def pi(N):

    ' 计算pi的值 '

    # step 1: 创建一个奇数序列: 1, 3, 5, 7, 9, ...

    odd_num_seq = itertools.count(1, 2)

    # step 2: 取该序列的前N项: 1, 3, 5, 7, 9, ..., 2*N-1.

    odd_num = itertools.takewhile(lambda x: x <= (2*N-1), odd_num_seq)

    # step 3: 添加正负符号并用4除: 4/1, -4/3, 4/5, -4/7, 4/9, ...

    plus_or_minus_sign = 1

    pi_value = 0

    for i in odd_num:

        pi_value += plus_or_minus_sign * (4 / i)

        plus_or_minus_sign = plus_or_minus_sign * -1

    # step 4: 求和:

    return pi_value