How many times is this function called?

Question

I have this subalgorithm on recursion and I know that it's called 5 times, but I don't understand why. The initial values are m=1, n=2.

I've thought the function is called for 7 times.

int Ack(int m, int n)
{
    if (m==0) 
        return n+1;
    else 
         {
            if (m>0 && n==0) 
                return Ack(m-1,1);
            else 
                return Ack(m-1,Ack(m,n-1));
        }
}

I expect that it's called 7 times or even more, but the actual number is 5.

This how 7 is arrived at:

1. Ack(1,2)
2. Ack(0,Ack(1,1))
3. Ack(1,1)
4. Ack(0,Ack(1,0))
5. Ack(1,0)
6. Ack(0,1), a function which returns 2. Ack(0,1)=Ack(1,0)=2 ==>
7. Ack(0,2) (we came back to number 4) = 3
8. Ack(0,3) (we came back to number 2)

Answer 1

您重复计算了 2 个调用：#7 与 #4 相同，#8 与 #2 相同（仅显示Ack返回的值）：“回来”与调用不同。