有没有办法用 Python 计算一个集合的所有合法分区？

Question

Wiki给出了这个definition的一个分区集

In mathematics, a partition of a set is a grouping of the set's elements into non-empty subsets, in such a way that every element is included in exactly one subset.

还有这个例子

集合{1,2,3}有这五个分区

{ {1}, {2}, {3} }, sometimes written 1|2|3.
{ {1, 2}, {3} }, or 12|3.
{ {1, 3}, {2} }, or 13|2.
{ {1}, {2, 3} }, or 1|23.
{ {1, 2, 3} }, or 123

有没有办法用 Python 计算集合的所有合法分区？

我试过了the partitions in sympy

from sympy.combinatorics.partitions import Partition
a = Partition([1, 2, 3])
a.members

我得到了

(1, 2, 3)

这显然是不正确的。

Answer 1

如果您使用的是 Sympy，那么您需要 sympy.utilities.iterables.multiset_partitions:

>>> from sympy.utilities.iterables import multiset_partitions
>>> for p in multiset_partitions([1, 2, 3]):
...     print(p)
...
[[1, 2, 3]]
[[1, 2], [3]]
[[1, 3], [2]]
[[1], [2, 3]]
[[1], [2], [3]]

有没有办法用 Python 计算一个集合的所有合法分区？

Is there a way to compute all the legit partitions of a set with Python?

python

math

set-theory

sympy