Compute the fraction of combinations of Set cards that contain a Set; see http://math.stackexchange.com/questions/202862

Question202862.java

public class Question202862 {
    final static int nfeatures = 4;
    final static int nvalues = 3;
    final static int ncards = (int) Math.pow (nvalues,nfeatures);

    static int thirdFeature (int f1,int f2) {
        return f1 == f2 ? f1 : 3 - (f1 + f2);
    }

    static int thirdCard (int c1,int c2) {
        int thirdCard = 0;
        for (int i = 0,pow = 1;i < nfeatures;i++,pow *= nvalues)
            thirdCard += pow * thirdFeature ((c1 / pow) % nvalues,(c2 / pow) % nvalues);
        return thirdCard;
    }

    static int [] nvetos = new int [ncards];
    final static int ndealt = 9;
    static int [] dealt = new int [ndealt + 1];

    static void add (int i,int sign) {
        for (int j = 0;j < ndealt;j++)
            if (j != i)
                nvetos [thirdCard (dealt [i],dealt [j])] += sign;
    }

    static void change (int i,int value) {
        add (i,-1);
        dealt [i] = value;
        add (i,1);
    }

    public static void main (String [] args) {
        dealt [ndealt] = ncards; // sentinel
        for (int i = 0;i < ndealt;i++)
            dealt [i] = i;

        for (int i = 1;i < ndealt;i++)
            for (int j = 0;j < i;j++)
                nvetos [thirdCard (dealt [i],dealt [j])]++;

        long count = 0;
        long total = 0;

        outer:
        for (;;) {
            // check this combination for a set
            for (int i = 0;i < ndealt;i++)
                if (nvetos [dealt [i]] != 0) {
                    count++;
                    break;
                }
            total++;

            // move to the next combination
            for (int i = ndealt;;i--) {
                if (i == 2)
                    break outer;
                if (dealt [i - 1] != dealt [i] - 1) {
                    change (i - 1,dealt [i - 1] + 1);
                    while (i < ndealt) {
                        change (i,dealt [i - 1] + 1);
                        i++;
                    }
                    break;
                }
            }
        }

        System.out.println (count + " / " + total + " = " + count / (double) total);
    }
}