How to take product of two list in OCaml?

Question

I have two lists :

let a = ["a";"b"];
let b = ["c";"d"];

I want an output list c such as :

c = ["a";"c";"a";"d";"b";"c";"b";"d"];

How to do it in ocaml as lists are immutable? I am new to it.

Answer 1

You would return a new list. If you really are interested in the cartesian product of the lists, then this should be enough:

let cartesian l l' = 
  List.concat (List.map (fun e -> List.map (fun e' -> (e,e')) l') l)

# cartesian ["a";"b"] ["c";"d"];;
- : (string * string) list = [("a", "c"); ("a", "d"); ("b", "c"); ("b", "d")]

If you need that strange flat structure instead, you can use an additional list concatenation.

let flat_cartesian l l' = 
  List.concat (List.concat (
    List.map (fun e -> List.map (fun e' -> [e;e']) l') l))

Answer 2

If you do not want to use concatenation, because this is not a tail recursive operation, you can use the following (which should be more efficient):

let product l1 l2 =
  List.rev (
   List.fold_left
    (fun x a ->
      List.fold_left
       (fun y b ->
         b::a::y
       )
       x
       l2
   )
   []
   l1
 )
;;

For the cartesian product, just change

b::a::y

into

(a,b)::y

Answer 3

I would break the problem into two sub problems:

• Firstly consider a function appendeach with takes a value and a list and returns the result of adding that value infront of each item in the list

  let rec appendeach x lst = match lst with [] -> [] 
                                          | hd::tl -> x::hd::(appendeach x tl);;
  

• Then consider a function product with takes two lists and calls appendeach for each item in the first list and the whole second list

  let rec product lst1 lst2 = match lst1 with [] -> [] | 
                                           hd::tl -> (appendeach hd lst2)@(product tl lst2);;