Algorithm Design

Hi

My maths is really rusty. I'm wondering if you guys could give me a hand with an algorithm.

I need to write a algorithm for generating combinations from n number of sets.

I can write code that will take my fixed number of sets and produce the combinations but Im lost on how I would be able to do this for n number of sets.

Here is my existing fixed number of sets combination generator:

int[] firstSet = new int[] { 1, 2, 3, 4, 5 };
int[] secondSet = new int[] { 6, 7, 8, 9, 10, 11 };
int[] thirdSet = new int[] { 12, 13, 14 };
int[] fourthSet = new int[] { 15, 16, 17, 18 };
int counter = 0;

foreach (int firstSetVariable in firstSet)
{
foreach (int secondSetVariable in secondSet)
{
foreach (int thirdSetVariable in thirdSet)
{
foreach (int fourthSetVariable in fourthSet)
{
Response.Write(counter + ": " + firstSetVariable + "," + secondSetVariable + "," + thirdSetVariable + "," + fourthSetVariable + "<br />");
counter += 1;
}
}
}
}

Will appreciate anyones help or guidance.

Thanks

This naturally suggests a recursive solution.

Here's one way in Python using generators: In words: recursively get the combinations ignoring the first set, and prepend each element of the first set in turn to each of those combinations.

(There is no math involved, by the way.)