Nested recursive function in python -

i tried implement nested recursive function in python giving error "runtimeerror: maximum recursion depth exceeded" can see function in following code. regarding question appreciated.

n=10  def test(n):     if n<=0:         return 1     else:         return test(test(n-1)+1)  print test(n) 

one important part of recursion every recursive call have closer anchor case, in case is:

if n<=0:     return 1 

however, code not getting close case. problem line:

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

since test returns 1 when reaches end case , add 1 result, let's see happens when call test(2):

the anchor case isn't executed , go straight else. return

test(test(1)+1) 

since 2-1=1. inner test call going go else case , call:

test(test(0)+1) 

here inner test call returns 1 (it has reached end case) means in line calling

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

again. here can see recursion never ending, hence maximum recursion depth exceeded error.

just clarify how make code (which example) work:

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

follow question:

why changing recursive call test(test(n-2)) result in infinite recursion?

well because of same reason pointed out right @ beginning. need closer anchor case. while can reach case of n<=0 inside nested recursive call test(n-2) can not reach inside outer function call.

note function returns 1 when reaches it's end case, if test(n-2) doesn't cause more recursions returns 1 (not 0), means end with

test(1) 

which again going cause infinite loop (since can not n <= 0 outer function call).

you have multiple options make recursion work case: changing return value or changing anchor case. changing if statement either of these prevent infinite recursion:

if n <= 0:     return 0 

or

if n <= 1:     return 1    //you return other value <= 1