Question

Can someone please explain to me why "return 1" in this Python code returns the factorial of a given number? I understand recursion, but I do not understand why factorial(5) returns 120 when it clearly says to return 1.

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

Answer 1

ANS:

#factorial function
def factorial(n):
    #if n equals 0
    if n == 0:
        #returns 1
        return 1
    #if n not equals 0
    else:
        #returns n * factorial(n-1)
        return n * factorial(n - 1)

      
return 1 is applicable only if n equals 0
otherwise the else block will be executed

Example:
   factorial(5) is called
  
   n = 5 and not equals 0
   else block is executed
   ie., factorial(5) returns 5 * factorial(5 - 1) = 5 * factorial(4)
  
   now factorial(5) = 5 * factorial(4)
  
   in the else block factorial(4) is called
   n = 4 and not equals 0
   else block is executed
   ie., factorial(4) returns 4 * factorial(4 -1) = 4 * factorial(3)
  
  
   now factorial(5) = 5 * 4 * factorial(3)
  
   factorial(3) = 3 * factorial(3 - 1) = 3 * factorial(2)
  
   now factorial(5) = 5 * 4 * 3 * factorial(2)
  
   factorial(2) = 2 * factorial(2 - 1) = 2 * factorial(1)
  
   now factorial(5) = 5 * 4 * 3 * 2 * factorial(1)
  
   factorial(1) = 1 * factorial(1 - 1) = 1 * factorial(0)
  
   now factorial(5) = 5 * 4 * 3 * 2 * 1 * factorial(0)
  
   factorial(0) is called
   n == 0
   if block is executed
   ie., factorial(0) returns 1
  
   now factorial(5) = 5 * 4 * 3 * 2 * 1 * 1
  
   no more function calls.
   ie., factorial(5) returns 5 * 4 * 3 * 2 * 1 * 1
   ie., factorial(5) returns 120