Homework help converting an iterative function to recursive

Question

For an assignment, i have written the following code in recursion. It takes a list of a vector data type, and a vector and calculates to closeness of the two vectors. This method works fine, but i don't know how to do the recursive version.

let romulus_iter (x:vector list) (vec:vector) = 
  let vector_close_hash = Hashtbl.create 10 in 
  let prevkey = ref 10000.0 in (* Define previous key to be a large value since we intially want to set closefactor to prev key*)
  if List.length x = 0 then
    {a=0.;b=0.}
  else
    begin
      Hashtbl.clear vector_close_hash; 
      for i = 0 to (List.length x)-1 do
        let vecinquestion = {a=(List.nth x i).a;b=(List.nth x i).b} in
        let closefactor = vec_close vecinquestion vec in
        if (closefactor < !prevkey) then 
          begin
            prevkey := closefactor;
            Hashtbl.add vector_close_hash closefactor vecinquestion
          end
      done; 
      Hashtbl.find vector_close_hash !prevkey
    end;;

Answer 1

The general recursive equivalent of

for i = 0 to (List.length x)-1 do
    f (List.nth x i)
done

is this:

let rec loop = function
  | x::xs -> f x; loop xs
  | [] -> ()

Note that just like a for-loop, this function only returns unit, though you can define a similar recursive function that returns a meaningful value (and in fact that's what most do). You can also use List.iter, which is meant just for this situation where you're applying an impure function that doesn't return anything meaningful to each item in the list:

List.iter f x