/* An instance of this class deems numbers whose absolute value is prime
** to be RED and others to be BLUE.
*/
public class PrimeVsComposite implements RedBlueClassifier<Integer> {

   // constructor
   // -----------

   // No constructor needed, as there are no instance variables to initialize.


   // methods of interest
   // -------------------

   /* Returns true if the absolute value of the given number is prime,
   ** false otherwise.
   */
   public boolean isRed(Integer num) {
      return isPrime(Math.abs(num));
   }

   /* Returns true if the given number is not RED.
   */
   public boolean isBlue(Integer num) { return !isRed(num); }


   // private
   // -------

   /* Returns true iff the given number is prime.
   ** A number is prime iff it is positive and has exactly two
   ** divisors (1 and itself).
   ** pre: num >= 0
   */
   private boolean isPrime(int num) {
      boolean result;
      if (num == 2) 
         { result = true; }
      else if (num == 1  ||  num % 2 == 0)
         // Neither 1 nor any even number other than 2 is prime.
         { result = false; }
      else {
         // num must be an odd number greater than 2.  Such a number is
         // prime iff it has no odd divisor that is <= to its square root.
         // What follows is a search for such a divisor.
         int numSqrt = (int)(Math.sqrt(num));
         int cand = 3;  // candidate divisor
         // loop invariant: 3 <= cand <= numSqrt + 2 &&
         //                 num has no divisors in [3..cand)
         while (cand <= numSqrt  &&  num % cand != 0) {
            cand = cand + 2;
         }
         // If cand > numSqrt, num has no divisors in [3..numSqrt] and 
         // thus is prime; otherwise cand is equal to num's smallest 
         // nontrivial divisor, making num non-prime.
         result = cand > numSqrt;
      }
      return result;
   }
}