def pi(N): """ 计算pi的值 """ # # step 1: 创建一个奇数序列: 1, 3, 5, 7, 9, ... # odd_list = itertools.count(1, 2) # 1开始 步长为2 # # step 2: 取该序列的前N项: 1, 3, 5, 7, 9, ..., 2*N-1. # odds = itertools.takewhile(lambda x: x <= 2 * N - 1, odd_list) odds = (x * 2 + 1 for x in range(N)) # step 3: 添加正负符号并用4除: 4/1, -4/3, 4/5, -4/7, 4/9, ... symbol = itertools.cycle([1, -1]) # step 4: 求和: sum = 0 for i in odds: sum += 4 * next(symbol) / i return sum# 测试:print(pi(10))print(pi(100))print(pi(1000))print(pi(10000))assert 3.04 < pi(10) < 3.05assert 3.13 < pi(100) < 3.14assert 3.140 < pi(1000) < 3.141assert 3.1414 < pi(10000) < 3.1415print('ok')
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