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