import itertools
def pi(N):
    ' 计算pi的值 '
    # step 1: 创建一个奇数序列: 1, 3, 5, 7, 9, ...
    number = itertools.count(start=1, step=2)
    # step 2: 取该序列的前N项: 1, 3, 5, 7, 9, ..., 2*N-1.
    result = itertools.takewhile(lambda x:x<=2*N-1, number)
    # step 3: 添加正负符号并用4除: 4/1, -4/3, 4/5, -4/7, 4/9, ...
    n = map(lambda x:(-1)**((x//2)%2)*4/x, result)
    # step 4: 求和:
    return sum(n)