# Generate successive k-length permutations.
 
def permutations(iterable, k=None):
    def detail(a, k):
        if k == 0:
            yield ()
        else:
            for i, first in enumerate(a):
                for rest in detail(a[:i] + a[i+1:], k-1):
                    yield (first, *rest)
    a = list(iterable)
    return detail(a, len(a) if k is None else k)
 
# Test.
 
import itertools
import time
 
n = 3
a = list(range(n))
for k in range(2+len(a)):
    print(list(permutations(a, k)))
    print(list(itertools.permutations(a, k)))
 
def test(f, a):
    t = time.process_time()
    for _ in f(a):
        pass
    t = time.process_time() - t
    print('Elapsed: {:.6f}s'.format(t))
    m = sum(1 for _ in f(a))
    n = sum(1 for _ in itertools.permutations(a))
    assert m == n
    for x, y in zip(f(a), itertools.permutations(a)):
        assert x == y
 
n = 8
a = list(range(n))
test(permutations, a)
test(itertools.permutations, a)

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