exception Cycle
type mark = NotVisited | InProgress | Visited

type 'a graph =
    { mutable g_nodes : 'a node list }
and 'a node = {
  n_label : 'a;
  mutable n_mark : mark;
  mutable n_link_to : 'a node list;
  mutable n_linked_by : 'a node list;
}

let mk_graph () = { g_nodes = [] }

let add_node g x =
  let n = { n_label = x; n_mark = NotVisited; n_link_to = []; n_linked_by = [] } in
  g.g_nodes <- n::g.g_nodes

let node_for_label g x =
  List.find (fun n -> n.n_label = x) g.g_nodes

let add_edge g id1 id2 =
  let n1 = node_for_label g id1 in
  let n2 = node_for_label g id2 in
  n1.n_link_to <- n2::n1.n_link_to;
  n2.n_linked_by <- n1::n2.n_linked_by

let clear_marks g =
  List.iter (fun n -> n.n_mark <- NotVisited) g.g_nodes

let find_roots g =
  List.filter (fun n -> n.n_linked_by = []) g.g_nodes

let has_cycle g =
  clear_marks g;
  let rec visit n =
    match n.n_mark with
    | InProgress -> true
    | Visited -> false
    | NotVisited ->
      n.n_mark <- InProgress;
      let ret = List.fold_left (fun x n -> x || (visit n)) false n.n_link_to in
      n.n_mark <- Visited;
      ret
  in
  let ret = List.fold_left (fun x n -> x || (if n.n_mark = Visited then false else visit n)) false g.g_nodes
  in clear_marks g; ret

let topological g =
  clear_marks g;
  let rec aux acc n =
    if n.n_mark = Visited
      then acc
      else begin
        n.n_mark <- Visited;
        n.n_label :: (List.fold_left (fun x n -> aux x n) acc n.n_linked_by)
      end
  in
  let ret = List.fold_left (fun x n -> aux x n) [] g.g_nodes
  in clear_marks g; List.rev ret