Question

i have question how write program which calculates following procedures

http://en.wikipedia.org/wiki/Tetration

i have exponential program which returns x^n here is code

public class Exp{
public static long  exp(long x,long n){
   long t=0;
 if (n==0){
     t= 1;
}
else{
       if (n %2==0){
   t=  exp(x,n/2)* exp(x,n/2);

}
else{

 t= x*exp(x,n-1);
}

}
 return t;
}


public static  void main(String[]args){
long x=5L;
long n=4L;
 System.out.println(exp(x,n));


}
}

but how use it in Tetration program?please help

Answer 1

Tetration x ↑↑ n can be defined recursively as

x ↑↑ n  =  x ^ (x ↑↑ (n-1))

So you could write

long tetration(long x, long n) {
   if (n == 0)
     return 1;
   else
     return exp(x, tetration(x, n-1));
}

But notice that the tetration grows extremely fast, a long is will not be big enough to store even 4 ↑↑ 3 (= 1.3 × 10¹⁵⁴). Perhaps you need a BigInteger.

(BTW, exp usually refers to the unary function e^x, the binary function x^y is usually called pow.)