子集

class sympy.combinatorics.subsets.Subset(subset, superset)

表示基本子集对象。

解释

我们主要使用两种技术来生成子集：二进制枚举和字典式枚举。Subset类接受两个参数，第一个参数描述要考虑的初始子集，第二个参数描述超集。

实例

>>> from sympy.combinatorics import Subset
>>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd'])
>>> a.next_binary().subset
['b']
>>> a.prev_binary().subset
['c']

classmethod bitlist_from_subset(subset, superset)

获取与子集对应的位列表。

实例

>>> from sympy.combinatorics import Subset
>>> Subset.bitlist_from_subset(['c', 'd'], ['a', 'b', 'c', 'd'])
'0011'

参见

subset_from_bitlist

property cardinality

返回所有可能的子集的数目。

实例

>>> from sympy.combinatorics import Subset
>>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd'])
>>> a.cardinality
16

参见

subset, superset, size, superset_size

iterate_binary(k)

This is a helper function. It iterates over the binary subsets by k steps. This variable can be both positive or negative.

实例

>>> from sympy.combinatorics import Subset
>>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd'])
>>> a.iterate_binary(-2).subset
['d']
>>> a = Subset(['a', 'b', 'c'], ['a', 'b', 'c', 'd'])
>>> a.iterate_binary(2).subset
[]

参见

next_binary, prev_binary

iterate_graycode(k)

Helper function used for prev_gray and next_gray. It performs k step overs to get the respective Gray codes.

实例

>>> from sympy.combinatorics import Subset
>>> a = Subset([1, 2, 3], [1, 2, 3, 4])
>>> a.iterate_graycode(3).subset
[1, 4]
>>> a.iterate_graycode(-2).subset
[1, 2, 4]

参见

next_gray, prev_gray

next_binary()

生成下一个二进制有序子集。

实例

>>> from sympy.combinatorics import Subset
>>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd'])
>>> a.next_binary().subset
['b']
>>> a = Subset(['a', 'b', 'c', 'd'], ['a', 'b', 'c', 'd'])
>>> a.next_binary().subset
[]

参见

prev_binary, iterate_binary

next_gray()

生成下一个格雷码有序子集。

实例

>>> from sympy.combinatorics import Subset
>>> a = Subset([1, 2, 3], [1, 2, 3, 4])
>>> a.next_gray().subset
[1, 3]

参见

iterate_graycode, prev_gray

next_lexicographic()

生成下一个按字典顺序排列的子集。

实例

>>> from sympy.combinatorics import Subset
>>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd'])
>>> a.next_lexicographic().subset
['d']
>>> a = Subset(['d'], ['a', 'b', 'c', 'd'])
>>> a.next_lexicographic().subset
[]

参见

prev_lexicographic

prev_binary()

生成上一个二进制有序子集。

实例

>>> from sympy.combinatorics import Subset
>>> a = Subset([], ['a', 'b', 'c', 'd'])
>>> a.prev_binary().subset
['a', 'b', 'c', 'd']
>>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd'])
>>> a.prev_binary().subset
['c']

参见

next_binary, iterate_binary

prev_gray()

生成上一个格雷码有序子集。

实例

>>> from sympy.combinatorics import Subset
>>> a = Subset([2, 3, 4], [1, 2, 3, 4, 5])
>>> a.prev_gray().subset
[2, 3, 4, 5]

参见

iterate_graycode, next_gray

prev_lexicographic()

生成上一个按字典顺序排列的子集。

实例

>>> from sympy.combinatorics import Subset
>>> a = Subset([], ['a', 'b', 'c', 'd'])
>>> a.prev_lexicographic().subset
['d']
>>> a = Subset(['c','d'], ['a', 'b', 'c', 'd'])
>>> a.prev_lexicographic().subset
['c']

参见

next_lexicographic

property rank_binary

计算二进制有序秩。

实例

>>> from sympy.combinatorics import Subset
>>> a = Subset([], ['a','b','c','d'])
>>> a.rank_binary
0
>>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd'])
>>> a.rank_binary
3

参见

iterate_binary, unrank_binary

property rank_gray

计算该子集的格雷码排序。

实例

>>> from sympy.combinatorics import Subset
>>> a = Subset(['c','d'], ['a','b','c','d'])
>>> a.rank_gray
2
>>> a = Subset([2, 4, 5], [1, 2, 3, 4, 5, 6])
>>> a.rank_gray
27

参见

iterate_graycode, unrank_gray

property rank_lexicographic

计算子集的字典排序。

实例

>>> from sympy.combinatorics import Subset
>>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd'])
>>> a.rank_lexicographic
14
>>> a = Subset([2, 4, 5], [1, 2, 3, 4, 5, 6])
>>> a.rank_lexicographic
43

property size

获取子集的大小。

实例

>>> from sympy.combinatorics import Subset
>>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd'])
>>> a.size
2

参见

subset, superset, superset_size, cardinality

property subset

获取当前实例表示的子集。

实例

>>> from sympy.combinatorics import Subset
>>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd'])
>>> a.subset
['c', 'd']

参见

superset, size, superset_size, cardinality

classmethod subset_from_bitlist(super_set, bitlist)

获取由位列表定义的子集。

实例

>>> from sympy.combinatorics import Subset
>>> Subset.subset_from_bitlist(['a', 'b', 'c', 'd'], '0011').subset
['c', 'd']

参见

bitlist_from_subset

classmethod subset_indices(subset, superset)

Return indices of subset in superset in a list; the list is empty if all elements of subset are not in superset.

实例

>>> from sympy.combinatorics import Subset
>>> superset = [1, 3, 2, 5, 4]
>>> Subset.subset_indices([3, 2, 1], superset)
[1, 2, 0]
>>> Subset.subset_indices([1, 6], superset)
[]
>>> Subset.subset_indices([], superset)
[]

property superset

获取子集的超集。

实例

>>> from sympy.combinatorics import Subset
>>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd'])
>>> a.superset
['a', 'b', 'c', 'd']

参见

subset, size, superset_size, cardinality

property superset_size

返回超集的大小。

实例

>>> from sympy.combinatorics import Subset
>>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd'])
>>> a.superset_size
4

参见

subset, superset, size, cardinality

classmethod unrank_binary(rank, superset)

获取指定列组的二进制有序子集。

实例

>>> from sympy.combinatorics import Subset
>>> Subset.unrank_binary(4, ['a', 'b', 'c', 'd']).subset
['b']

参见

iterate_binary, rank_binary

classmethod unrank_gray(rank, superset)

获取指定等级的格雷码排序子集。

实例

>>> from sympy.combinatorics import Subset
>>> Subset.unrank_gray(4, ['a', 'b', 'c']).subset
['a', 'b']
>>> Subset.unrank_gray(0, ['a', 'b', 'c']).subset
[]

参见

iterate_graycode, rank_gray

subsets.ksubsets(k)

Finds the subsets of size k in lexicographic order.

它使用itertools生成器。

实例

>>> from sympy.combinatorics.subsets import ksubsets
>>> list(ksubsets([1, 2, 3], 2))
[(1, 2), (1, 3), (2, 3)]
>>> list(ksubsets([1, 2, 3, 4, 5], 2))
[(1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4),     (2, 5), (3, 4), (3, 5), (4, 5)]

参见

Subset