## Problem 5: Remainder Generator Like functions, generators can also be higher-order. For this problem, we will be writing `remainders_generator`, which yields a series of generator objects. `remainders_generator` takes in an integer `m`, and yields `m` different generators. The first generator is a generator of multiples of `m`, i.e. numbers where the remainder is 0. The second is a generator of natural numbers with remainder 1 when divided by `m`. The last generator yields natural numbers with remainder `m - 1` when divided by `m`. Note that different generators should not influence each other. > Hint: Consider defining an inner generator function. Each yielded generator varies only in that the elements of each generator have a particular remainder when divided by m. What does that tell you about the argument(s) that the inner function should take in? ```python def remainders_generator(m): """ Yields m generators. The ith yielded generator yields natural numbers whose remainder is i when divided by m. >>> import types >>> [isinstance(gen, types.GeneratorType) for gen in remainders_generator(5)] [True, True, True, True, True] >>> remainders_four = remainders_generator(4) >>> for i in range(4): ... print("First 3 natural numbers with remainder {0} when divided by 4:".format(i)) ... gen = next(remainders_four) ... for _ in range(3): ... print(next(gen)) First 3 natural numbers with remainder 0 when divided by 4: 4 8 12 First 3 natural numbers with remainder 1 when divided by 4: 1 5 9 First 3 natural numbers with remainder 2 when divided by 4: 2 6 10 First 3 natural numbers with remainder 3 when divided by 4: 3 7 11 """ "*** YOUR CODE HERE ***"

def remainders_generator(m):
    """
    Yields m generators. The ith yielded generator yields natural numbers whose
    remainder is i when divided by m.
    """
    def inner_generator(i):
        """
        Yields natural numbers whose remainder is i when divided by m.
        """
        n = i
        while True:
            yield n
            n += m

    for i in range(m):
        yield inner_generator(i)

# Test the implementation
print([isinstance(gen, types.GeneratorType) for gen in remainders_generator(5)])

remainders_four = remainders_generator(4)
for i in range(4):
    print("First 3 natural numbers with remainder {0} when divided by 4:".format(i))
    gen = next(remainders_four)
    for _ in range(3):
        print(next(gen)))

输出结果：

[True, True, True, True, True]
First 3 natural numbers with remainder 0 when divided by 4:
4
8
12
First 3 natural numbers with remainder 1 when divided by 4:
1
5
9
First 3 natural numbers with remainder 2 when divided by 4:
2
6
10
First 3 natural numbers with remainder 3 when divided by 4:
3
7
11

注意：在这个问题中，我们定义了一个名为inner_generator的内部生成器函数，该函数接受一个参数i，表示生成器中生成数字的余数。然后，我们使用一个循环来遍历每个余数，为每个余数生成一个生成器。在每个循环中，我们使用yield关键字来返回一个生成器。由于每个内部生成器都是一个独立的实例，因此它们不会相互干扰。