Projecting a list of lists efficiently in F#

Question

I have to do projection of a list of lists which returns all combinations with each element from each list. For example:

projection([[1]; [2; 3]]) = [[1; 2]         


        

Answer 1

Here's a tail-recursive version. It's not as fast as some of the other solutions (only 25% faster than your original function), but memory usage is constant, so it works for extremely large result sets.

let cartesian l = 
  let rec aux f = function
    | [] -> f (Seq.singleton [])
    | h::t -> aux (fun acc -> f (Seq.collect (fun x -> (Seq.map (fun y -> y::x) h)) acc)) t
  aux id l