General algorithm for cartesian product

Question

i am looking for an algorithm to get the cartesian product from a set of sets like {{1,2,3,4},{a,b,c},{x,y,z,7,15}...} - this means in most general form.
google yields no results :-(. i think implementing it by myself is not a good idea.

Answer 1

dermoritz wrote:
prometheuzz is your algorithm better than n*mi n: number of sets mi: cardinality of the set i ?
can you short explain the algorithm?You can't do any better than that because for n sets: S(0), S(1), S(2) ... S(n-1) there are prod(i in [0, n), |S(i)|) elements of the caresian product. Prometeuzz algorithm generates
one at ever pass of the loop executing n steps per element. If you're afraid that the product number will be too large you can also fiddle with the indexes themselves:
// scard[i] == |S(i)|
// prod[i] == element of S(i) in product
int[] next(int[] scard, int[] prod) {
   for (int i= prod.lerngth; i-- > 0; prod= 0)
if (++prod[i] < scard[i]) return prod; // return indexes of next product
return null; // no next product anymore
}kind regards,
Jos