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Can every recursion be converted into iteration?

Can always or which cases a recursive function be converted into a non-recursive function or set of non-recursive functions?

Can you point me to examples which work and do not work?

Thanks

Answer 1

This is always possible, because you can emulate the call stack yourself. However, it’s not always easy to do.

The easy cases are tail recursion: these don’t even require a stack. For example, this guy is trivially converted into a for loop:

def countdown(n):
    if n >= 0:
        print n
        countdown(n-1)

Even if the function is not strictly tail-recursive, you can sometimes still get away without a stack. For example, the classical factorial function:

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

It gets harder when there are multiple recursive calls. Consider, for example, quicksort:

def quicksort(array):
    if len(array) <= 1:
        return array
    else:
        pivot = array[0]
        left = quicksort([x for x in array[1:] if x < pivot])
        right = quicksort([x for x in array[1:] if x >= pivot])
        return left + [pivot] + right

Although it’s definitely possible to do this without recursion, you’ll have to build a stack yourself, and construct a while loop that iterates until the stack is empty.