(*
copyright (c) 2013, simon cruanes
all rights reserved.

redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:

redistributions of source code must retain the above copyright notice, this
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form must reproduce the above copyright notice, this list of conditions and the
following disclaimer in the documentation and/or other materials provided with
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
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DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*)

(** {6 Multimap} *)

module type S = sig
  type key
  type value
  type t

  val empty : t
    (** Empty multimap *)

  val is_empty : t -> bool
    (** Empty multimap? *)

  val add : t -> key -> value -> t
    (** Add a key/value binding *)

  val remove : t -> key -> value -> t
    (** Remove the binding *)

  val remove_all : t -> key -> t
    (** Remove the key from the map *)

  val mem : t -> key -> bool
    (** Is there a binding for this key? *)

  val find : t -> key -> value list
    (** List of values for this key *)

  val find_iter : t -> key -> (value -> unit) -> unit
    (** Iterate on bindings for this key *)

  val count : t -> key -> int
    (** Number of bindings for this key *)

  val iter : t -> (key -> value -> unit) -> unit
    (** Iterate on all key/value *)

  val fold : t -> 'a -> ('a -> key -> value -> 'a) -> 'a
    (** Fold on all key/value *)

  val size : t -> int
    (** Number of keys *)

  val union : t -> t -> t
    (** Union of multimaps *)

  val inter : t -> t -> t
    (** Intersection of multimaps *)

  val diff : t -> t -> t
    (** Difference of maps, ie bindings of the first that are not
        in the second *)

  val equal : t -> t -> bool
    (** Same multimap *)

  val compare : t -> t -> int
    (** Total order on multimaps *)

  val submap : t -> t -> bool
    (** [submap m1 m2] is true iff all bindings of [m1] are also in [m2] *)

  val to_seq : t -> (key * value) Sequence.t

  val of_seq : ?init:t -> (key * value) Sequence.t -> t

  val keys : t -> key Sequence.t

  val values : t -> value Sequence.t
    (** Some values may occur several times *)
end

module type OrderedType = sig
  type t
  val compare : t -> t -> int
end

module Make(K : OrderedType)(V : OrderedType) = struct
  type key = K.t
  type value = V.t

  module M = Map.Make(K)
  module S = Set.Make(V)

  type t = S.t M.t
    (** Map of sets *)

  let empty = M.empty

  let is_empty = M.is_empty

  let add m k v =
    let set = try M.find k m with Not_found -> S.empty in
    M.add k (S.add v set) m

  let remove m k v =
    try
      let set = M.find k m in
      let set' = S.remove v set in
      if S.is_empty set'
        then M.remove k m
        else M.add k set' m
    with Not_found ->
      m

  let remove_all m k =
    M.remove k m

  let mem m k = M.mem k m

  let find m k =
    try
      let set = M.find k m in
      S.elements set
    with Not_found ->
      []

  let find_iter m k f =
    try
      let set = M.find k m in
      S.iter f set
    with Not_found ->
      ()

  let count m k =
    try
      let set = M.find k m in
      S.cardinal set
    with Not_found ->
      0

  let iter m f =
    M.iter (fun k set -> S.iter (fun v -> f k v) set) m

  let fold m acc f =
    M.fold (fun k set acc -> S.fold (fun v acc -> f acc k v) set acc) m acc

  let size m = M.cardinal m

  let union m1 m2 =
    M.merge
      (fun k v1 v2 -> match v1, v2 with
        | None, None -> None
        | Some set1, Some set2 -> Some (S.union set1 set2)
        | Some set, None
        | None, Some set -> Some set)
      m1 m2

  let inter m1 m2 =
    M.merge
      (fun k v1 v2 -> match v1, v2 with
        | None, _
        | _, None -> None
        | Some set1, Some set2 ->
          let set = S.inter set1 set2 in
          if S.is_empty set
            then None
            else Some set)
      m1 m2

  let diff m1 m2 =
    M.merge
      (fun k v1 v2 -> match v1, v2 with
        | None, _ -> None
        | Some set, None -> Some set
        | Some set1, Some set2 ->
          let set' = S.diff set1 set2 in
          if S.is_empty set'
            then None
            else Some set')
      m1 m2

  let equal m1 m2 =
    M.equal S.equal m1 m2

  let compare m1 m2 =
    M.compare S.compare m1 m2

  let submap m1 m2 =
    M.for_all
      (fun k set1 ->
        try
          let set2 = M.find k m2 in
          S.subset set1 set2
        with Not_found ->
          false)
      m1

  let to_seq m =
    Sequence.from_iter (fun k -> iter m (fun x y -> k (x,y)))

  let of_seq ?(init=empty) seq =
    Sequence.fold (fun m (k,v) -> add m k v) init seq

  let keys m =
    Sequence.from_iter (fun k -> M.iter (fun x _ -> k x) m)

  let values m =
    Sequence.from_iter (fun k -> iter m (fun _ v -> k v))
end