/*
 *   Intro to Programming CSE 1310
 * University of Texas at Arlington
 */

package coderecursion2nov17;

import java.util.Scanner;

/**
 *
 * @author jcmtiernan
 */
public class CodeRecursion2Nov17 
{

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) 
    {
       // calling a recursive method
        int testValue = 0;
        double testFac = 0;
        Scanner input = new Scanner(System.in);
        System.out.print("Please enter a positive integer value as an index to find Fibonacci value of: ");
        testValue = input.nextInt();
        testFac = fib(testValue);
        System.out.println("");
        System.out.println("The result of fib for "+testValue+" is "+testFac);
        
    }
    /**
     * Method fac - factorial function written recursively.
     * The function factorial can be generalized as shown below.
     * Method fac takes the generalization and implements it.

        0! = 1   // base case – stops the recursion

        1! = 0! * 1  // examples
        2! = 1! * 2
        3! = 2! * 3

        k! = (k – 1)! * k    // general (recursive) case – calls itself with different parameters

        To write a recursive function you must have:
                At least one base case, may have more than one base case
                At least one recursive case
                May also have an error case (or condition)

        Function header ( with access “static” return_type name (parameters)
        {
                test for the base case
                        return action for base case

                possible other tests
                        with other actions

                recursive call using return statement
        }
        public static int fac( int k )
        {
                if ( k == 0 )
                        return 1;
                return fac(k – 1) * k ;   
        }

        * @param k
     * @return 
     */
    public static int fac(int k)
    {
        
        if (k < 0)
            return 0;
        if (k == 0)
            return 1;
        System.out.println("in fac, k is "+k);
        return (fac(k-1) * k);
    }
    /**
     * Fibonacci series
     * Values: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144
     *  Index: 0, 1, 2, 3, 4, 5, 6, 7,  8,  9,  10, 11, 12
     * 
     * m is the index
     * fib(m) = fib(m-1) + fib(m-2)
    */
    public static int fib(int m)
    {
        System.out.println("in fib with m = "+m);
        if ((m == 0) || (m == 1)) // base cases
            return m;
        if (m < 0)   // error case
            return -1;
        return fib(m-1)+fib(m-2);
        
    }
}