# -*- coding: utf-8 -*-
"""\
The :class:`set` type brings the practical expressiveness of
set theory to Python. It has a very rich API overall, but lacks a
couple of fundamental features. For one, sets are not ordered. On top
of this, sets are not indexable, i.e, ``my_set[8]`` will raise an
:exc:`TypeError`. The :class:`IndexedSet` type remedies both of these
issues without compromising on the excellent complexity
characteristics of Python's built-in set implementation.
"""
from __future__ import print_function
from bisect import bisect_left
from itertools import chain, islice
import operator
try:
from collections.abc import MutableSet
except ImportError:
from collections import MutableSet
try:
from typeutils import make_sentinel
_MISSING = make_sentinel(var_name='_MISSING')
except ImportError:
_MISSING = object()
__all__ = ['complement']
_COMPACTION_FACTOR = 8
# TODO: inherit from set()
# TODO: .discard_many(), .remove_many()
# TODO: raise exception on non-set params?
# TODO: technically reverse operators should probably reverse the
# order of the 'other' inputs and put self last (to try and maintain
# insertion order)
def complement(wrapped):
"""Given a :class:`set`, convert it to a **complement set**.
Whereas a :class:`set` keeps track of what it contains, a
`complement set
<https://en.wikipedia.org/wiki/Complement_(set_theory)>`_ keeps
track of what it does *not* contain. For example, look what
happens when we intersect a normal set with a complement set::
>>> list(set(range(5)) & complement(set([2, 3])))
[0, 1, 4]
We get the everything in the left that wasn't in the right,
because intersecting with a complement is the same as subtracting
a normal set.
Args:
wrapped (set): A set or any other iterable which should be
turned into a complement set.
All set methods and operators are supported by complement sets,
between other :func:`complement`-wrapped sets and/or regular
:class:`set` objects.
Because a complement set only tracks what elements are *not* in
the set, functionality based on set contents is unavailable:
:func:`len`, :func:`iter` (and for loops), and ``.pop()``. But a
complement set can always be turned back into a regular set by
complementing it again:
>>> s = set(range(5))
>>> complement(complement(s)) == s
True
.. note::
An empty complement set corresponds to the concept of a
`universal set <https://en.wikipedia.org/wiki/Universal_set>`_
from mathematics.
Complement sets by example
^^^^^^^^^^^^^^^^^^^^^^^^^^
Many uses of sets can be expressed more simply by using a
complement. Rather than trying to work out in your head the proper
way to invert an expression, you can just throw a complement on
the set. Consider this example of a name filter::
>>> class NamesFilter(object):
... def __init__(self, allowed):
... self._allowed = allowed
...
... def filter(self, names):
... return [name for name in names if name in self._allowed]
>>> NamesFilter(set(['alice', 'bob'])).filter(['alice', 'bob', 'carol'])
['alice', 'bob']
What if we want to just express "let all the names through"?
We could try to enumerate all of the expected names::
``NamesFilter({'alice', 'bob', 'carol'})``
But this is very brittle -- what if at some point over this
object is changed to filter ``['alice', 'bob', 'carol', 'dan']``?
Even worse, what about the poor programmer who next works
on this piece of code? They cannot tell whether the purpose
of the large allowed set was "allow everything", or if 'dan'
was excluded for some subtle reason.
A complement set lets the programmer intention be expressed
succinctly and directly::
NamesFilter(complement(set()))
Not only is this code short and robust, it is easy to understand
the intention.
"""
if type(wrapped) is _ComplementSet:
return wrapped.complemented()
if type(wrapped) is frozenset:
return _ComplementSet(excluded=wrapped)
return _ComplementSet(excluded=set(wrapped))
def _norm_args_typeerror(other):
'''normalize args and raise type-error if there is a problem'''
if type(other) in (set, frozenset):
inc, exc = other, None
elif type(other) is _ComplementSet:
inc, exc = other._included, other._excluded
else:
raise TypeError('argument must be another set or complement(set)')
return inc, exc
def _norm_args_notimplemented(other):
'''normalize args and return NotImplemented (for overloaded operators)'''
if type(other) in (set, frozenset):
inc, exc = other, None
elif type(other) is _ComplementSet:
inc, exc = other._included, other._excluded
else:
return NotImplemented, None
return inc, exc
class _ComplementSet(object):
"""
helper class for complement() that implements the set methods
"""
__slots__ = ('_included', '_excluded')
def __init__(self, included=None, excluded=None):
if included is None:
assert type(excluded) in (set, frozenset)
elif excluded is None:
assert type(included) in (set, frozenset)
else:
raise ValueError('one of included or excluded must be a set')
self._included, self._excluded = included, excluded
def __repr__(self):
if self._included is None:
return 'complement({0})'.format(repr(self._excluded))
return 'complement(complement({0}))'.format(repr(self._included))
def complemented(self):
'''return a complement of the current set'''
if type(self._included) is frozenset or type(self._excluded) is frozenset:
return _ComplementSet(included=self._excluded, excluded=self._included)
return _ComplementSet(
included=None if self._excluded is None else set(self._excluded),
excluded=None if self._included is None else set(self._included))
__invert__ = complemented
def complement(self):
'''convert the current set to its complement in-place'''
self._included, self._excluded = self._excluded, self._included
def __contains__(self, item):
if self._included is None:
return not item in self._excluded
return item in self._included
def add(self, item):
if self._included is None:
if item in self._excluded:
self._excluded.remove(item)
else:
self._included.add(item)
def remove(self, item):
if self._included is None:
self._excluded.add(item)
else:
self._included.remove(item)
def pop(self):
if self._included is None:
raise NotImplementedError # self.missing.add(random.choice(gc.objects()))
return self._included.pop()
def intersection(self, other):
try:
return self & other
except NotImplementedError:
raise TypeError('argument must be another set or complement(set)')
def __and__(self, other):
inc, exc = _norm_args_notimplemented(other)
if inc is NotImplemented:
return NotImplemented
if self._included is None:
if exc is None: # - +
return _ComplementSet(included=inc - self._excluded)
else: # - -
return _ComplementSet(excluded=self._excluded.union(other._excluded))
else:
if inc is None: # + -
return _ComplementSet(included=exc - self._included)
else: # + +
return _ComplementSet(included=self._included.intersection(inc))
__rand__ = __and__
def __iand__(self, other):
inc, exc = _norm_args_notimplemented(other)
if inc is NotImplemented:
return NotImplemented
if self._included is None:
if exc is None: # - +
self._excluded = inc - self._excluded # TODO: do this in place?
else: # - -
self._excluded |= exc
else:
if inc is None: # + -
self._included -= exc
self._included, self._excluded = None, self._included
else: # + +
self._included &= inc
return self
def union(self, other):
try:
return self | other
except NotImplementedError:
raise TypeError('argument must be another set or complement(set)')
def __or__(self, other):
inc, exc = _norm_args_notimplemented(other)
if inc is NotImplemented:
return NotImplemented
if self._included is None:
if exc is None: # - +
return _ComplementSet(excluded=self._excluded - inc)
else: # - -
return _ComplementSet(excluded=self._excluded.intersection(exc))
else:
if inc is None: # + -
return _ComplementSet(excluded=exc - self._included)
else: # + +
return _ComplementSet(included=self._included.union(inc))
__ror__ = __or__
def __ior__(self, other):
inc, exc = _norm_args_notimplemented(other)
if inc is NotImplemented:
return NotImplemented
if self._included is None:
if exc is None: # - +
self._excluded -= inc
else: # - -
self._excluded &= exc
else:
if inc is None: # + -
self._included, self._excluded = None, exc - self._included # TODO: do this in place?
else: # + +
self._included |= inc
return self
def update(self, items):
if type(items) in (set, frozenset):
inc, exc = items, None
elif type(items) is _ComplementSet:
inc, exc = items._included, items._excluded
else:
inc, exc = frozenset(items), None
if self._included is None:
if exc is None: # - +
self._excluded &= inc
else: # - -
self._excluded.discard(exc)
else:
if inc is None: # + -
self._included &= exc
self._included, self._excluded = None, self._excluded
else: # + +
self._included.update(inc)
def discard(self, items):
if type(items) in (set, frozenset):
inc, exc = items, None
elif type(items) is _ComplementSet:
inc, exc = items._included, items._excluded
else:
inc, exc = frozenset(items), None
if self._included is None:
if exc is None: # - +
self._excluded.update(inc)
else: # - -
self._included, self._excluded = exc - self._excluded, None
else:
if inc is None: # + -
self._included &= exc
else: # + +
self._included.discard(inc)
def symmetric_difference(self, other):
try:
return self ^ other
except NotImplementedError:
raise TypeError('argument must be another set or complement(set)')
def __xor__(self, other):
inc, exc = _norm_args_notimplemented(other)
if inc is NotImplemented:
return NotImplemented
if inc is NotImplemented:
return NotImplemented
if self._included is None:
if exc is None: # - +
return _ComplementSet(excluded=self._excluded - inc)
else: # - -
return _ComplementSet(included=self._excluded.symmetric_difference(exc))
else:
if inc is None: # + -
return _ComplementSet(excluded=exc - self._included)
else: # + +
return _ComplementSet(included=self._included.symmetric_difference(inc))
__rxor__ = __xor__
def symmetric_difference_update(self, other):
inc, exc = _norm_args_typeerror(other)
if self._included is None:
if exc is None: # - +
self._excluded |= inc
else: # - -
self._excluded.symmetric_difference_update(exc)
self._included, self._excluded = self._excluded, None
else:
if inc is None: # + -
self._included |= exc
self._included, self._excluded = None, self._included
else: # + +
self._included.symmetric_difference_update(inc)
def isdisjoint(self, other):
inc, exc = _norm_args_typeerror(other)
if inc is NotImplemented:
return NotImplemented
if self._included is None:
if exc is None: # - +
return inc.issubset(self._excluded)
else: # - -
return False
else:
if inc is None: # + -
return self._included.issubset(exc)
else: # + +
return self._included.isdisjoint(inc)
def issubset(self, other):
'''everything missing from other is also missing from self'''
try:
return self <= other
except NotImplementedError:
raise TypeError('argument must be another set or complement(set)')
def __le__(self, other):
inc, exc = _norm_args_notimplemented(other)
if inc is NotImplemented:
return NotImplemented
if inc is NotImplemented:
return NotImplemented
if self._included is None:
if exc is None: # - +
return False
else: # - -
return self._excluded.issupserset(exc)
else:
if inc is None: # + -
return self._included.isdisjoint(exc)
else: # + +
return self._included.issubset(inc)
def __lt__(self, other):
inc, exc = _norm_args_notimplemented(other)
if inc is NotImplemented:
return NotImplemented
if inc is NotImplemented:
return NotImplemented
if self._included is None:
if exc is None: # - +
return False
else: # - -
return self._excluded > exc
else:
if inc is None: # + -
return self._included.isdisjoint(exc)
else: # + +
return self._included < inc
def issuperset(self, other):
'''everything missing from self is also missing from super'''
try:
return self >= other
except NotImplementedError:
raise TypeError('argument must be another set or complement(set)')
def __ge__(self, other):
inc, exc = _norm_args_notimplemented(other)
if inc is NotImplemented:
return NotImplemented
if self._included is None:
if exc is None: # - +
return not self._excluded.intersection(inc)
else: # - -
return self._excluded.issubset(exc)
else:
if inc is None: # + -
return False
else: # + +
return self._included.issupserset(inc)
def __gt__(self, other):
inc, exc = _norm_args_notimplemented(other)
if inc is NotImplemented:
return NotImplemented
if self._included is None:
if exc is None: # - +
return not self._excluded.intersection(inc)
else: # - -
return self._excluded < exc
else:
if inc is None: # + -
return False
else: # + +
return self._included > inc
def difference(self, other):
try:
return self - other
except NotImplementedError:
raise TypeError('argument must be another set or complement(set)')
def __sub__(self, other):
inc, exc = _norm_args_notimplemented(other)
if inc is NotImplemented:
return NotImplemented
if self._included is None:
if exc is None: # - +
return _ComplementSet(excluded=self._excluded | inc)
else: # - -
return _ComplementSet(included=exc - self._excluded)
else:
if inc is None: # + -
return _ComplementSet(included=self._included & exc)
else: # + +
return _ComplementSet(included=self._included.difference(inc))
def __rsub__(self, other):
inc, exc = _norm_args_notimplemented(other)
if inc is NotImplemented:
return NotImplemented
# rsub, so the expression being evaluated is "other - self"
if self._included is None:
if exc is None: # - +
return _ComplementSet(included=inc & self._excluded)
else: # - -
return _ComplementSet(included=self._excluded - exc)
else:
if inc is None: # + -
return _ComplementSet(excluded=exc | self._included)
else: # + +
return _ComplementSet(included=inc.difference(self._included))
def difference_update(self, other):
try:
self -= other
except NotImplementedError:
raise TypeError('argument must be another set or complement(set)')
def __isub__(self, other):
inc, exc = _norm_args_notimplemented(other)
if inc is NotImplemented:
return NotImplemented
if self._included is None:
if exc is None: # - +
self._excluded |= inc
else: # - -
self._included, self._excluded = exc - self._excluded, None
else:
if inc is None: # + -
self._included &= exc
else: # + +
self._included.difference_update(inc)
return self
def __eq__(self, other):
return (
type(self) is type(other)
and self._included == other._included
and self._excluded == other._excluded) or (
type(other) in (set, frozenset) and self._included == other)
def __hash__(self):
return hash(self._included) ^ hash(self._excluded)
def __len__(self):
if self._included is not None:
return len(self._included)
raise NotImplementedError('complemented sets have undefined length')
def __iter__(self):
if self._included is not None:
return iter(self._included)
raise NotImplementedError('complemented sets have undefined contents')
def __bool__(self):
if self._included is not None:
return bool(self._included)
return True
__nonzero__ = __bool__ # py2 compat
raise exception on non-set params?
https://github.com/rjdbcm/Aspidites/blob/455d40b5b90785a1d554b66b38930c8fafa16e5b/Aspidites/woma/setutils.py#L38
e7c5dfc70f8c4ab23dae1c89f3b170c2bc2db22a