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 1
else:
res = n * fact(n - 1)
print("intermediate result for ", n, " * fact(", n - 1, "): ", res)
return res print(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
1814400000 Process 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=1
for i in range(2,n+1):
result=result*i
return result print(fact(1))
print(fact(2))
print(fact(10))