import java.util.Scanner;

/** Formula2.java - Example program illustrating how to use recursion
 *  in simple examples involving some recursive formula.
 *  Note that in each recursive function there is a base case, and
 *  a recursive case.  We need the base case to know when the recursion stops.
 *  (This time, with diagnostic output to show the recursion.)
 */
public class Formula2
{
  public static void main(String [] args)
  {
    System.out.print("Enter a positive integer:  ");
    Scanner kbd = new Scanner(System.in);
    int a = Integer.parseInt(kbd.nextLine());
    System.out.printf("You entered %d\n", a);

    System.out.printf("Odd number # %d is %d\n", a, odd(a));
    System.out.printf("%d factorial is %d\n", a, fact(a));
    System.out.printf("Term # %d in Fibonacci sequence is %d\n", a, fib(a));
  }

  public static int odd(int n)
  {
    System.out.printf("odd(%d):  start\n", n);
    if (n == 1)
    {
      System.out.printf("odd(%d):  base case, returning 1\n", n);
      return 1;
    }
    else
    {
      System.out.printf("odd(%d):  Making recursive call odd(%d)\n", n, n-1);
      int returnValue = 2 + odd(n-1);
      System.out.printf("odd(%d):  After recursive call, returning %d\n",
			 n, returnValue);
      return returnValue;
    }
  }

  public static int fact(int n)
  {
    System.out.printf("fact(%d):  start\n", n);
    if (n == 0)
    {
      System.out.printf("fact(%d):  base case, returning 1\n", n);
      return 1;
    }
    else
    {
      System.out.printf("fact(%d):  Making recursive call fact(%d)\n", n, n-1);
      int returnValue = n * fact(n-1);
      System.out.printf("fact(%d):  After recursive call, returning %d\n",
			 n, returnValue);
      return returnValue;
    }
  }

  public static int fib(int n)
  {
    System.out.printf("fib(%d):  start\n", n);
    if (n <= 2)
    {
      System.out.printf("fib(%d):  base case, returning 1\n", n);
      return 1;
    }
    else
    {
      System.out.printf("fib(%d):  Making left recursive call to fib(%d)\n",
			 n, n-1);
      int leftValue = fib(n-1);
      System.out.printf("fib(%d):  Left recursive call came back with %d\n",
                         n, leftValue);

      System.out.printf("fib(%d):  Making right recursive call to fib(%d)\n",
			 n, n-2);
      int rightValue = fib(n-2);
      System.out.printf("fib(%d):  Right recursive call came back with %d\n",
                         n, rightValue);

      int returnValue = leftValue + rightValue;
      System.out.printf("fib(%d):  After recursive calls, returning %d\n",
			 n, returnValue);
      return returnValue;
    }
  }
}