返回不同长度输出的笛卡尔积

Question

所以我有这些列表：

a = [1, 2, 3]
b = [11, 12, 13, 14]
c = [21, 22, 23, 24, 25, 26]

我想获取所有可能的组合（重复即可），其中包含来自 a 的 2 个元素、来自 b 的 3 个元素和来自 c 的 3 个元素。像这样：

([1, 2], [11, 12, 13], [21, 22, 23]) # 1
([1, 2], [11, 12, 13], [22, 23, 24]) # 2
# all the way to...
([2, 3], [12, 13, 14], [24, 25, 26]) # 16

如果我使用itertools.product()，它只会给我每个列表中的 1 个：

import itertools

def cartesian(the_list):
    for i in itertools.product(*the_list):
        yield i

a = [1, 2, 3]
b = [11, 12, 13, 14]
c = [21, 22, 23, 24, 25, 26]

test = cartesian([a, b, c])

print(next(test)) 
# Gives (1, 11, 21). But I need ([1, 2], [11, 12, 13], [21, 22, 23])

print(next(test)) 
# Gives (1, 11, 22). But I need ([1, 2], [11, 12, 13], [22, 23, 24])

我可以使用多个嵌套的for 循环，但如果我有很多列表，我将需要太多循环。

那么我该如何实现一个算法，它可以给我所有可能的组合，每个组合都由每个输入列表中的一定数量的元素组成？

Answer 1

构建一个生成器函数，它可以产生任意数量的值，并在product 中使用它，就像这样

>>> from itertools import product
>>> def get_chunks(items, number=3):
...     for i in range(len(items) - number + 1): 
...         yield items[i: i + number]
...     
... 

然后定义你的cartesian 生成器，像这样

>>> def cartesian(a, b, c):
...     for items in product(get_chunks(a, 2), get_chunks(b), get_chunks(c)):
...         yield items
...     
... 

如果你使用的是 Python 3.3+，你实际上可以在这里使用yield from，像这样

>>> def cartesian(a, b, c):
...     yield from product(get_chunks(a, 2), get_chunks(b), get_chunks(c))
... 

然后，当您将所有元素作为列表获取时，您将得到

>>> from pprint import pprint
>>> pprint(list(cartesian([1, 2, 3],[11, 12, 13, 14],[21, 22, 23, 24, 25, 26])))
[([1, 2], [11, 12, 13], [21, 22, 23]),
 ([1, 2], [11, 12, 13], [22, 23, 24]),
 ([1, 2], [11, 12, 13], [23, 24, 25]),
 ([1, 2], [11, 12, 13], [24, 25, 26]),
 ([1, 2], [12, 13, 14], [21, 22, 23]),
 ([1, 2], [12, 13, 14], [22, 23, 24]),
 ([1, 2], [12, 13, 14], [23, 24, 25]),
 ([1, 2], [12, 13, 14], [24, 25, 26]),
 ([2, 3], [11, 12, 13], [21, 22, 23]),
 ([2, 3], [11, 12, 13], [22, 23, 24]),
 ([2, 3], [11, 12, 13], [23, 24, 25]),
 ([2, 3], [11, 12, 13], [24, 25, 26]),
 ([2, 3], [12, 13, 14], [21, 22, 23]),
 ([2, 3], [12, 13, 14], [22, 23, 24]),
 ([2, 3], [12, 13, 14], [23, 24, 25]),
 ([2, 3], [12, 13, 14], [24, 25, 26])]