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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 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.
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