1 2:mod:`sets` --- Unordered collections of unique elements 3======================================================== 4 5.. module:: sets 6 :synopsis: Implementation of sets of unique elements. 7 :deprecated: 8.. moduleauthor:: Greg V. Wilson <gvwilson@nevex.com> 9.. moduleauthor:: Alex Martelli <aleax@aleax.it> 10.. moduleauthor:: Guido van Rossum <guido@python.org> 11.. sectionauthor:: Raymond D. Hettinger <python@rcn.com> 12 13 14.. versionadded:: 2.3 15 16.. deprecated:: 2.6 17 The built-in :class:`set`/:class:`frozenset` types replace this module. 18 19The :mod:`sets` module provides classes for constructing and manipulating 20unordered collections of unique elements. Common uses include membership 21testing, removing duplicates from a sequence, and computing standard math 22operations on sets such as intersection, union, difference, and symmetric 23difference. 24 25Like other collections, sets support ``x in set``, ``len(set)``, and ``for x in 26set``. Being an unordered collection, sets do not record element position or 27order of insertion. Accordingly, sets do not support indexing, slicing, or 28other sequence-like behavior. 29 30Most set applications use the :class:`Set` class which provides every set method 31except for :meth:`__hash__`. For advanced applications requiring a hash method, 32the :class:`ImmutableSet` class adds a :meth:`__hash__` method but omits methods 33which alter the contents of the set. Both :class:`Set` and :class:`ImmutableSet` 34derive from :class:`BaseSet`, an abstract class useful for determining whether 35something is a set: ``isinstance(obj, BaseSet)``. 36 37The set classes are implemented using dictionaries. Accordingly, the 38requirements for set elements are the same as those for dictionary keys; namely, 39that the element defines both :meth:`__eq__` and :meth:`__hash__`. As a result, 40sets cannot contain mutable elements such as lists or dictionaries. However, 41they can contain immutable collections such as tuples or instances of 42:class:`ImmutableSet`. For convenience in implementing sets of sets, inner sets 43are automatically converted to immutable form, for example, 44``Set([Set(['dog'])])`` is transformed to ``Set([ImmutableSet(['dog'])])``. 45 46 47.. class:: Set([iterable]) 48 49 Constructs a new empty :class:`Set` object. If the optional *iterable* 50 parameter is supplied, updates the set with elements obtained from iteration. 51 All of the elements in *iterable* should be immutable or be transformable to an 52 immutable using the protocol described in section :ref:`immutable-transforms`. 53 54 55.. class:: ImmutableSet([iterable]) 56 57 Constructs a new empty :class:`ImmutableSet` object. If the optional *iterable* 58 parameter is supplied, updates the set with elements obtained from iteration. 59 All of the elements in *iterable* should be immutable or be transformable to an 60 immutable using the protocol described in section :ref:`immutable-transforms`. 61 62 Because :class:`ImmutableSet` objects provide a :meth:`__hash__` method, they 63 can be used as set elements or as dictionary keys. :class:`ImmutableSet` 64 objects do not have methods for adding or removing elements, so all of the 65 elements must be known when the constructor is called. 66 67 68.. _set-objects: 69 70Set Objects 71----------- 72 73Instances of :class:`Set` and :class:`ImmutableSet` both provide the following 74operations: 75 76+-------------------------------+------------+---------------------------------+ 77| Operation | Equivalent | Result | 78+===============================+============+=================================+ 79| ``len(s)`` | | number of elements in set *s* | 80| | | (cardinality) | 81+-------------------------------+------------+---------------------------------+ 82| ``x in s`` | | test *x* for membership in *s* | 83+-------------------------------+------------+---------------------------------+ 84| ``x not in s`` | | test *x* for non-membership in | 85| | | *s* | 86+-------------------------------+------------+---------------------------------+ 87| ``s.issubset(t)`` | ``s <= t`` | test whether every element in | 88| | | *s* is in *t* | 89+-------------------------------+------------+---------------------------------+ 90| ``s.issuperset(t)`` | ``s >= t`` | test whether every element in | 91| | | *t* is in *s* | 92+-------------------------------+------------+---------------------------------+ 93| ``s.union(t)`` | ``s | t`` | new set with elements from both | 94| | | *s* and *t* | 95+-------------------------------+------------+---------------------------------+ 96| ``s.intersection(t)`` | ``s & t`` | new set with elements common to | 97| | | *s* and *t* | 98+-------------------------------+------------+---------------------------------+ 99| ``s.difference(t)`` | ``s - t`` | new set with elements in *s* | 100| | | but not in *t* | 101+-------------------------------+------------+---------------------------------+ 102| ``s.symmetric_difference(t)`` | ``s ^ t`` | new set with elements in either | 103| | | *s* or *t* but not both | 104+-------------------------------+------------+---------------------------------+ 105| ``s.copy()`` | | new set with a shallow copy of | 106| | | *s* | 107+-------------------------------+------------+---------------------------------+ 108 109Note, the non-operator versions of :meth:`union`, :meth:`intersection`, 110:meth:`difference`, and :meth:`symmetric_difference` will accept any iterable as 111an argument. In contrast, their operator based counterparts require their 112arguments to be sets. This precludes error-prone constructions like 113``Set('abc') & 'cbs'`` in favor of the more readable 114``Set('abc').intersection('cbs')``. 115 116.. versionchanged:: 2.3.1 117 Formerly all arguments were required to be sets. 118 119In addition, both :class:`Set` and :class:`ImmutableSet` support set to set 120comparisons. Two sets are equal if and only if every element of each set is 121contained in the other (each is a subset of the other). A set is less than 122another set if and only if the first set is a proper subset of the second set 123(is a subset, but is not equal). A set is greater than another set if and only 124if the first set is a proper superset of the second set (is a superset, but is 125not equal). 126 127The subset and equality comparisons do not generalize to a complete ordering 128function. For example, any two disjoint sets are not equal and are not subsets 129of each other, so *all* of the following return ``False``: ``a<b``, ``a==b``, 130or ``a>b``. Accordingly, sets do not implement the :meth:`__cmp__` method. 131 132Since sets only define partial ordering (subset relationships), the output of 133the :meth:`list.sort` method is undefined for lists of sets. 134 135The following table lists operations available in :class:`ImmutableSet` but not 136found in :class:`Set`: 137 138+-------------+------------------------------+ 139| Operation | Result | 140+=============+==============================+ 141| ``hash(s)`` | returns a hash value for *s* | 142+-------------+------------------------------+ 143 144The following table lists operations available in :class:`Set` but not found in 145:class:`ImmutableSet`: 146 147+--------------------------------------+-------------+---------------------------------+ 148| Operation | Equivalent | Result | 149+======================================+=============+=================================+ 150| ``s.update(t)`` | *s* \|= *t* | return set *s* with elements | 151| | | added from *t* | 152+--------------------------------------+-------------+---------------------------------+ 153| ``s.intersection_update(t)`` | *s* &= *t* | return set *s* keeping only | 154| | | elements also found in *t* | 155+--------------------------------------+-------------+---------------------------------+ 156| ``s.difference_update(t)`` | *s* -= *t* | return set *s* after removing | 157| | | elements found in *t* | 158+--------------------------------------+-------------+---------------------------------+ 159| ``s.symmetric_difference_update(t)`` | *s* ^= *t* | return set *s* with elements | 160| | | from *s* or *t* but not both | 161+--------------------------------------+-------------+---------------------------------+ 162| ``s.add(x)`` | | add element *x* to set *s* | 163+--------------------------------------+-------------+---------------------------------+ 164| ``s.remove(x)`` | | remove *x* from set *s*; raises | 165| | | :exc:`KeyError` if not present | 166+--------------------------------------+-------------+---------------------------------+ 167| ``s.discard(x)`` | | removes *x* from set *s* if | 168| | | present | 169+--------------------------------------+-------------+---------------------------------+ 170| ``s.pop()`` | | remove and return an arbitrary | 171| | | element from *s*; raises | 172| | | :exc:`KeyError` if empty | 173+--------------------------------------+-------------+---------------------------------+ 174| ``s.clear()`` | | remove all elements from set | 175| | | *s* | 176+--------------------------------------+-------------+---------------------------------+ 177 178Note, the non-operator versions of :meth:`update`, :meth:`intersection_update`, 179:meth:`difference_update`, and :meth:`symmetric_difference_update` will accept 180any iterable as an argument. 181 182.. versionchanged:: 2.3.1 183 Formerly all arguments were required to be sets. 184 185Also note, the module also includes a :meth:`union_update` method which is an 186alias for :meth:`update`. The method is included for backwards compatibility. 187Programmers should prefer the :meth:`update` method because it is supported by 188the built-in :class:`set()` and :class:`frozenset()` types. 189 190 191.. _set-example: 192 193Example 194------- 195 196 >>> from sets import Set 197 >>> engineers = Set(['John', 'Jane', 'Jack', 'Janice']) 198 >>> programmers = Set(['Jack', 'Sam', 'Susan', 'Janice']) 199 >>> managers = Set(['Jane', 'Jack', 'Susan', 'Zack']) 200 >>> employees = engineers | programmers | managers # union 201 >>> engineering_management = engineers & managers # intersection 202 >>> fulltime_management = managers - engineers - programmers # difference 203 >>> engineers.add('Marvin') # add element 204 >>> print engineers # doctest: +SKIP 205 Set(['Jane', 'Marvin', 'Janice', 'John', 'Jack']) 206 >>> employees.issuperset(engineers) # superset test 207 False 208 >>> employees.update(engineers) # update from another set 209 >>> employees.issuperset(engineers) 210 True 211 >>> for group in [engineers, programmers, managers, employees]: # doctest: +SKIP 212 ... group.discard('Susan') # unconditionally remove element 213 ... print group 214 ... 215 Set(['Jane', 'Marvin', 'Janice', 'John', 'Jack']) 216 Set(['Janice', 'Jack', 'Sam']) 217 Set(['Jane', 'Zack', 'Jack']) 218 Set(['Jack', 'Sam', 'Jane', 'Marvin', 'Janice', 'John', 'Zack']) 219 220 221.. _immutable-transforms: 222 223Protocol for automatic conversion to immutable 224---------------------------------------------- 225 226Sets can only contain immutable elements. For convenience, mutable :class:`Set` 227objects are automatically copied to an :class:`ImmutableSet` before being added 228as a set element. 229 230The mechanism is to always add a :term:`hashable` element, or if it is not 231hashable, the element is checked to see if it has an :meth:`__as_immutable__` 232method which returns an immutable equivalent. 233 234Since :class:`Set` objects have a :meth:`__as_immutable__` method returning an 235instance of :class:`ImmutableSet`, it is possible to construct sets of sets. 236 237A similar mechanism is needed by the :meth:`__contains__` and :meth:`remove` 238methods which need to hash an element to check for membership in a set. Those 239methods check an element for hashability and, if not, check for a 240:meth:`__as_temporarily_immutable__` method which returns the element wrapped by 241a class that provides temporary methods for :meth:`__hash__`, :meth:`__eq__`, 242and :meth:`__ne__`. 243 244The alternate mechanism spares the need to build a separate copy of the original 245mutable object. 246 247:class:`Set` objects implement the :meth:`__as_temporarily_immutable__` method 248which returns the :class:`Set` object wrapped by a new class 249:class:`_TemporarilyImmutableSet`. 250 251The two mechanisms for adding hashability are normally invisible to the user; 252however, a conflict can arise in a multi-threaded environment where one thread 253is updating a set while another has temporarily wrapped it in 254:class:`_TemporarilyImmutableSet`. In other words, sets of mutable sets are not 255thread-safe. 256 257 258.. _comparison-to-builtin-set: 259 260Comparison to the built-in :class:`set` types 261--------------------------------------------- 262 263The built-in :class:`set` and :class:`frozenset` types were designed based on 264lessons learned from the :mod:`sets` module. The key differences are: 265 266* :class:`Set` and :class:`ImmutableSet` were renamed to :class:`set` and 267 :class:`frozenset`. 268 269* There is no equivalent to :class:`BaseSet`. Instead, use ``isinstance(x, 270 (set, frozenset))``. 271 272* The hash algorithm for the built-ins performs significantly better (fewer 273 collisions) for most datasets. 274 275* The built-in versions have more space efficient pickles. 276 277* The built-in versions do not have a :meth:`union_update` method. Instead, use 278 the :meth:`update` method which is equivalent. 279 280* The built-in versions do not have a ``_repr(sorted=True)`` method. 281 Instead, use the built-in :func:`repr` and :func:`sorted` functions: 282 ``repr(sorted(s))``. 283 284* The built-in version does not have a protocol for automatic conversion to 285 immutable. Many found this feature to be confusing and no one in the community 286 reported having found real uses for it. 287 288