来自n大小列表的k大小的python组合（递归）

Question

我需要一个递归函数，它可以对给定列表和长度进行所有可能的排列，并带有替换：

>>> rec_offspring(3,[2,3])
[[2, 2, 2], [3, 2, 2], [2, 3, 2], [3, 3, 2], [2, 2, 3], [3, 2, 3], [2, 3, 3], [3, 3, 3]]

我找到了下面的代码，但它只给出了组合；它不会重复一个元素，例如 [222] [322] 等。

def choose_sets(mylist,length):
    mylen = len(mylist)

    if length == 1:
        return [[i] for i in mylist]
    if length > mylen:
        return []

    ToRet = []
    for k in xrange(mylen): 
        if mylen - k + 1> length :
            for j in choose_sets(mylist[k+1:],length-1):
                New = [mylist[k]]
                New.extend(j)
                ToRet.append(New)
    return ToRet
print choose_sets([1,2,3,4,5],3)

Answer 1

这称为笛卡尔积。你可以使用itertoolsmodule：

>>> from itertools import product
>>> list(product([2,3], repeat=3))
[(2, 2, 2), (2, 2, 3), (2, 3, 2), (2, 3, 3), (3, 2, 2), (3, 2, 3), (3, 3, 2), (3, 3, 3)]

Answer 2

你有三个基本问题：

(1) 在您的递归调用中，您切断了所选元素。相反，将它们全部传递到下一个级别。替换

for j in choose_sets(mylist[k+1:],length-1):

与

for j in choose_sets(mylist,length-1):

(2) 您限制了要考虑的元素数量，使得元素处于非递减顺序。删除线

    if mylen - k + 1> length:

(3) 最后，您将返回列表限制为输入列表的长度。这意味着只有 2 个元素（例如 [2, 3]），您不能返回包含 3 个元素的选择列表（例如 [2, 3, 2]）。删除违规代码：

if length > mylen:
    return []

生成的程序似乎在执行您想要的操作，并返回：

>>> print choose_sets([2,3], 3)
[[2, 2, 2], [2, 2, 3], [2, 3, 2], [2, 3, 3], [3, 2, 2], [3, 2, 3], [3, 3, 2], [3, 3, 3]]
>>> print choose_sets([1,2,3,4,5], 3)
[[1, 1, 1], [1, 1, 2], [1, 1, 3], [1, 1, 4], [1, 1, 5], [1, 2, 1], [1, 2, 2], [1, 2, 3], [1, 2, 4], [1, 2, 5], [1, 3, 1], [1, 3, 2], [1, 3, 3], [1, 3, 4], [1, 3, 5], [1, 4, 1], [1, 4, 2], [1, 4, 3], [1, 4, 4], [1, 4, 5], [1, 5, 1], [1, 5, 2], [1, 5, 3], [1, 5, 4], [1, 5, 5], [2, 1, 1], [2, 1, 2], [2, 1, 3], [2, 1, 4], [2, 1, 5], [2, 2, 1], [2, 2, 2], [2, 2, 3], [2, 2, 4], [2, 2, 5], [2, 3, 1], [2, 3, 2], [2, 3, 3], [2, 3, 4], [2, 3, 5], [2, 4, 1], [2, 4, 2], [2, 4, 3], [2, 4, 4], [2, 4, 5], [2, 5, 1], [2, 5, 2], [2, 5, 3], [2, 5, 4], [2, 5, 5], [3, 1, 1], [3, 1, 2], [3, 1, 3], [3, 1, 4], [3, 1, 5], [3, 2, 1], [3, 2, 2], [3, 2, 3], [3, 2, 4], [3, 2, 5], [3, 3, 1], [3, 3, 2], [3, 3, 3], [3, 3, 4], [3, 3, 5], [3, 4, 1], [3, 4, 2], [3, 4, 3], [3, 4, 4], [3, 4, 5], [3, 5, 1], [3, 5, 2], [3, 5, 3], [3, 5, 4], [3, 5, 5], [4, 1, 1], [4, 1, 2], [4, 1, 3], [4, 1, 4], [4, 1, 5], [4, 2, 1], [4, 2, 2], [4, 2, 3], [4, 2, 4], [4, 2, 5], [4, 3, 1], [4, 3, 2], [4, 3, 3], [4, 3, 4], [4, 3, 5], [4, 4, 1], [4, 4, 2], [4, 4, 3], [4, 4, 4], [4, 4, 5], [4, 5, 1], [4, 5, 2], [4, 5, 3], [4, 5, 4], [4, 5, 5], [5, 1, 1], [5, 1, 2], [5, 1, 3], [5, 1, 4], [5, 1, 5], [5, 2, 1], [5, 2, 2], [5, 2, 3], [5, 2, 4], [5, 2, 5], [5, 3, 1], [5, 3, 2], [5, 3, 3], [5, 3, 4], [5, 3, 5], [5, 4, 1], [5, 4, 2], [5, 4, 3], [5, 4, 4], [5, 4, 5], [5, 5, 1], [5, 5, 2], [5, 5, 3], [5, 5, 4], [5, 5, 5]]