python中的嵌套递归函数

Question

I tried to implement a nested recursive function in python it is giving an error "RuntimeError: maximum recursion depth exceeded" you can see the function in the following code. your help regarding the question is appreciated.

n=10

def test(n):
    if n<=0:
        return 1
    else:
        return test(test(n-1)+1)

print test(n)

Answer 1

One very important part of recursion is that with every recursive call you have to get closer to your anchor case, which in this case is:

if n<=0:
    return 1

However, with your code you are not getting close to this case. The problem is this line:

return test(test(n-1)+1)

Since test returns 1 when it reaches the end case and you add 1 to this result, let's see what happens when we call test(2) :

The anchor case isn't executed and you go straight into the else . The you return

test(test(1)+1)

since 2-1=1 . Your inner test call is also going to go to the else case and call:

test(test(0)+1)

Here your inner test call returns 1 (it has already reached the end case) which means that essentially in this line you are calling

test(2) //test(1+1)

again. Here you can see that your recursion is never ending, hence your maximum recursion depth exceeded error .

Just to clarify how you could make this code (which is obviously just an example) work:

def test(n):
    if n <= 0:
        return 1
    else:
        return test(test(n-1)-1)    //notice the -1 instead of +1

Follow up question:

Why does changing the recursive call to test(test(n-2)) also result in infinite recursion?

Well this is basically because of the same reason that I pointed out right at the beginning. You need to get closer to your anchor case. While you can reach the case of n<=0 inside the nested recursive call test(n-2) you can certainly not reach it inside the outer function call.

Note that your function returns 1 when it reaches it's end case, so even if test(n-2) doesn't cause any more recursions it returns 1 (not 0), which means you end up with

test(1)

which is again going to cause an infinite loop (since you can not get n to be <= 0 for this outer function call).

You have multiple options to make the recursion work for this case: By changing your return value or by changing your anchor case. So changing the if statement to either of these will prevent an infinite recursion:

if n <= 0:
    return 0

or

if n <= 1:
    return 1    //you could also return any other value <= 1