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Ordered subsets over a finite domain

Bitsets

|PyPI version| |License| |Supported Python| |Wheel|

|Build| |Codecov| |Readthedocs-stable| |Readthedocs-latest|

This package provides a memory-efficient pure-python immutable ordered set data type for working with large numbers of subsets from a predetermined pool of objects.

Given a name and a tuple of hashable objects, the bitset()-function returns a custom integer subclass for creating ordered subsets from the object pool. Each instance is a Python integer where the presence/absence of the nth pool item is its nth bit being set/unset (a.k.a. bit strings, powers of two, rank in colexicographical order).

Being just a regular (arbitrary precision) integer with some convenience methods for translating between unique object collections and bit patterns allows to perform certain tasks in a more natural way, e.g. sorting a collection of sets lexicographically, or enumerating possible combinations in an ordered fashion.

Links

  • GitHub: https://github.com/xflr6/bitsets
  • PyPI: https://pypi.org/project/bitsets/
  • Documentation: https://bitsets.readthedocs.io
  • Changelog: https://bitsets.readthedocs.io/en/latest/changelog.html
  • Issue Tracker: https://github.com/xflr6/bitsets/issues
  • Download: https://pypi.org/project/bitsets/#files

Installation

This package runs under Python 3.8+ and has no required dependencies, use pip_ to install:

.. code:: bash

$ pip install bitsets

Quickstart

Create a class for sets taken from your pool of objects:

.. code:: python

>>> from bitsets import bitset

>>> PYTHONS = ('Chapman', 'Cleese', 'Gilliam', 'Idle', 'Jones', 'Palin')

>>> Pythons = bitset('Pythons', PYTHONS)

Access its maximal and minimal instances. Retrieve instance members in definition order:

.. code:: python

>>> Pythons.supremum
Pythons(['Chapman', 'Cleese', 'Gilliam', 'Idle', 'Jones', 'Palin'])

>>> Pythons.infimum
Pythons()

>>> Pythons(['Idle', 'Gilliam', 'Idle', 'Idle']).members()
('Gilliam', 'Idle')

Translate to/from bit string, boolean sequence, and int:

.. code:: python

>>> Pythons(['Chapman', 'Gilliam']).bits()
'101000'

>>> Pythons.frombits('101000')
Pythons(['Chapman', 'Gilliam'])

>>> Pythons(['Chapman', 'Gilliam']).bools()
(True, False, True, False, False, False)

>>> Pythons.frombools([True, None, 1, False, 0])
Pythons(['Chapman', 'Gilliam'])

>>> int(Pythons(['Chapman', 'Gilliam']))
5

>>> Pythons.fromint(5)
Pythons(['Chapman', 'Gilliam'])

Set operation and comparison methods (cf. build-in frozenset):

.. code:: python

>>> Pythons(['Jones', 'Cleese', 'Idle']).intersection(Pythons(['Idle']))
Pythons(['Idle'])

>>> Pythons(['Idle']).union(Pythons(['Jones', 'Cleese']))
Pythons(['Cleese', 'Idle', 'Jones'])

>>> Pythons.supremum.difference(Pythons(['Chapman', 'Cleese']))
Pythons(['Gilliam', 'Idle', 'Jones', 'Palin'])

>>> Pythons(['Palin', 'Jones']).symmetric_difference(Pythons(['Cleese', 'Jones']))
Pythons(['Cleese', 'Palin'])

>>> Pythons(['Gilliam']).issubset(Pythons(['Cleese', 'Palin']))
False

>>> Pythons(['Cleese', 'Palin']).issuperset(Pythons())
True

Further reading

  • https://wiki.python.org/moin/BitManipulation

  • https://wiki.python.org/moin/BitArrays

  • https://en.wikipedia.org/wiki/Bit_array

  • https://en.wikipedia.org/wiki/Bit_manipulation

  • https://en.wikipedia.org/wiki/Lexicographical_order

  • https://en.wikipedia.org/wiki/Colexicographical_order

See also

  • bitarray_ |--| efficient boolean array implemented as C extension
  • bitstring_ |--| pure-Python bit string based on bytearray
  • BitVector_ |--| pure-Python bit array based on unsigned short array
  • Bitsets_ |--| Cython interface to fast bitsets in Sage
  • bitfield_ |--| Cython positive integer sets
  • intbitset_ |--| integer bit sets as C extension
  • gmpy2_ |--| fast arbitrary precision integer arithmetic

License

Bitsets is distributed under the MIT license_.

.. _pip: https://pip.readthedocs.io

.. _bitarray: https://pypi.org/project/bitarray/ .. _bitstring: https://pypi.org/project/bitstring/ .. _BitVector: https://pypi.org/project/BitVector/ .. _Bitsets: https://www.sagemath.org/doc/reference/data_structures/sage/data_structures/bitset.html .. _bitfield: https://pypi.org/project/bitfield/ .. _intbitset: https://pypi.org/project/intbitset/ .. _gmpy2: https://pypi.org/project/gmpy2/

.. _MIT license: https://opensource.org/licenses/MIT

.. |--| unicode:: U+2013

.. |PyPI version| image:: https://img.shields.io/pypi/v/bitsets.svg :target: https://pypi.org/project/bitsets/ :alt: Latest PyPI Version .. |License| image:: https://img.shields.io/pypi/l/bitsets.svg :target: https://github.com/xflr6/bitsets/blob/master/LICENSE.txt :alt: License .. |Supported Python| image:: https://img.shields.io/pypi/pyversions/bitsets.svg :target: https://pypi.org/project/bitsets/ :alt: Supported Python Versions .. |Wheel| image:: https://img.shields.io/pypi/wheel/bitsets.svg :target: https://pypi.org/project/bitsets/#files :alt: Wheel format

.. |Build| image:: https://github.com/xflr6/bitsets/actions/workflows/build.yaml/badge.svg?branch=master :target: https://github.com/xflr6/bitsets/actions/workflows/build.yaml?query=branch%3Amaster :alt: Build .. |Codecov| image:: https://codecov.io/gh/xflr6/bitsets/branch/master/graph/badge.svg :target: https://codecov.io/gh/xflr6/bitsets :alt: Codecov .. |Readthedocs-stable| image:: https://readthedocs.org/projects/bitsets/badge/?version=stable :target: https://bitsets.readthedocs.io/en/stable/?badge=stable :alt: Readthedocs stable .. |Readthedocs-latest| image:: https://readthedocs.org/projects/bitsets/badge/?version=latest :target: https://bitsets.readthedocs.io/en/latest/?badge=latest :alt: Readthedocs latest

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Ordered subsets over a finite domain

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