/*
 * Chapter8Number15.java
 *
 * JM 8 (15)
 *
 * Consider all proper fractions that have positive denominators on [1, 100].
 * Write a program that finds the two such fractions that are closest to
 * 17 / 76, one from above and one from below.
 * Hint: http://en.wikipedia.org/wiki/1985 & http://en.wikipedia.org/wiki/1567
 *
 * @author Nick Ku <nicholasku@gmail.com>
 */


public class Chapter8Number15
{
    public static double num = 1;
    public static double denominator = 1;

    public static void main(String[] args)
    {
        // Initialize variables.
        int targetNumerator = 17, targetDenominator = 76, maxDivisions = 100;
        int // These values insure that the fractions start out at 1.
            lessNumerator = 0,
            lessDenominator = maxDivisions,
            greaterNumerator = maxDivisions,
            greaterDenominator = maxDivisions;
        double target = (double) targetNumerator / targetDenominator;

            for (denominator = 1; denominator < 100; denominator ++)
     {
       for (num = 1; num < denominator; num++)
       {
         if (1.0 * greaterNumerator / greaterDenominator > 1.0 * num / denominator && num / denominator > target)
         {
           greaterNumerator = (int)num;
           greaterDenominator = (int)denominator;
         }
                if (1.0 * lessNumerator / lessDenominator <  1.0 * num / denominator && num / denominator < target)
         {
           lessNumerator = (int)num;
           lessDenominator = (int)denominator;
         }
       }
     }


        // Print results.
        System.out.printf("Result: %d / %d < %.5f & %d / %d > %.5f\n",
                          lessNumerator, lessDenominator, target,
                          greaterNumerator, greaterDenominator, target);
        System.out.println("Expected: 19 / 85 < 0.22368 & 15 / 67 > 0.22368");
    }
}