给定列表中项目的组合

Question

我目前在 Python 领域。这就是我需要做的。我已经研究过 itertools 库，但它似乎只做排列。

我想要一个输入列表，例如 ['yahoo'、'wikipedia'、'freebase'] 并生成一个项目与零个或多个其他项目的每个独特组合......

['yahoo', 'wikipedia', 'freebase']
['yahoo', 'wikipedia']
['yahoo', 'freebase']
['wikipedia', 'freebase']
['yahoo']
['freebase']
['wikipedia']

一些注释。顺序并不重要，我正在尝试设计一种方法来获取任何大小的列表。另外，这种组合有名字吗？

感谢您的帮助！

Answer 1

>>> l = ['yahoo', 'wikipedia', 'freebase']
>>> import itertools
>>> for i in range(1, len(l) +1):
    print(list(itertools.combinations(l, r=i)))


[('yahoo',), ('wikipedia',), ('freebase',)]
[('yahoo', 'wikipedia'), ('yahoo', 'freebase'), ('wikipedia', 'freebase')]
[('yahoo', 'wikipedia', 'freebase')]

PS 为什么这是维基？

Answer 2

它被称为动力集。这是 itertools 文档 的实现：

def powerset(iterable):
    "powerset([1,2,3]) --> () (1,) (2,) (3,) (1,2) (1,3) (2,3) (1,2,3)"
    s = list(iterable)
    return chain.from_iterable(combinations(s, r) for r in range(len(s)+1))

Answer 3

您基本上是在二进制中从 1 数到 2ⁿ-1：

0 0 1    ['freebase']
0 1 0    ['wikipedia']
0 1 1    ['wikipedia', 'freebase']
1 0 0    ['yahoo']
1 0 1    ['yahoo', 'freebase']
1 1 0    ['yahoo', 'wikipedia']
1 1 1    ['yahoo', 'wikipedia', 'freebase']

Answer 4

这就是所谓的幂集。只需遵循这个算法即可。这是一个简单的实现：

def powerset(seq):
  if len(seq):
    head = powerset(seq[:-1])
    return head + [item + [seq[-1]] for item in head]
  else:
    return [[]]

>>> powerset(['yahoo', 'wikipedia', 'freebase'])
[[], ['yahoo'], ['wikipedia'], ['yahoo', 'wikipedia'], ['freebase'], ['yahoo', 'freebase'], ['wikipedia', 'freebase'], ['yahoo', 'wikipedia', 'freebase']]

还有另一个：

def powerset(s):
  sets = []
  indicator = lambda x: x & 1
  for element in xrange(2**len(s)):
    n = element
    subset = []
    for x in s:
        if indicator(n):
            subset.append(x)
        n >>= 1
    sets.append(subset)
  return sets