Changing an iterative function into a recursive one

Question

Consider:

def itr(n):
    s = 0
    for i in range(0, n+1):
        s = s + i * i
    return s

This is a simple iterative function that I would like to change into a recursive function.

def rec(n):
    import math
    if n!=0:
        s=n-(2*math.sqrt(n))
        if s!=0:
            return(s+rec(n))
        else:
            return(n)
    else:
        return n

This is my try at doing the said thing, but I cannot quite get it right.

Why does not my solution work? What is the solution?

Answer 1

Use:

def recursive(total, n):
    if n == 0:
        return total
    else:
        return recursive(total + n * n, n - 1)

A couple of thoughts:

• This can be refactored to using only a single argument, but by supplying both the total and the current iteration count, it is easier to see how to transform the iterative approach to a recursive one.
• While this function can be made recursive, it should not be, as there isn't any advantage over the iterative approach.