Finding all combinations from sets of possibilities

Question

I have multiple sets of arrays that contain additional arrays that have values attached that I use for figuring out math. In order to find the best combination of these things,

Answer 1

The accepted answer appears to be correct but is a very strange way to do a Cartesian product in C#. If you have a given number of sequences you can take their Cartesian product idiomatically like this:

    var aList = new[] { "a1", "a2", "a3" };
    var bList = new[] { "b1", "b2", "b3" };
    var cList = new[] { "c1", "c2", "c3" };
    var product = from a in aList
                  from b in bList
                  from c in cList
                  select new[] { a, b, c };

    foreach (var p in product)
        Console.WriteLine(string.Join(",", p));

If you have arbitrarily many sequences that you need to take their Cartesian product then you can do it like this:

static class Extensions
{
  public static IEnumerable> CartesianProduct(
    this IEnumerable> sequences) 
  { 
    IEnumerable> emptyProduct = new[] { Enumerable.Empty() }; 
    return sequences.Aggregate( 
      emptyProduct, 
      (accumulator, sequence) => 
        from accseq in accumulator 
        from item in sequence 
        select accseq.Concat(new[] {item})); 
  }
}

And then:

    var aList = new[] { "a1", "a2", "a3" };
    var bList = new[] { "b1", "b2", "b3" };
    var cList = new[] { "c1", "c2", "c3" };
    var lists = new[] { aList, bList, cList };
    var product = lists.CartesianProduct();
    foreach (var p in product)
        Console.WriteLine(string.Join(",", p));

See

http://ericlippert.com/2010/06/28/computing-a-cartesian-product-with-linq/

and my answer to

Generating all Possible Combinations

for more discussion of this problem.