/**
 * Class for doing recursive maths. Assumes all integers are
 * non-negative (for simplicity no checks are made).  
 * @author Cara MacNish
 */
public class RMaths {

  /** 
   * increment an integer
   * @param i the integer to increment
   * @return i + 1
   */
  public static int increment(int i) {return i + 1;}

  /** 
   * decrement an integer
   * @param i the integer to decrement
   * @return i - 1
   */
  public static int decrement(int i) {return i - 1;}

  /**
   * add two integers
   * @param x the first integer
   * @param y the second integer, must be >= 0
   * @return x + y
   */
  public static int add(int x, int y) {
    if (y == 0) return x;
    else return add(increment(x), decrement(y));
  }

  /**
   * multiply two integers
   * @param x the first integer
   * @param y the second integer, must be >= 0
   * @return x × y
   */
  public static int multiply(int x, int y) {
    if (y == 0) return 0;
    else return add(x, multiply(x, decrement(y)));
  }


}