Lesson 3

Now let's implement the enumeration ourselves. The code will resemble binary sequence enumeration. For binary sequences it was simple: each position could be either zero or one. With permutations it's a bit more complex: at the first position, we can place any of the \(n\) elements; at the second — any of the remaining \((n-1)\); at the third — any of the remaining \((n-2)\); and so on.

def permutations(universe, k):
    def helper(perm, k):
        if len(perm) == k:
            yield perm
        else:
            for i in universe:
                if i not in perm:
                    yield from helper(perm + [i], k)

    yield from helper([], k)


for p in permutations('abc', 2):
    print(*p, sep='', end=' ')

ab ac ba bc ca cb