# bitsets 0.1.4

Ordered subsets over a predefined domain

Bitsets are ordered sets which are subsets of a predefined finite domain of hashable items.

They are implemented as python integers representing the rank of the set in colexicographical order (a.k.a bit strings, binary strings). Hence, they are very space-efficient e.g. if a large number of subsets from a collection needs to be present in memory. Furthermore, they can be compared, intersected, etc. using normal bitwise operations of integers.

## Installation

```\$ pip install bitsets
```

## Creation

Use the bitset function to create a class representing ordered subsets from a fixed set of items (the domain):

```>>> from bitsets import bitset

>>> Pythons = bitset('Pythons', ('Chapman', 'Cleese', 'Gilliam', 'Idle', 'Jones', 'Palin'))
```

The domain collection needs to be a hashable sequence (e.g. a tuple).

The resulting class is an integer (long) subclass, so its instances (being integers) are immutable and hashable and thus in many ways similar to pythons built-in frozenset.

```>>> issubclass(Pythons, long)
True
```

The class provides access to the minimal (infimum) and maximal (supremum) sets from its domain:

```>>> Pythons.infimum
Pythons()

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

## Basic usage

Bitsets can be created from members, bit strings, boolean sequences, and integers. Members always occur in the definition order:

```>>> Pythons(['Palin', 'Cleese'])
Pythons(['Cleese', 'Palin'])

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

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

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

Bitsets cannot contain items other than those from their domain:

```>>> Pythons(['Brian'])
Traceback (most recent call last):
....
KeyError: 'Brian'
```

Bitsets can be converted to members, bit strings, boolean sequences and integers:

```>>> Pythons(['Chapman', 'Gilliam']).members()
('Chapman', 'Gilliam')

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

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

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

## Sorting

To facilitate sorting collections of bitsets, they have key methods for different sort orders (shortlex, longlex, shortcolex, and longcolex):

```>>> Pythons(['Idle']).shortlex() < Pythons(['Palin']).shortlex()
True
```

Sorting a collection of bitsets without using a keyfunction will order them in colexicographical order.

## Powersets

Iterate over a bitsetsâ€™ powerset in short lexicographic order:

```>>> for p in Pythons(['Palin', 'Idle']).powerset():
...     print p.members()
()
('Idle',)
('Palin',)
('Idle', 'Palin')
```

## frozenset compatibility

For convenience, bitsets provide the same methods as frozenset (i.e. issubset, issuperset, isdisjoint, intersection, union, difference, symmetric_difference, __len__, __iter__, __nonzero__, and __contains__).

```>>> 'Cleese' in Pythons(['Idle'])
False

>>> 'Idle' in Pythons(['Idle'])
True

>>> Pythons(['Chapman', 'Idle']).intersection(Pythons(['Idle', 'Palin']))
Pythons(['Idle'])
```

Note, however that all the operators methods retain their integer semantics:

```>>> Pythons(['Chapman', 'Idle']) - Pythons(['Idle'])
1L
```

That is, because in tight loops it might be worth to use bitwise expressions for set comparisons/operation instead of the frozenset-compatible methods:

```>>> # is subset ?
>>> Pythons(['Idle']) & Pythons(['Chapman', 'Idle']) == Pythons(['Idle'])
True
```

Differing from frozenset, you can also retrieve the complement set of a bitset:

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

>>> Pythons().complement().complement()
Pythons()
```

To use a customized bitset, extend a class from the bitsets.bases module and pass it to the bitset function.

```>>> import bitsets

>>> class ProperSet(bitsets.bases.BitSet):
...     def issubset_proper(self, other):
...         return self & other == self != other

>>> Ints = bitsets.bitset('Ints', tuple(range(1, 7)), base=ProperSet)

>>> issubclass(Ints, ProperSet)
True

>>> Ints([1]).issubset_proper(Ints([1, 2]))
True
```

When activated, each bitset class comes with tailored collection classes (bitset list and bitset tuple) for its instances.

```>>> Letters = bitsets.bitset('Letters', 'abcdef', list=True)

>>> Letters.List.from_members(['a', 'bcd', 'ef'])
LettersList('100000', '011100', '000011')
```

To use a customized bitset collection class, extend a class from the bitsets.series module and pass it to the bitset function

```>>> class ReduceList(bitsets.series.List):
...     def intersection(self):
...         return self.BitSet.from_int(reduce(long.__and__, self))
...     def union(self):
...         return self.BitSet.from_int(reduce(long.__or__, self))

>>> Nums = bitsets.bitset('Nums', (1, 2, 3), list=ReduceList)

>>> issubclass(Nums.List, ReduceList)
True

>>> numslist = Nums.List.from_members([(1, 2, 3), (1, 2), (2, 3)])

>>> numslist.intersection()
Nums([2])

>>> numslist.union()
Nums([1, 2, 3])
```

Bitset classes, collection classes and their instances are pickleable:

```>>> import pickle

True

Pythons()

>>> pickle.loads(pickle.dumps(Nums.List)) is Nums.List  # doctest: +SKIP
True