Simple loop Ackermann function

Question

How to write the Ackermann function with a simple non-recursive loop?

Answer 1

The following "iterative" version of Ackermann’s function (using lists of natural numbers) is a simple loop, expressed using tail recursion.

ackloop (n::0::list) = ackloop (n+1::list)
ackloop (0::m::list) = ackloop (1::m-1::list)
ackloop (n::m::list) = ackloop (n-1::m::m-1::list)
ackloop [m] = m

Now ack(m,n) = ackloop [n,m].

Answer 2

Here's a possible implementation:

import java.util.ArrayList;

public class LinearAckermann {

    static ArrayList<Long> mList = new ArrayList<Long>();

    public static long ackermann(long m, long n) {
        while (true) {
            if (m == 0) {
                n += 1;
                if (mList.isEmpty()) {
                    return n;
                } else {
                    int index = mList.size() - 1;
                    m = mList.get(index);
                    mList.remove(index);
                }
            } else if (n == 0) {
                m -= 1;
                n = 1;
            } else {
                mList.add(m - 1);
                n -= 1;
            }
        }
    }

    public static void main(String[] args) {
        System.out.println(ackermann(4, 1));
    }
}

It uses mList instead of a stack to hold pending work; when the stack becomes empty, it can return the accumulated value.