递归生成器中的调用顺序？

Question

def powerset(seq):
    """
    Returns all the subsets of this set. This is a generator.
    """
    if len(seq) <= 1:
        yield seq
        yield []
    else:
        for item in powerset(seq[1:]):
            yield [seq[0]]+item
            yield item

上面是一个递归生成器，可以生成所有幂集。例如，

powerset([1,2,3])=>[1, 2, 3][2, 3][1, 3][3][1, 2][2][1][]

但我对它的工作原理感到困惑。看来它是按这个顺序产生的：

powerset([1,2,3])=>powerset([2,3])=>powerset([3]) 

which is outside=>inside，与我理解的“递归”含义相反，inside=>outside，例如递归求解阶乘（5）：

factorial has been called with n = 5
factorial has been called with n = 4
factorial has been called with n = 3
factorial has been called with n = 2
factorial has been called with n = 1
intermediate result for  2  * factorial( 1 ):  2
intermediate result for  3  * factorial( 2 ):  6
intermediate result for  4  * factorial( 3 ):  24
intermediate result for  5  * factorial( 4 ):  120
120

那么如何理解递归生成器呢？

Answer 1

让我们看看：

这是递归部分：

for item in powerset(seq[1:]):
            yield [seq[0]]+item
            yield item

基本上这意味着

for every result in a smaller powerset:

    return the not used value + the result

    then return result alone

如果我们看一下 powerset([3]);这首先返回 [3] 然后返回 [] 因为它的长度为 1

powerset([2,3]) 调用 powerset([3]) 然后执行：

1. 返回 2 和 第一个项的 powerset([3]) (=[2,3])
2. 只返回 第一个项的 powerset([3]) (=[3])
3. 返回 2 和 第二个 项的 powerset([3]) (=[2])
4. 返回 第二个项 powerset([3]) (=[])

这导致[2,3] [3] [2] []

如果我们调用 powerset([1,2,3]) 会发生同样的事情

1. 1+[2,3]
2. [2,3]
3. 1+[3]
4. [3]
5. 1+[2]
6. [2]
7. 1+[]
8. []

Answer 2

基本上，您的生成器实现了回溯算法：在到达任何yield 之前，已经进行了许多递归调用。程序文本中首先出现的 yield 调用只有在递归嵌套足够深以使剩余列表的长度为 1 时才会进行，并且只有在此之后才会进入 for 循环，因为这需要最里面的生成器来产生一些东西。

powerset([1,2,3]) level 1: seq1=[1,2,3]
| powerset([2,3]) level 2: seq2=[2,3]
| | powerset([3]) level 3: seq3=[3]
| | | yield [3]   3: yield seq3, becomes item2 in level 2
| | yield [2,3]   2: yield [seq2[0]] + item2, becomes item1 in level 1
| yield [1,2,3]   1: yield [seq1[0]] + item1, output
| yield [2,3]     1: yield item1, output
...

只有在for 循环的最后一行“冒泡”时，最内层生成的短序列才会出现在最外层调用的输出中。在此之前，会产生与seq[0] 的组合。

如果您想反过来输出，请尝试在循环内交换两个 yield 行。