在 Python 3 中创建层次组合？

Question

我有一个有趣的问题。我有一个包含分层数据的列表。

relation = [('grandfather'), ('father'), ('son')]

从某种意义上说，它是分层的，没有grandfather 就不可能有son，但没有son 就可以有father。

每个条目都可以有一个状态。

status = [('tall'), ('short')]

我试图找到所有可能的组合，这是有道理的。就是这样的组合

combination_sense = [('grandfather', 'tall'), ('father', 'short'), ('son', 'short')]

可能存在，但组合

combination_no_sense  = [('grandfather', 'tall'), ('son', 'short')]

可能不存在，因为没有father，就不可能有son。

同样，组合

combination_sense = [('grandfather', 'tall'), ('father', 'short')]

可能确实存在。

我尝试了itertools。我尝试了list(itertools.product()) 和itertools.permutations()，但我无法让它工作到现在。

如何处理层级关系？

Answer 1

如果我理解正确，您希望从两个列表中生成所有值的组合，但您对列表的处理方式彼此不同。

对于第一个分层列表，您必须始终使用第一个值，并且可以将值序列扩展任意数量，只要您不跳过任何值。因此，对于您的示例列表，您将生成 ['grandfather'], ['grandfather', 'father'], ['grandfather', 'father', 'son']。

对于第二个列表，您希望所有组合（带有替换）与您配对的层次结构值的长度相同。

使用自定义生成器函数应该不难做到：

import itertools as it

def combine(relations, statuses):
    for i in range(len(relations)):
        relation = relations[:i+1]
        for status_combination in it.product(statuses, repeat=i+1):
            yield list(zip(relation, status_combination))

首先从较小的结果开始（例如，只有 'grandfather' 的结果）。如果您想从最长的那些（包括'son' 的那些）开始，您可以将上面代码中i+1 的两个实例替换为len(relations)-i。

如果您想要relations 的所有连续子序列（因此['father', 'son'] 将被允许，['father'] 和['son'] 本身也一样），您只需进行一些更改即可获得该结果：

import itertools as it

def combine(relations, statuses):
    for start, stop in it.combinations(range(len(relations) + 1), 2): # get two indexes
        relation = relations[start:stop]                              # slice using both
        for status_combination in it.product(statuses, repeat=stop-start): # use difference
            yield list(zip(relation, status_combination))

Answer 2

这个版本产生了更多连续生成的可能性，这是我从我们的谈话中理解的。我不知道这是否是你真正想要的。

from itertools import product

relations = ['grandfather', 'father', 'son']
statuses = ['tall', 'short']

possibilities = []
for per in range(1,4):
    contiguous_relations = [relations[i: i+per] for i in range(-per+1+len(relations))]
    possibilities.extend(contiguous_relations)

for possibility in possibilities:
    print('---', possibility)
    for p in product(statuses, repeat=len(possibility)):
        print (list(zip(possibility, p)))

结果：

--- ['grandfather']
[('grandfather', 'tall')]
[('grandfather', 'short')]
--- ['father']
[('father', 'tall')]
[('father', 'short')]
--- ['son']
[('son', 'tall')]
[('son', 'short')]
--- ['grandfather', 'father']
[('grandfather', 'tall'), ('father', 'tall')]
[('grandfather', 'tall'), ('father', 'short')]
[('grandfather', 'short'), ('father', 'tall')]
[('grandfather', 'short'), ('father', 'short')]
--- ['father', 'son']
[('father', 'tall'), ('son', 'tall')]
[('father', 'tall'), ('son', 'short')]
[('father', 'short'), ('son', 'tall')]
[('father', 'short'), ('son', 'short')]
--- ['grandfather', 'father', 'son']
[('grandfather', 'tall'), ('father', 'tall'), ('son', 'tall')]
[('grandfather', 'tall'), ('father', 'tall'), ('son', 'short')]
[('grandfather', 'tall'), ('father', 'short'), ('son', 'tall')]
[('grandfather', 'tall'), ('father', 'short'), ('son', 'short')]
[('grandfather', 'short'), ('father', 'tall'), ('son', 'tall')]
[('grandfather', 'short'), ('father', 'tall'), ('son', 'short')]
[('grandfather', 'short'), ('father', 'short'), ('son', 'tall')]
[('grandfather', 'short'), ('father', 'short'), ('son', 'short')]