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:mod:`sets` --- Unordered collections of unique elements ======================================================== .. module:: sets :synopsis: Implementation of sets of unique elements. :deprecated: .. 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 :class:`set`/:class:`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)`` | | number of elements in set *s* | | | | (cardinality) | +-------------------------------+------------+---------------------------------+ | ``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 built-in :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 # doctest: +SKIP 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]: # doctest: +SKIP ... 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 :term:`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.