(********************************************************************)
(*  OCaml code from the book ``Learn Programming with OCaml''       *)
(*  See https://usr.lmf.cnrs.fr/lpo/                                *)
(*                                                                  *)
(*  Sylvain Conchon and Jean-Christophe Filliâtre                   *)
(*  Copyright 2025 Université Paris-Saclay and CNRS                 *)
(*                                                                  *)
(*  Openly licensed via CC BY SA 4.0                                *)
(*  See https://creativecommons.org/licenses/by-sa/4.0/deed.en      *)
(********************************************************************)

(* Program 101 on page 424
   Shortest path (Dijkstra’s algorithm) *)

  module VertexDistance = struct
    type t = vertex * float
    let compare (_, d1) (_, d2) = Stdlib.compare d1 d2
  end
  module P = PriorityQueue(VertexDistance)

  let rec dijkstra f g s =
    let visited = H.create () in
    let distance = H.create () in
    let queue = P.create () in
    let add v d = H.replace distance v d; P.add queue (v, d) in
    add s 0.;
    while not (P.is_empty queue) do
      let (u, du) = P.extract_min queue in
      if not (H.mem visited u) then begin
        H.add visited u ();
        f u du;
        let visit v =
          let d = du +. weight g u v in
          if not (H.mem distance v) || d < H.find distance v then
            add v d
        in
        iter_succ visit g u
      end
    done

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