/Doc/library/sets.rst
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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 ``set``/``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)`` | | cardinality of set *s* | 80+-------------------------------+------------+---------------------------------+ 81| ``x in s`` | | test *x* for membership in *s* | 82+-------------------------------+------------+---------------------------------+ 83| ``x not in s`` | | test *x* for non-membership in | 84| | | *s* | 85+-------------------------------+------------+---------------------------------+ 86| ``s.issubset(t)`` | ``s <= t`` | test whether every element in | 87| | | *s* is in *t* | 88+-------------------------------+------------+---------------------------------+ 89| ``s.issuperset(t)`` | ``s >= t`` | test whether every element in | 90| | | *t* is in *s* | 91+-------------------------------+------------+---------------------------------+ 92| ``s.union(t)`` | ``s | t`` | new set with elements from both | 93| | | *s* and *t* | 94+-------------------------------+------------+---------------------------------+ 95| ``s.intersection(t)`` | ``s & t`` | new set with elements common to | 96| | | *s* and *t* | 97+-------------------------------+------------+---------------------------------+ 98| ``s.difference(t)`` | ``s - t`` | new set with elements in *s* | 99| | | but not in *t* | 100+-------------------------------+------------+---------------------------------+ 101| ``s.symmetric_difference(t)`` | ``s ^ t`` | new set with elements in either | 102| | | *s* or *t* but not both | 103+-------------------------------+------------+---------------------------------+ 104| ``s.copy()`` | | new set with a shallow copy of | 105| | | *s* | 106+-------------------------------+------------+---------------------------------+ 107 108Note, the non-operator versions of :meth:`union`, :meth:`intersection`, 109:meth:`difference`, and :meth:`symmetric_difference` will accept any iterable as 110an argument. In contrast, their operator based counterparts require their 111arguments to be sets. This precludes error-prone constructions like 112``Set('abc') & 'cbs'`` in favor of the more readable 113``Set('abc').intersection('cbs')``. 114 115.. versionchanged:: 2.3.1 116 Formerly all arguments were required to be sets. 117 118In addition, both :class:`Set` and :class:`ImmutableSet` support set to set 119comparisons. Two sets are equal if and only if every element of each set is 120contained in the other (each is a subset of the other). A set is less than 121another set if and only if the first set is a proper subset of the second set 122(is a subset, but is not equal). A set is greater than another set if and only 123if the first set is a proper superset of the second set (is a superset, but is 124not equal). 125 126The subset and equality comparisons do not generalize to a complete ordering 127function. For example, any two disjoint sets are not equal and are not subsets 128of each other, so *all* of the following return ``False``: ``a<b``, ``a==b``, 129or ``a>b``. Accordingly, sets do not implement the :meth:`__cmp__` method. 130 131Since sets only define partial ordering (subset relationships), the output of 132the :meth:`list.sort` method is undefined for lists of sets. 133 134The following table lists operations available in :class:`ImmutableSet` but not 135found in :class:`Set`: 136 137+-------------+------------------------------+ 138| Operation | Result | 139+=============+==============================+ 140| ``hash(s)`` | returns a hash value for *s* | 141+-------------+------------------------------+ 142 143The following table lists operations available in :class:`Set` but not found in 144:class:`ImmutableSet`: 145 146+--------------------------------------+-------------+---------------------------------+ 147| Operation | Equivalent | Result | 148+======================================+=============+=================================+ 149| ``s.update(t)`` | *s* \|= *t* | return set *s* with elements | 150| | | added from *t* | 151+--------------------------------------+-------------+---------------------------------+ 152| ``s.intersection_update(t)`` | *s* &= *t* | return set *s* keeping only | 153| | | elements also found in *t* | 154+--------------------------------------+-------------+---------------------------------+ 155| ``s.difference_update(t)`` | *s* -= *t* | return set *s* after removing | 156| | | elements found in *t* | 157+--------------------------------------+-------------+---------------------------------+ 158| ``s.symmetric_difference_update(t)`` | *s* ^= *t* | return set *s* with elements | 159| | | from *s* or *t* but not both | 160+--------------------------------------+-------------+---------------------------------+ 161| ``s.add(x)`` | | add element *x* to set *s* | 162+--------------------------------------+-------------+---------------------------------+ 163| ``s.remove(x)`` | | remove *x* from set *s*; raises | 164| | | :exc:`KeyError` if not present | 165+--------------------------------------+-------------+---------------------------------+ 166| ``s.discard(x)`` | | removes *x* from set *s* if | 167| | | present | 168+--------------------------------------+-------------+---------------------------------+ 169| ``s.pop()`` | | remove and return an arbitrary | 170| | | element from *s*; raises | 171| | | :exc:`KeyError` if empty | 172+--------------------------------------+-------------+---------------------------------+ 173| ``s.clear()`` | | remove all elements from set | 174| | | *s* | 175+--------------------------------------+-------------+---------------------------------+ 176 177Note, the non-operator versions of :meth:`update`, :meth:`intersection_update`, 178:meth:`difference_update`, and :meth:`symmetric_difference_update` will accept 179any iterable as an argument. 180 181.. versionchanged:: 2.3.1 182 Formerly all arguments were required to be sets. 183 184Also note, the module also includes a :meth:`union_update` method which is an 185alias for :meth:`update`. The method is included for backwards compatibility. 186Programmers should prefer the :meth:`update` method because it is supported by 187the builtin :class:`set()` and :class:`frozenset()` types. 188 189 190.. _set-example: 191 192Example 193------- 194 195 >>> from sets import Set 196 >>> engineers = Set(['John', 'Jane', 'Jack', 'Janice']) 197 >>> programmers = Set(['Jack', 'Sam', 'Susan', 'Janice']) 198 >>> managers = Set(['Jane', 'Jack', 'Susan', 'Zack']) 199 >>> employees = engineers | programmers | managers # union 200 >>> engineering_management = engineers & managers # intersection 201 >>> fulltime_management = managers - engineers - programmers # difference 202 >>> engineers.add('Marvin') # add element 203 >>> print engineers # doctest: +SKIP 204 Set(['Jane', 'Marvin', 'Janice', 'John', 'Jack']) 205 >>> employees.issuperset(engineers) # superset test 206 False 207 >>> employees.update(engineers) # update from another set 208 >>> employees.issuperset(engineers) 209 True 210 >>> for group in [engineers, programmers, managers, employees]: # doctest: +SKIP 211 ... group.discard('Susan') # unconditionally remove element 212 ... print group 213 ... 214 Set(['Jane', 'Marvin', 'Janice', 'John', 'Jack']) 215 Set(['Janice', 'Jack', 'Sam']) 216 Set(['Jane', 'Zack', 'Jack']) 217 Set(['Jack', 'Sam', 'Jane', 'Marvin', 'Janice', 'John', 'Zack']) 218 219 220.. _immutable-transforms: 221 222Protocol for automatic conversion to immutable 223---------------------------------------------- 224 225Sets can only contain immutable elements. For convenience, mutable :class:`Set` 226objects are automatically copied to an :class:`ImmutableSet` before being added 227as a set element. 228 229The mechanism is to always add a :term:`hashable` element, or if it is not 230hashable, the element is checked to see if it has an :meth:`__as_immutable__` 231method which returns an immutable equivalent. 232 233Since :class:`Set` objects have a :meth:`__as_immutable__` method returning an 234instance of :class:`ImmutableSet`, it is possible to construct sets of sets. 235 236A similar mechanism is needed by the :meth:`__contains__` and :meth:`remove` 237methods which need to hash an element to check for membership in a set. Those 238methods check an element for hashability and, if not, check for a 239:meth:`__as_temporarily_immutable__` method which returns the element wrapped by 240a class that provides temporary methods for :meth:`__hash__`, :meth:`__eq__`, 241and :meth:`__ne__`. 242 243The alternate mechanism spares the need to build a separate copy of the original 244mutable object. 245 246:class:`Set` objects implement the :meth:`__as_temporarily_immutable__` method 247which returns the :class:`Set` object wrapped by a new class 248:class:`_TemporarilyImmutableSet`. 249 250The two mechanisms for adding hashability are normally invisible to the user; 251however, a conflict can arise in a multi-threaded environment where one thread 252is updating a set while another has temporarily wrapped it in 253:class:`_TemporarilyImmutableSet`. In other words, sets of mutable sets are not 254thread-safe. 255 256 257.. _comparison-to-builtin-set: 258 259Comparison to the built-in :class:`set` types 260--------------------------------------------- 261 262The built-in :class:`set` and :class:`frozenset` types were designed based on 263lessons learned from the :mod:`sets` module. The key differences are: 264 265* :class:`Set` and :class:`ImmutableSet` were renamed to :class:`set` and 266 :class:`frozenset`. 267 268* There is no equivalent to :class:`BaseSet`. Instead, use ``isinstance(x, 269 (set, frozenset))``. 270 271* The hash algorithm for the built-ins performs significantly better (fewer 272 collisions) for most datasets. 273 274* The built-in versions have more space efficient pickles. 275 276* The built-in versions do not have a :meth:`union_update` method. Instead, use 277 the :meth:`update` method which is equivalent. 278 279* The built-in versions do not have a ``_repr(sorted=True)`` method. 280 Instead, use the built-in :func:`repr` and :func:`sorted` functions: 281 ``repr(sorted(s))``. 282 283* The built-in version does not have a protocol for automatic conversion to 284 immutable. Many found this feature to be confusing and no one in the community 285 reported having found real uses for it. 286