How to use LINQ to find all combinations of n items from a set of numbers?

Question

I'm trying to write an algorithm to select all combinations of n values from a set of numbers.

For instance, given the set: 1, 2, 3, 7, 8, 9

All combinations of 2 values from the set is:

(1, 2), (1, 3), (1, 7), (1, 8), (1, 9), (2, 3), (2, 7), (2, 8), (2, 9), (3, 7), (3, 8), (3, 9), (7, 8), (7, 9), (8, 9)

And 3 is:

(1, 2, 3), (1, 2, 7), (1, 2, 8), (1, 2, 9), (1, 3, 7), (1, 3, 8), (1, 3, 9), (1, 7, 8), (1, 7, 9), (1, 8, 9), (2, 3, 7), (2, 3, 8), (2, 3, 9), (2, 7, 8), (2, 7, 9), (2, 8, 9), (3, 7, 8), (3, 7, 9), (3, 8, 9), (7, 8, 9)

etc!

I'm currently using methods to to yield return sets of combinations of 2, 3 and 4 values, but it seems to me this could be generalised in a LINQ query.

Thanks for your help!

Answer 1

Usage:

var results = new[] { 1, 2, 3, 4, 5, 6, 7, 8, 9 }.DifferentCombinations(3);

Code:

public static class Ex
{
    public static IEnumerable<IEnumerable<T>> DifferentCombinations<T>(this IEnumerable<T> elements, int k)
    {
        return k == 0 ? new[] { new T[0] } :
          elements.SelectMany((e, i) =>
            elements.Skip(i + 1).DifferentCombinations(k - 1).Select(c => (new[] {e}).Concat(c)));
    }
}