为了节省您可能的搜索和实验时间，下面是Python中的非递归置换解决方案，它也适用于Numba（从0.41版开始）：

@numba.njit()
def permutations(A, k):
    r = [[i for i in range(0)]]
    for i in range(k):
        r = [[a] + b for a in A for b in r if (a in b)==False]
    return r
permutations([1,2,3],3)
[[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]

要给人留下绩效印象：

%timeit permutations(np.arange(5),5)

243 µs ± 11.1 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)
time: 406 ms

%timeit list(itertools.permutations(np.arange(5),5))
15.9 µs ± 8.61 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)
time: 12.9 s

因此，只有在必须从njit函数调用它时才使用此版本，否则更倾向于itertools实现。

为了节省您可能的搜索和实验时间，下面是Python中的非递归置换解决方案，它也适用于Numba（从0.41版开始）：

@numba.njit()
def permutations(A, k):
    r = [[i for i in range(0)]]
    for i in range(k):
        r = [[a] + b for a in A for b in r if (a in b)==False]
    return r
permutations([1,2,3],3)
[[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]

要给人留下绩效印象：

%timeit permutations(np.arange(5),5)

243 µs ± 11.1 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)
time: 406 ms

%timeit list(itertools.permutations(np.arange(5),5))
15.9 µs ± 8.61 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)
time: 12.9 s

因此，只有在必须从njit函数调用它时才使用此版本，否则更倾向于itertools实现。

另一种解决方案：

def permutation(flag, k =1 ):
    N = len(flag)
    for i in xrange(0, N):
        if flag[i] != 0:
            continue
        flag[i] = k 
        if k == N:
            print flag
        permutation(flag, k+1)
        flag[i] = 0

permutation([0, 0, 0])

此解决方案实现了一个生成器，以避免在内存中保留所有排列：

def permutations (orig_list):
    if not isinstance(orig_list, list):
        orig_list = list(orig_list)

    yield orig_list

    if len(orig_list) == 1:
        return

    for n in sorted(orig_list):
        new_list = orig_list[:]
        pos = new_list.index(n)
        del(new_list[pos])
        new_list.insert(0, n)
        for resto in permutations(new_list[1:]):
            if new_list[:1] + resto <> orig_list:
                yield new_list[:1] + resto

def permutation(word, first_char=None):
    if word == None or len(word) == 0: return []
    if len(word) == 1: return [word]

    result = []
    first_char = word[0]
    for sub_word in permutation(word[1:], first_char):
        result += insert(first_char, sub_word)
    return sorted(result)

def insert(ch, sub_word):
    arr = [ch + sub_word]
    for i in range(len(sub_word)):
        arr.append(sub_word[i:] + ch + sub_word[:i])
    return arr


assert permutation(None) == []
assert permutation('') == []
assert permutation('1')  == ['1']
assert permutation('12') == ['12', '21']

print permutation('abc')

输出：['abc'，'acb'，'bac'，'bca'，'cab'，'cba']

使用标准库中的itertools.permutations：

import itertools
list(itertools.permutations([1, 2, 3]))

从这里改编的是itertools.permutations如何实现的演示：

def permutations(elements):
    if len(elements) <= 1:
        yield elements
        return
    for perm in permutations(elements[1:]):
        for i in range(len(elements)):
            # nb elements[0:1] works in both string and list contexts
            yield perm[:i] + elements[0:1] + perm[i:]

itertools.permutations文档中列出了两种替代方法

def permutations(iterable, r=None):
    # permutations('ABCD', 2) --> AB AC AD BA BC BD CA CB CD DA DB DC
    # permutations(range(3)) --> 012 021 102 120 201 210
    pool = tuple(iterable)
    n = len(pool)
    r = n if r is None else r
    if r > n:
        return
    indices = range(n)
    cycles = range(n, n-r, -1)
    yield tuple(pool[i] for i in indices[:r])
    while n:
        for i in reversed(range(r)):
            cycles[i] -= 1
            if cycles[i] == 0:
                indices[i:] = indices[i+1:] + indices[i:i+1]
                cycles[i] = n - i
            else:
                j = cycles[i]
                indices[i], indices[-j] = indices[-j], indices[i]
                yield tuple(pool[i] for i in indices[:r])
                break
        else:
            return

另一个基于itertools.product：

def permutations(iterable, r=None):
    pool = tuple(iterable)
    n = len(pool)
    r = n if r is None else r
    for indices in product(range(n), repeat=r):
        if len(set(indices)) == r:
            yield tuple(pool[i] for i in indices)