/**
 * Computing fibonacci numbers recursively.
 * The core idea here is that there is a public method which allows the user 
 * to say "I want the nth fibb number", and a private recursive function that
 * does the wark using some extra parameters that the public metod does not, and
 * should not, have
 * 
 * @author gtowell
 * Created: Aug 11, 2021
 */
import java.math.BigInteger;

public class Fibb {
    /**
     * Private recursive function for doign fibonacci
     * @param fibNumA the smaller number
     * @param fibNumB the larger number
     * @param counter home much work is still to be done
     * @return the Nth fibb number
     */
    private BigInteger fibonacciUtil(BigInteger fibNumA, BigInteger fibNumB, int counter)
    {
        //System.out.println(counter + " " + fibNumA + " " + fibNumB);
        if (counter==1)
            return fibNumA.add(fibNumB);
        return fibonacciUtil(fibNumB, fibNumA.add(fibNumB), counter-1);
    }

    /**
     * Return the Nth fibonacci number.
     * @param n the fibb number to calculate
     * @return the Nth fibb number
     */
    public BigInteger fibonacci(int n) {
        // check that n is valid
        if (n<=0) return BigInteger.valueOf(0);
        if (n < 3)
            return BigInteger.valueOf(1);
        // call private func to do the calculation
        return fibonacciUtil(BigInteger.valueOf(1), BigInteger.valueOf(1), n-2);
    }

    public static void main(String[] args) {
        Fibb fib = new Fibb();
        for (int i=0; i<16; i++)
            System.out.println("Fibb number " + i + " = " + fib.fibonacci(i));
    }
}