Converting a function with two recursive calls into an interative function

Question

I've got a function that has two recursive calls and I'm trying to convert it to an iterative function. I've got it figured out where I can do it with one call fairly easily, but I can't figure out how to incorporate the other call.

the function:

def specialMultiplication(n):
    if n < 2:
        return 1
    return n * specialMultiplication(n-1) * specialMultiplication(n-2)

If I just had one of them, it would be really easily:

def specialMult(n, mult = 1):
    while n > 1: 
        (n, mult) = (n-1, n * mult) # Or n-2 for the second one
    return mult

I just can't figure out how to add the second call in to get the right answer overall. Thanks!

Answer 1

If you don't mind changing the structure of your algorithm a bit more, you can calculate the values in a bottom-up fashion, starting with the smallest values.

def specialMultiplication(max_n):
    a = b = 1
    for n in range(1, max_n+1):
        a, b = b, a*b*n
    return b