let of_string x = Str.(split (regexp " *> *")) (String.trim x)

let topic x =
  let path = of_string x in
  try List.nth path (List.length path - 1) with _ -> ""

module Map = Map.Make(String)

let edges x map = try Map.find x map with Not_found -> (String_set.empty, String_set.empty)

let edges_with_context context (contexts, subtopics) = (String_set.add context contexts, subtopics)
let edges_with_subtopic subtopic (contexts, subtopics) = (contexts, String_set.add subtopic subtopics)

let rec list_to_map map = function
  | [] -> map
  | [topic] ->
     let edges = edges topic map in
     Map.add topic edges map
  | context :: topic :: tail ->
     let context_edges = edges context map in
     let topic_edges = edges topic map in
     let map =
       map
       |> Map.add context (edges_with_subtopic topic context_edges)
       |> Map.add topic (edges_with_context context topic_edges)
     in
     list_to_map map (topic :: tail)

let to_map map set =
  List.fold_left (fun acc elt -> list_to_map acc (of_string elt)) map @@ String_set.elements set

let roots map =
  let root_keys acc (key, (contexts, _topics)) = if String_set.is_empty contexts then key :: acc else acc in
  List.fold_left root_keys [] @@ Map.bindings map