Question

I’m really trying to wrap my brain around how recursion works and understand recursive algorithms. For example, the code below returns 120 when I enter 5, excuse my ignorance, and I’m just not seeing why?

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

answer = int (raw_input('Enter some number: '))

print fact(answer)

Answer 1

lets walk through the execution.

fact(5):
   5 is not 0, so fact(5) = 5 * fact(4)
   what is fact(4)?
fact(4):
   4 is not 0, so fact(4) = 4 * fact(3)
   what is fact(3)?
fact(3):
   3 is not 0, so fact(3) = 3 * fact(2)
   what is fact(2)?
fact(2):
   2 is not 0, so fact(2) = 2 * fact(1)
   what is fact(1)?
fact(1):
   1 is not 0, so fact(1) = 1 * fact(0)
   what is fact(0)?
fact(0):
   0 IS 0, so fact(0) is 1

Now lets gather our result.

fact(5) = 5* fact(4)

substitute in our result for fact(4)

fact(5) = 5 * 4 * fact(3)

substitute in our result for fact(3)

fact(5) = 5 * 4 * 3 * fact(2)

substitute in our result for fact(2)

fact(5) = 5 * 4 * 3 * 2 * fact(1)

substitute in our result for fact(1)

fact(5) = 5 * 4 * 3 * 2 * 1 * fact(0)

substitute in our result for fact(0)

fact(5) = 5 * 4 * 3 * 2 * 1 * 1 = 120

And there you have it. Recursion is the process of breaking a larger problem down by looking at it as successfully smaller problems until you reach a trivial (or “base”) case.