Why is a factorial recursive function iterating from lowest to highest number and not from highest to lowest number?

Question

I have this simple recursive function, which is calculating the factorial of a number. The result is good and it works like a charm.

def factorial(y):
  if y == 0:
    return 1

  elif y == 1:
    return 1

  else:
    result = y * factorial(y - 1)
    print(result)

return result

To understand the process I've added the print(result) function to see the value of the result variable at each iteration of the recursive function.

The output is:
2
6
24
120

I was expecting this output instead :
120
24
6
2

So, why is my recursive function iterating from the lowest number to the highest and not from the highest to the lowest number ?

Answer 1

The inner-most call finishes first, so that one prints first.

The outer-most call is only ready once all the inner calls finish, so it necessarily has to be printed only after the inner calls finish.

Try this for funsies:

def factorial(y, level=0):
  if y == 0:
    return 1

  elif y == 1:
    return 1

  else:
    print(level*" ", "pre-call, y=", y)
    result = y * factorial(y - 1, level=level+2)
    print(level*" ", "post-call, result=", result)

  return result


factorial(5)

Output is:

 pre-call, y= 5
   pre-call, y= 4
     pre-call, y= 3
       pre-call, y= 2
       post-call, result= 2
     post-call, result= 6
   post-call, result= 24
 post-call, result= 120

The nesting helps show the recursion level.