生成包含集合中所有元素的子集的所有可能排列 [英] Generate all possible permutations of subsets containing all the element of a set
问题描述
让S(w)为一组单词.我想生成子集s的所有可能的n组合,以便这些子集的并集始终等于S(w).
Let S(w) be a set of words. I want to generate all the possible n-combination of subsets s so that the union of those subsets are always equal to S(w).
因此,您有一组(a,b,c,d,e),并且不需要所有3种组合:
So you have a set (a, b, c, d, e) and you wan't all the 3-combinations:
(((a,b,c),(d),(e))
((a, b, c), (d), (e))
(((a,b),(c,d),(e))
((a, b), (c, d), (e))
(((a),(b,c,d),(e))
((a), (b, c, d), (e))
(((a),(b,c),(d,e))
((a), (b, c), (d, e))
等...
对于每个组合,您有3个组合,这些组合的并集是原始组合.没有空集,没有丢失的元素.
For each combination you have 3 set and the union of those set is the original set. No empty set, no missing element.
一定有一种使用itertools.combination + collection.Counter来做到这一点的方法,但我什至无法从某处开始... 有人可以帮忙吗?
There must be a way to do that using itertools.combination + collection.Counter but I can't even start somewhere... Can someone help ?
卢克
我需要捕获所有可能的组合,包括:
I would need to capture all the possible combination, including:
(((a,e),(b,d)(c))
((a, e), (b, d) (c))
等...
推荐答案
类似的东西?
from itertools import combinations, permutations
t = ('a', 'b', 'c', 'd', 'e')
slicer = [x for x in combinations(range(1, len(t)), 2)]
result = [(x[0:i], x[i:j], x[j:]) for i, j in slicer for x in permutations(t, len(t))]
一般解,对于任何n和任何元组长度:
general solution, for any n and any tuple length:
from itertools import combinations, permutations
t = ("a", "b", "c")
n = 2
slicer = [x for x in combinations(range(1, len(t)), n - 1)]
slicer = [(0,) + x + (len(t),) for x in slicer]
perm = list(permutations(t, len(t)))
result = [tuple(p[s[i]:s[i + 1]] for i in range(len(s) - 1)) for s in slicer for p in perm]
[
(('a',), ('b', 'c')),
(('a',), ('c', 'b')),
(('b',), ('a', 'c')),
(('b',), ('c', 'a')),
(('c',), ('a', 'b')),
(('c',), ('b', 'a')),
(('a', 'b'), ('c',)),
(('a', 'c'), ('b',)),
(('b', 'a'), ('c',)),
(('b', 'c'), ('a',)),
(('c', 'a'), ('b',)),
(('c', 'b'), ('a',))
]
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