+---------------------------------+
+| ``s.issubset(t)`` | ``s <= t`` | test whether every element in |
+| | | *s* is in *t* |
++-------------------------------+------------+---------------------------------+
+| ``s.issuperset(t)`` | ``s >= t`` | test whether every element in |
+| | | *t* is in *s* |
++-------------------------------+------------+---------------------------------+
+| ``s.union(t)`` | ``s | t`` | new set with elements from both |
+| | | *s* and *t* |
++-------------------------------+------------+---------------------------------+
+| ``s.intersection(t)`` | ``s & t`` | new set with elements common to |
+| | | *s* and *t* |
++-------------------------------+------------+---------------------------------+
+| ``s.difference(t)`` | ``s - t`` | new set with elements in *s* |
+| | | but not in *t* |
++-------------------------------+------------+---------------------------------+
+| ``s.symmetric_difference(t)`` | ``s ^ t`` | new set with elements in either |
+| | | *s* or *t* but not both |
++-------------------------------+------------+---------------------------------+
+| ``s.copy()`` | | new set with a shallow copy of |
+| | | *s* |
++-------------------------------+------------+---------------------------------+
+
+Note, the non-operator versions of :meth:`union`, :meth:`intersection`,
+:meth:`difference`, and :meth:`symmetric_difference` will accept any iterable as
+an argument. In contrast, their operator based counterparts require their
+arguments to be sets. This precludes error-prone constructions like
+``Set('abc') & 'cbs'`` in favor of the more readable
+``Set('abc').intersection('cbs')``.
+
+.. versionchanged:: 2.3.1
+ Formerly all arguments were required to be sets.
+
+In addition, both :class:`Set` and :class:`ImmutableSet` support set to set
+comparisons. Two sets are equal if and only if every element of each set is
+contained in the other (each is a subset of the other). A set is less than
+another set if and only if the first set is a proper subset of the second set
+(is a subset, but is not equal). A set is greater than another set if and only
+if the first set is a proper superset of the second set (is a superset, but is
+not equal).
+
+The subset and equality comparisons do not generalize to a complete ordering
+function. For example, any two disjoint sets are not equal and are not subsets
+of each other, so *all* of the following return ``False``: ``a<b``, ``a==b``,
+or ``a>b``. Accordingly, sets do not implement the :meth:`__cmp__` method.
+
+Since sets only define partial ordering (subset relationships), the output of
+the :meth:`list.sort` method is undefined for lists of sets.
+
+The following table lists operations available in :class:`ImmutableSet` but not
+found in :class:`Set`:
+
++-------------+------------------------------+
+| Operation | Result |
++=============+==============================+
+| ``hash(s)`` | returns a hash value for *s* |
++-------------+------------------------------+
+
+The following table lists operations available in :class:`Set` but not found in
+:class:`ImmutableSet`:
+
++--------------------------------------+-------------+---------------------------------+
+| Operation | Equivalent | Result |
++======================================+=============+=================================+
+| ``s.update(t)`` | *s* \|= *t* | return set *s* with elements |
+| | | added from *t* |
++--------------------------------------+-------------+---------------------------------+
+| ``s.intersection_update(t)`` | *s* &= *t* | return set *s* keeping only |
+| | | elements also found in *t* |
++--------------------------------------+-------------+---------------------------------+
+| ``s.difference_update(t)`` | *s* -= *t* | return set *s* after removing |
+| | | elements found in *t* |
++--------------------------------------+-------------+---------------------------------+
+| ``s.symmetric_difference_update(t)`` | *s* ^= *t* | return set *s* with elements |
+| | | from *s* or *t* but not both |
++--------------------------------------+-------------+---------------------------------+
+| ``s.add(x)`` | | add element *x* to set *s* |
++--------------------------------------+-------------+---------------------------------+
+| ``s.remove(x)`` | | remove *x* from set *s*; raises |
+| | | :exc:`KeyError` if not present |
++--------------------------------------+-------------+---------------------------------+
+| ``s.discard(x)`` | | removes *x* from set *s* if |
+| | | present |
++--------------------------------------+-------------+---------------------------------+
+| ``s.pop()`` | | remove and return an arbitrary |
+| | | element from *s*; raises |
+| | | :exc:`KeyError` if empty |
++--------------------------------------+-------------+---------------------------------+
+| ``s.clear()`` | | remove all elements from set |
+| | | *s* |
++--------------------------------------+-------------+---------------------------------+
+
+Note, the non-operator versions of :meth:`update`, :meth:`intersection_update`,
+:meth:`difference_update`, and :meth:`symmetric_difference_update` will accept
+any iterable as an argument.
+
+.. versionchanged:: 2.3.1
+ Formerly all arguments were required to be sets.
+
+Also note, the module also includes a :meth:`union_update` method which is an
+alias for :meth:`update`. The method is included for backwards compatibility.
+Programmers should prefer the :meth:`update` method because it is supported by
+the builtin :class:`set()` and :class:`frozenset()` types.
+
+
+.. _set-example:
+
+Example
+-------
+
+::
+
+ >>> from sets import Set
+ >>> engineers = Set(['John', 'Jane', 'Jack', 'Janice'])
+ >>> programmers = Set(['Jack', 'Sam', 'Susan', 'Janice'])
+ >>> managers = Set(['Jane', 'Jack', 'Susan', 'Zack'])
+ >>> employees = engineers | programmers | managers # union
+ >>> engineering_management = engineers & managers # intersection
+ >>> fulltime_management = managers - engineers - programmers # difference
+ >>> engineers.add('Marvin') # add element
+ >>> print engineers
+ Set(['Jane', 'Marvin', 'Janice', 'John', 'Jack'])
+ >>> employees.issuperset(engineers) # superset test
+ False
+ >>> employees.update(engineers) # update from another set
+ >>> employees.issuperset(engineers)
+ True
+ >>> for group in [engineers, programmers, managers, employees]:
+ ... group.discard('Susan') # unconditionally remove element
+ ... print group
+ ...
+ Set(['Jane', 'Marvin', 'Janice', 'John', 'Jack'])
+ Set(['Janice', 'Jack', 'Sam'])
+ Set(['Jane', 'Zack', 'Jack'])
+ Set(['Jack', 'Sam', 'Jane', 'Marvin', 'Janice', 'John', 'Zack'])
+
+
+.. _immutable-transforms:
+
+Protocol for automatic conversion to immutable
+----------------------------------------------
+
+Sets can only contain immutable elements. For convenience, mutable :class:`Set`
+objects are automatically copied to an :class:`ImmutableSet` before being added
+as a set element.
+
+The mechanism is to always add a hashable element, or if it is not hashable, the
+element is checked to see if it has an :meth:`__as_immutable__` method which
+returns an immutable equivalent.
+
+Since :class:`Set` objects have a :meth:`__as_immutable__` method returning an
+instance of :class:`ImmutableSet`, it is possible to construct sets of sets.
+
+A similar mechanism is needed by the :meth:`__contains__` and :meth:`remove`
+methods which need to hash an element to check for membership in a set. Those
+methods check an element for hashability and, if not, check for a
+:meth:`__as_temporarily_immutable__` method which returns the element wrapped by
+a class that provides temporary methods for :meth:`__hash__`, :meth:`__eq__`,
+and :meth:`__ne__`.
+
+The alternate mechanism spares the need to build a separate copy of the original
+mutable object.
+
+:class:`Set` objects implement the :meth:`__as_temporarily_immutable__` method
+which returns the :class:`Set` object wrapped by a new class
+:class:`_TemporarilyImmutableSet`.
+
+The two mechanisms for adding hashability are normally invisible to the user;
+however, a conflict can arise in a multi-threaded environment where one thread
+is updating a set while another has temporarily wrapped it in
+:class:`_TemporarilyImmutableSet`. In other words, sets of mutable sets are not
+thread-safe.
+
+
+.. _comparison-to-builtin-set:
+
+Comparison to the built-in :class:`set` types
+---------------------------------------------
+
+The built-in :class:`set` and :class:`frozenset` types were designed based on
+lessons learned from the :mod:`sets` module. The key differences are:
+
+* :class:`Set` and :class:`ImmutableSet` were renamed to :class:`set` and
+ :class:`frozenset`.
+
+* There is no equivalent to :class:`BaseSet`. Instead, use ``isinstance(x,
+ (set, frozenset))``.
+
+* The hash algorithm for the built-ins performs significantly better (fewer
+ collisions) for most datasets.
+
+* The built-in versions have more space efficient pickles.
+
+* The built-in versions do not have a :meth:`union_update` method. Instead, use
+ the :meth:`update` method which is equivalent.
+
+* The built-in versions do not have a ``_repr(sorted=True)`` method.
+ Instead, use the built-in :func:`repr` and :func:`sorted` functions:
+ ``repr(sorted(s))``.
+
+* The built-in version does not have a protocol for automatic conversion to
+ immutable. Many found this feature to be confusing and no one in the community
+ reported having found real uses for it.
+