/Doc/library/sets.rst
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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 ``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 # 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.