递归函数
在函数内部，可以调用其他函数。如果一个函数在内部调用自身本身，这个函数就是递归函数。
举个例子，我们来计算阶乘 n! = 1 * 2 * 3 * ... * n，用函数 fact(n)表示，可以看出：
fact(n) = n! = 1 * 2 * 3 * ... * (n-1) * n = (n-1)! * n = fact(n-1) * n
所以，fact(n)可以表示为 n * fact(n-1)，只有n=1时需要特殊处理。
于是，fact(n)用递归的方式写出来就是：
def fact(n): if n==1:return 1 return n * fact(n - 1)
如果要计算2的n次方，那就是：
def fact(n): if n==1:return 1 return 2 * fact(n - 1)
我们可以修改一下代码，详细的列出每一步(注意打印出来的内容的顺序哦）：
def fact(n):print("factorial has been called with n = " + str(n))if n == 1:return 1else:res = n * fact(n - 1)print("intermediate result for ", n, " * fact(", n - 1, "): ", res)return resprint(fact(10))
结果是：
C:\Python35\python.exe C:/pylearn/bottlelearn/4.py factorial has been called with n = 10 factorial has been called with n = 9 factorial has been called with n = 8 factorial has been called with n = 7 factorial has been called with n = 6 factorial has been called with n = 5 factorial has been called with n = 4 factorial has been called with n = 3 factorial has been called with n = 2 factorial has been called with n = 1 intermediate result for 2 * fact( 1 ): 2 intermediate result for 3 * fact( 2 ): 6 intermediate result for 4 * fact( 3 ): 24 intermediate result for 5 * fact( 4 ): 120 intermediate result for 6 * fact( 5 ): 720 intermediate result for 7 * fact( 6 ): 5040 intermediate result for 8 * fact( 7 ): 40320 intermediate result for 9 * fact( 8 ): 362880 intermediate result for 10 * fact( 9 ): 3628800 1814400000Process finished with exit code 0
进一步思考，如果，我们想实现递归的效果，但是，却不想用到递归，在python怎么实现呢：
def fact(n):result=1for i in range(2,n+1):result=result*ireturn resultprint(fact(1)) print(fact(2)) print(fact(10))
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