/**Demonstration of three types of recursion

 *

 * @author TK Rogers

 * @version 10-16-08

 */

public class RecursiveMultiplication {

    public static void main ( ) {

        System.out.println ("Note that \"a\" remains constant while \"b\"

                                       decreases by 1 in each iteration.");

        System.out.println ("4 x 2 = " + multiply(4, 2) + "\n");

                                                                               // ^ creates a new line.

        System.out.println ("Note that \"name\" remains constant while \"n\"

                                        decreases by 1 in each iteration.");

        hi ("Bob" , 3);

        System.out.println ("\nNote that \"x\" decreases by 1 in each iteration.");

        System.out.println ("       Total = " + addFractions(3));

    }

 

    /** Purpose: Method returns a * b

     *  Preconditions: two integers

     *  Postconditions: returns a * b.

        */

    public static int multiply (int a, int b) {

        System.out.println ("a = " + a + ", b = " + b);

        if (b <= 1) { //stops the recursion

            return a;

        }

        return a + multiply(a,b-1);

    }

     /**Purpose: Method causes "hello " + name to be output on n lines

     *  Preconditions: a string representing a name to output, an integer

     *                           representing the number of times the sting is output.

     *  Postconditions: none.

     */

    static int hi (String name, int n) {

        if (n==0) { //stops the recursion

            System.out.println ("saying hello to " + name + " has stopped, n = " + n);

            return 0;

        }

        System.out.println ("hello " + name + ", n = " + n);

        return hi (name, n-1);               

    }

 

    /**Purpose: Method returns the series 1/1 + 1/2 + 1/3 + ... + 1/x

     * Preconditions: an integer x for the above series

     * Postconditions: returns the value for the above series.

*/

    static double addFractions (int x) {

        System.out.println ("x = " + x + ", 1.0 / x = " + 1.0 / x);

        if (x <= 1) return 1.0; //stops the recursion

        else return 1.0 / x + addFractions (x-1);

 

          // If x = 3, the recursion runs as follows:

      // return  1.0 / 3 + addFractions (x-1);

                                    // return  1.0 / 2 + addFractions (x-1);

                                                       // return  1.0 / 1;

                                                             // At this point, the computer adds 

                                                             //  the 3 bold print values from

                                                             // bottom to top.

    }

}