Question

Ackermann’s function is a recursive mathematical algorithm that can be used to test how well a computer performs recursion. Write a method ackermann(m, n), which solves Ackermann’s function. Use the following logic in your method:

If m = 0, then return n + 1

If n = 0, then return ackermann(m-1, 1)

Otherwise, return ackermann(m -1, ackermann(m, n - 1))

Test your method in a java program that displays the return values of the following method calls:

ackermann(0, 0), ackermann(0, 1), ackermann(1, 1), ackermann(1, 2) ackermann(1, 3), ackermann(2, 2), ackermann(3, 2)

Answer 1

Explanation:

Here is the code which has the method ackermann taking the integer values m and n.

Then the if conditions are applied using recursion as given in the pseudocode above.

Then the given calls are made.

Code:

public class Main
{
public static int ackermann(int m, int n)
{
if(m==0)
return n+1;
  
if(n==0)
return ackermann(m-1, 1);
  
return ackermann(m-1, ackermann(m, n-1));
}
  
   public static void main(String[] args) {
      
       System.out.println(ackermann(0, 0));
       System.out.println(ackermann(0, 1));
       System.out.println(ackermann(1, 1));
       System.out.println(ackermann(1, 2));
       System.out.println(ackermann(1, 3));
       System.out.println(ackermann(2, 2));
       System.out.println(ackermann(3, 2));
   }
}

output:

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