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"""
函数递归调用 - 函数直接或者间接的调用了自身
1. 收敛条件
2. 递归公式

n! = n * (n-1)!
f(n) = f(n-1) + f(n-2)
1 1 2 3 5 8 13 21 34 55 ...
"""
from contextlib import contextmanager
from time import perf_counter


def fac(num):
    """求阶乘"""
    assert num >= 0
    if num in (0, 1):
        return 1
    return num * fac(num - 1)


def fib2(num):
    """普通函数"""
    a, b = 1, 1
    for _ in range(num - 1):
        a, b = b, a + b
    return a


def fib3(num):
    """生成器"""
    a, b = 0, 1
    for _ in range(num):
        a, b = b, a + b
        yield a


# 动态规划 - 保存可能进行重复运算的中间结果（空间换时间）
def fib(num, results={}):
    """斐波拉切数"""
    assert num > 0
    if num in (1, 2):
        return 1
    try:
        return results[num]
    except KeyError:
        results[num] = fib(num - 1) + fib(num - 2)
        return results[num]


@contextmanager
def timer():
    try:
        start = perf_counter()
        yield
    finally:
        end = perf_counter()
        print(f'{end - start}秒')


def main():
    """主函数"""
    # for val in fib3(20):
    #     print(val)
    # gen = fib3(20)
    # for _ in range(10):
    #     print(next(gen))
    for num in range(1, 121):
        with timer():
            print(f'{num}: {fib(num)}')
    # print(fac(5))
    # print(fac(-5))


if __name__ == '__main__':
    main()

Hannoi

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def hannoi(n, a, b, c):
    if n == 1:
        print(a, '-->', c)
        return
    else:
        hannoi(n - 1, a, c, b)
        print(a, '-->', c)
        hannoi(n - 1, b, a, c)

hannoi(10, "a", "b", "c")

renyi停车常数

随机停车

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'''
renyi停车常数
0.7475972
'''
import random
def parking(low,high):
    if high-low<1:
        return 0
    else:
        x=random.uniform(low,high-1)
        return parking(low,x)+1+parking(x+1,high)
print parking(0,5)