Inside a function, other functions can be called. A function is recursive if it internally calls itself.
For example, let's calculate the factorial n! = 1 x 2 x 3 x ... x n, expressed as a function fact(n), we can see that:
fact(n) = n! = 1 x 2 x 3 x ... x (n-1) x n = (n-1)! x n = fact(n-1) x n
Therefore, fact(n)it can be expressed as n x fact(n-1), only when n=1 needs special processing.
So, fact(n)it can be written recursively as:
def fact(n):
if n==1: return 1 return n * fact(n - 1)If we calculate fact(5), we can see the calculation process as follows according to the function definition:
===> fact(5)
===> 5 * fact(4)
===> 5 * (4 * fact(3))
===> 5 * (4 * (3 * fact(2)))
===> 5 * (4 * (3 * (2 * fact(1))))
===> 5 * (4 * (3 * (2 * 1)))
===> 5 * (4 * (3 * 2))
===> 5 * (4 * 6)
===> 5 * 24
===> 120
使用递归函数需要注意防止栈溢出。在计算机中，函数调用是通过栈（stack）这种数据结构实现的，每当进入一个函数调用，栈就会加一层栈帧，每当函数返回，栈就会减一层栈帧。由于栈的大小不是无限的，所以，递归调用的次数过多，会导致栈溢出