python - Understanding factorial recursion -

i'm looking on factorial example of recursion , make sure i'm understanding correctly!

def factorial(n):     if(n == 0):         return 1     else:         return n * factorial(n-1) 

would right in saying:

factorial(4) = factorial(4-1) * 4 = factorial(3-1) *3 *4 = factorial(2-1) *2 *3 *4 = factorial(1-1) *1 *2 *3 *4 = 24

because factorial(1-1) = factorial(0) base case shows = 1 , multiply 2, 3 4.

is correct way of looking @ it?

thanks in advance!

yes is. since it's recursion, works opposite way. once had interviewer explain me :

say, fact(5) :

 - fact(5) = 5 * fact(4)            - fact(4) = 4 * fact(3)                      - fact(3) = 3 * fact(2)                                   - fact(2) = 2 * fact(1)                                          - fact(1) = 1 * fact(0)                                                     - fact(0) = 1                                                    // condition returns 1. 

now, imagine - sign above stands return. return whatever after - sign. lowest line, 1 returned. then, have 1 returned in fact(1) i.e. 1 * 1. happens in reverse cascade :

 = 120  - fact(5) = 5 * 24            - fact(4) = 4 * 6 = 24                      - fact(3) = 3 * 2 = 6                                  - fact(2) = 2 * 1 = 2                                          - fact(1) = 1 * 1 = 1                                                    - fact(0) = 1 

remember whenever work on recursion, works in reverse. should breaking recursion problem down.

this why tail recursion , related optimization important. in memory, each of calls delayed , can't return until calls above (below in diagram) finish , return. deep recursive call can cause stack overflow unless compiler/interpreter optimize turning version in op, such partial results evaluated , not delayed. python not perform optimization , must careful recursive calls.