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230 lines
10 KiB
TeX
230 lines
10 KiB
TeX
\section{\module{sets} ---
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Unordered collections of unique elements}
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\declaremodule{standard}{sets}
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\modulesynopsis{Implementation of sets of unique elements.}
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\moduleauthor{Greg V. Wilson}{gvwilson@nevex.com}
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\moduleauthor{Alex Martelli}{aleax@aleax.it}
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\moduleauthor{Guido van Rossum}{guido@python.org}
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\sectionauthor{Raymond D. Hettinger}{python@rcn.com}
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\versionadded{2.3}
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The \module{sets} module provides classes for constructing and manipulating
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unordered collections of unique elements. Common uses include membership
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testing, removing duplicates from a sequence, and computing standard math
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operations on sets such as intersection, union, difference, and symmetric
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difference.
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Like other collections, sets support \code{\var{x} in \var{set}},
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\code{len(\var{set})}, and \code{for \var{x} in \var{set}}. Being an
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unordered collection, sets do not record element position or order of
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insertion. Accordingly, sets do not support indexing, slicing, or
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other sequence-like behavior.
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Most set applications use the \class{Set} class which provides every set
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method except for \method{__hash__()}. For advanced applications requiring
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a hash method, the \class{ImmutableSet} class adds a \method{__hash__()}
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method but omits methods which alter the contents of the set. Both
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\class{Set} and \class{ImmutableSet} derive from \class{BaseSet}, an
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abstract class useful for determining whether something is a set:
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\code{isinstance(\var{obj}, BaseSet)}.
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The set classes are implemented using dictionaries. As a result, sets
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cannot contain mutable elements such as lists or dictionaries.
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However, they can contain immutable collections such as tuples or
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instances of \class{ImmutableSet}. For convenience in implementing
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sets of sets, inner sets are automatically converted to immutable
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form, for example, \code{Set([Set(['dog'])])} is transformed to
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\code{Set([ImmutableSet(['dog'])])}.
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\begin{classdesc}{Set}{\optional{iterable}}
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Constructs a new empty \class{Set} object. If the optional \var{iterable}
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parameter is supplied, updates the set with elements obtained from iteration.
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All of the elements in \var{iterable} should be immutable or be transformable
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to an immutable using the protocol described in
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section~\ref{immutable-transforms}.
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\end{classdesc}
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\begin{classdesc}{ImmutableSet}{\optional{iterable}}
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Constructs a new empty \class{ImmutableSet} object. If the optional
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\var{iterable} parameter is supplied, updates the set with elements obtained
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from iteration. All of the elements in \var{iterable} should be immutable or
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be transformable to an immutable using the protocol described in
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section~\ref{immutable-transforms}.
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Because \class{ImmutableSet} objects provide a \method{__hash__()} method,
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they can be used as set elements or as dictionary keys. \class{ImmutableSet}
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objects do not have methods for adding or removing elements, so all of the
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elements must be known when the constructor is called.
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\end{classdesc}
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\subsection{Set Objects \label{set-objects}}
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Instances of \class{Set} and \class{ImmutableSet} both provide
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the following operations:
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\begin{tableiii}{c|c|l}{code}{Operation}{Equivalent}{Result}
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\lineiii{len(\var{s})}{}{cardinality of set \var{s}}
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\hline
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\lineiii{\var{x} in \var{s}}{}
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{test \var{x} for membership in \var{s}}
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\lineiii{\var{x} not in \var{s}}{}
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{test \var{x} for non-membership in \var{s}}
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\lineiii{\var{s}.issubset(\var{t})}{\code{\var{s} <= \var{t}}}
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{test whether every element in \var{s} is in \var{t}}
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\lineiii{\var{s}.issuperset(\var{t})}{\code{\var{s} >= \var{t}}}
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{test whether every element in \var{t} is in \var{s}}
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\hline
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\lineiii{\var{s}.union(\var{t})}{\var{s} | \var{t}}
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{new set with elements from both \var{s} and \var{t}}
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\lineiii{\var{s}.intersection(\var{t})}{\var{s} \&\ \var{t}}
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{new set with elements common to \var{s} and \var{t}}
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\lineiii{\var{s}.difference(\var{t})}{\var{s} - \var{t}}
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{new set with elements in \var{s} but not in \var{t}}
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\lineiii{\var{s}.symmetric_difference(\var{t})}{\var{s} \^\ \var{t}}
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{new set with elements in either \var{s} or \var{t} but not both}
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\lineiii{\var{s}.copy()}{}
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{new set with a shallow copy of \var{s}}
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\end{tableiii}
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Note, the non-operator versions of \method{union()},
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\method{intersection()}, \method{difference()}, and
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\method{symmetric_difference()} will accept any iterable as an argument.
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In contrast, their operator based counterparts require their arguments to
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be sets. This precludes error-prone constructions like
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\code{Set('abc') \&\ 'cbs'} in favor of the more readable
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\code{Set('abc').intersection('cbs')}.
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\versionchanged[Formerly all arguments were required to be sets]{2.3.1}
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In addition, both \class{Set} and \class{ImmutableSet}
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support set to set comparisons. Two sets are equal if and only if
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every element of each set is contained in the other (each is a subset
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of the other).
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A set is less than another set if and only if the first set is a proper
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subset of the second set (is a subset, but is not equal).
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A set is greater than another set if and only if the first set is a proper
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superset of the second set (is a superset, but is not equal).
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The subset and equality comparisons do not generalize to a complete
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ordering function. For example, any two disjoint sets are not equal and
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are not subsets of each other, so \emph{all} of the following return
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\code{False}: \code{\var{a}<\var{b}}, \code{\var{a}==\var{b}}, or
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\code{\var{a}>\var{b}}.
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Accordingly, sets do not implement the \method{__cmp__} method.
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Since sets only define partial ordering (subset relationships), the output
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of the \method{list.sort()} method is undefined for lists of sets.
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The following table lists operations available in \class{ImmutableSet}
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but not found in \class{Set}:
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\begin{tableii}{c|l}{code}{Operation}{Result}
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\lineii{hash(\var{s})}{returns a hash value for \var{s}}
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\end{tableii}
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The following table lists operations available in \class{Set}
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but not found in \class{ImmutableSet}:
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\begin{tableiii}{c|c|l}{code}{Operation}{Equivalent}{Result}
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\lineiii{\var{s}.union_update(\var{t})}
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{\var{s} |= \var{t}}
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{return set \var{s} with elements added from \var{t}}
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\lineiii{\var{s}.intersection_update(\var{t})}
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{\var{s} \&= \var{t}}
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{return set \var{s} keeping only elements also found in \var{t}}
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\lineiii{\var{s}.difference_update(\var{t})}
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{\var{s} -= \var{t}}
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{return set \var{s} after removing elements found in \var{t}}
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\lineiii{\var{s}.symmetric_difference_update(\var{t})}
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{\var{s} \textasciicircum= \var{t}}
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{return set \var{s} with elements from \var{s} or \var{t}
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but not both}
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\hline
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\lineiii{\var{s}.add(\var{x})}{}
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{add element \var{x} to set \var{s}}
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\lineiii{\var{s}.remove(\var{x})}{}
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{remove \var{x} from set \var{s}; raises KeyError if not present}
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\lineiii{\var{s}.discard(\var{x})}{}
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{removes \var{x} from set \var{s} if present}
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\lineiii{\var{s}.pop()}{}
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{remove and return an arbitrary element from \var{s}; raises
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KeyError if empty}
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\lineiii{\var{s}.clear()}{}
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{remove all elements from set \var{s}}
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\end{tableiii}
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Note, the non-operator versions of \method{union_update()},
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\method{intersection_update()}, \method{difference_update()}, and
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\method{symmetric_difference_update()} will accept any iterable as
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an argument.
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\versionchanged[Formerly all arguments were required to be sets]{2.3.1}
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\subsection{Example \label{set-example}}
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\begin{verbatim}
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>>> from sets import Set
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>>> engineers = Set(['John', 'Jane', 'Jack', 'Janice'])
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>>> programmers = Set(['Jack', 'Sam', 'Susan', 'Janice'])
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>>> managers = Set(['Jane', 'Jack', 'Susan', 'Zack'])
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>>> employees = engineers | programmers | managers # union
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>>> engineering_management = engineers & managers # intersection
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>>> fulltime_management = managers - engineers - programmers # difference
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>>> engineers.add('Marvin') # add element
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>>> print engineers
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Set(['Jane', 'Marvin', 'Janice', 'John', 'Jack'])
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>>> employees.issuperset(engineers) # superset test
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False
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>>> employees.union_update(engineers) # update from another set
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>>> employees.issuperset(engineers)
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True
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>>> for group in [engineers, programmers, managers, employees]:
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... group.discard('Susan') # unconditionally remove element
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... print group
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...
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Set(['Jane', 'Marvin', 'Janice', 'John', 'Jack'])
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Set(['Janice', 'Jack', 'Sam'])
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Set(['Jane', 'Zack', 'Jack'])
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Set(['Jack', 'Sam', 'Jane', 'Marvin', 'Janice', 'John', 'Zack'])
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\end{verbatim}
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\subsection{Protocol for automatic conversion to immutable
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\label{immutable-transforms}}
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Sets can only contain immutable elements. For convenience, mutable
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\class{Set} objects are automatically copied to an \class{ImmutableSet}
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before being added as a set element.
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The mechanism is to always add a hashable element, or if it is not
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hashable, the element is checked to see if it has an
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\method{__as_immutable__()} method which returns an immutable equivalent.
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Since \class{Set} objects have a \method{__as_immutable__()} method
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returning an instance of \class{ImmutableSet}, it is possible to
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construct sets of sets.
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A similar mechanism is needed by the \method{__contains__()} and
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\method{remove()} methods which need to hash an element to check
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for membership in a set. Those methods check an element for hashability
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and, if not, check for a \method{__as_temporarily_immutable__()} method
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which returns the element wrapped by a class that provides temporary
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methods for \method{__hash__()}, \method{__eq__()}, and \method{__ne__()}.
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The alternate mechanism spares the need to build a separate copy of
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the original mutable object.
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\class{Set} objects implement the \method{__as_temporarily_immutable__()}
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method which returns the \class{Set} object wrapped by a new class
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\class{_TemporarilyImmutableSet}.
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The two mechanisms for adding hashability are normally invisible to the
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user; however, a conflict can arise in a multi-threaded environment
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where one thread is updating a set while another has temporarily wrapped it
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in \class{_TemporarilyImmutableSet}. In other words, sets of mutable sets
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are not thread-safe.
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