(*
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
list of conditions and the following disclaimer.  Redistributions in binary
form must reproduce the above copyright notice, this list of conditions and the
following disclaimer in the documentation and/or other materials provided with
the distribution.

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
FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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.
*)

(** {1 Imperative deque} *)

type 'a cell =
  | Zero
  | One of 'a
  | Two of 'a * 'a
  | Three of 'a * 'a * 'a
(** A cell holding a small number of elements *)

type 'a node = {
  mutable cell : 'a cell;
  mutable next : 'a node;
  mutable prev : 'a node;
}
(** Linked list of cells *)

type 'a t = {
  mutable cur : 'a node;
  mutable size : int;
}
(** The deque, a double linked list of cells *)

(*$inject
  let plist l = CCPrint.to_string (CCList.pp CCInt.pp) l
  let pint i = string_of_int i
*)

(*$R
  let q = create () in
  add_seq_back q Sequence.(3 -- 5);
  assert_equal [3;4;5] (to_list q);
  add_seq_front q Sequence.(of_list [2;1]);
  assert_equal [1;2;3;4;5] (to_list q);
  push_front q 0;
  assert_equal [0;1;2;3;4;5] (to_list q);
  assert_equal 5 (take_back q);
  assert_equal 0 (take_front q);
  assert_equal 4 (length q);
*)

exception Empty

let create () =
  let rec cur = { cell=Zero; prev=cur; next=cur } in
  { cur; size=0 }

let clear q =
  let rec cur = { cell=Zero; prev=cur; next=cur } in
  q.cur <- cur;
  q.size <- 0;
  ()

(*$R
  let q = of_seq Sequence.(1 -- 100) in
  assert_equal 100 (length q);
  clear q;
  assert_equal 0 (length q);
  assert_raises Empty (fun () -> peek_front q);
  assert_raises Empty (fun () -> peek_back q);
*)

let incr_size_ d = d.size <- d.size + 1
let decr_size_ d = d.size <- d.size - 1

let is_zero_ n = match n.cell with
  | Zero -> true
  | One _
  | Two _
  | Three _ -> false

let is_empty d =
  let res = d.size = 0 in
  assert (res = is_zero_ d.cur);
  res

let push_front d x =
  incr_size_ d;
  match d.cur.cell with
  | Zero -> d.cur.cell <- One x
  | One y -> d.cur.cell <- Two (x, y)
  | Two (y, z) -> d.cur.cell <- Three (x,y,z)
  | Three _ ->
    let node = { cell = One x; prev = d.cur.prev; next=d.cur; } in
    d.cur.prev.next <- node;
    d.cur.prev <- node;
    d.cur <- node (* always point to first node *)

let push_back d x =
  incr_size_ d;
  let n = d.cur.prev in (* last node *)
  match n.cell with
  | Zero -> n.cell <- One x
  | One y -> n.cell <- Two (y, x)
  | Two (y,z) -> n.cell <- Three (y, z, x)
  | Three _ ->
    let elt = { cell = One x; next=d.cur; prev=n; } in
    n.next <- elt;
    d.cur.prev <- elt

let peek_front d = match d.cur.cell with
  | Zero -> raise Empty
  | One x -> x
  | Two (x,_) -> x
  | Three (x,_,_) -> x

(*$T
  of_list [1;2;3] |> peek_front = 1
  try (ignore (of_list [] |> peek_front); false) with Empty -> true
  *)

(*$R
  let d = of_seq Sequence.(1 -- 10) in
  let printer = pint in
  OUnit.assert_equal ~printer 1 (peek_front d);
  push_front d 42;
  OUnit.assert_equal ~printer 42 (peek_front d);
  OUnit.assert_equal ~printer 42 (take_front d);
  OUnit.assert_equal ~printer 1 (take_front d);
  OUnit.assert_equal ~printer 2 (take_front d);
  OUnit.assert_equal ~printer 3 (take_front d);
  OUnit.assert_equal ~printer 10 (peek_back d);
*)

let peek_back d =
  if is_empty d then raise Empty
  else match d.cur.prev.cell with
    | Zero -> assert false
    | One x -> x
    | Two (_,x) -> x
    | Three (_,_,x) -> x

(*$T
  of_list [1;2;3] |> peek_back = 3
  try (ignore (of_list [] |> peek_back); false) with Empty -> true
*)

(*$R
  let d = of_seq Sequence.(1 -- 10) in
  let printer = pint in
  OUnit.assert_equal ~printer 1 (peek_front d);
  push_back d 42;
  OUnit.assert_equal ~printer 42 (peek_back d);
  OUnit.assert_equal ~printer 42 (take_back d);
  OUnit.assert_equal ~printer 10 (take_back d);
  OUnit.assert_equal ~printer 9 (take_back d);
  OUnit.assert_equal ~printer 8 (take_back d);
  OUnit.assert_equal ~printer 1 (peek_front d);
*)

let take_back_node_ n = match n.cell with
  | Zero -> assert false
  | One x -> n.cell <- Zero; x
  | Two (x,y) -> n.cell <- One x; y
  | Three (x,y,z) -> n.cell <- Two (x,y); z

let take_back d =
  if is_empty d then raise Empty
  else if d.cur == d.cur.prev
  then (
    (* only one cell *)
    decr_size_ d;
    take_back_node_ d.cur
  ) else (
    let n = d.cur.prev in
    let x = take_back_node_ n in
    decr_size_ d;
    if is_zero_ n
    then (  (* remove previous node *)
      d.cur.prev <- n.prev;
      n.prev.next <- d.cur;
    );
    x
  )

(*$T
  let q = of_list [1;2;3] in take_back q = 3 && to_list q = [1;2]
  *)

let take_front_node_ n = match n.cell with
  | Zero -> assert false
  | One x -> n.cell <- Zero; x
  | Two (x,y) -> n.cell <- One y; x
  | Three (x,y,z) -> n.cell <- Two (y,z); x

(*$T
  let q = of_list [1;2;3] in take_front q = 1 && to_list q = [2;3]
  *)

let take_front d =
  if is_empty d then raise Empty
  else if d.cur.prev == d.cur
  then (
    (* only one cell *)
    decr_size_ d;
    take_front_node_ d.cur
  ) else (
    decr_size_ d;
    let x = take_front_node_ d.cur in
    if is_zero_ d.cur then (
      d.cur.prev.next <- d.cur.next;
      d.cur.next.prev <- d.cur.prev;
      d.cur <- d.cur.next;
    );
    x
  )

let iter f d =
  let rec iter f ~first n =
    begin match n.cell with
    | Zero -> ()
    | One x -> f x
    | Two (x,y) -> f x; f y
    | Three (x,y,z) -> f x; f y; f z
    end;
    if n.next != first then iter f ~first n.next
  in
  iter f ~first:d.cur d.cur

(*$T
  let n = ref 0 in iter (fun _ -> incr n) (of_list [1;2;3]); !n = 3
*)

(*$R
  let d = of_seq Sequence.(1 -- 5) in
  let s = Sequence.from_iter (fun k -> iter k d) in
  let l = Sequence.to_list s in
  OUnit.assert_equal ~printer:plist [1;2;3;4;5] l;
*)

let append_front ~into q = iter (push_front into) q

let append_back ~into q = iter (push_back into) q

(*$R
  let q = of_list [3;4] in
  append_front ~into:q (of_list [2;1]);
  assert_equal [1;2;3;4] (to_list q);
  append_back ~into:q (of_list [5;6]);
  assert_equal [1;2;3;4;5;6] (to_list q);
*)

let fold f acc d =
  let rec aux ~first f acc n =
    let acc = match n.cell with
      | Zero -> acc
      | One x -> f acc x
      | Two (x,y) -> f (f acc x) y
      | Three (x,y,z) -> f (f (f acc x) y) z
    in
    if n.next == first then acc else aux ~first f acc n.next
  in
  aux ~first:d.cur f acc d.cur

(*$T
  fold (+) 0 (of_list [1;2;3]) = 6
  fold (fun acc x -> x::acc) [] (of_list [1;2;3]) = [3;2;1]
*)

let length d = d.size

(*$Q
  Q.(list int) (fun l -> \
    let q = of_list l in \
    append_front ~into:q (of_list l); \
    append_back ~into:q (of_list l); \
    length q = 3 * List.length l)
*)

(*$R
  let d = of_seq Sequence.(1 -- 10) in
  OUnit.assert_equal ~printer:pint 10 (length d)
*)

type 'a sequence = ('a -> unit) -> unit
type 'a gen = unit -> 'a option

let add_seq_back q seq = seq (fun x -> push_back q x)

let add_seq_front q seq = seq (fun x -> push_front q x)

(*$R
  let q = of_list [4;5] in
  add_seq_front q Sequence.(of_list [3;2;1]);
  assert_equal [1;2;3;4;5] (to_list q);
  add_seq_back q Sequence.(of_list [6;7]);
  assert_equal [1;2;3;4;5;6;7] (to_list q);
*)

let of_seq seq =
  let deque = create () in
  seq (fun x -> push_back deque x);
  deque

let to_seq d k = iter k d

(*$Q
  Q.(list int) (fun l -> \
    Sequence.of_list l |> of_seq |> to_seq |> Sequence.to_list = l)
  *)

let of_list l =
  let q = create() in
  List.iter (push_back q) l;
  q

(*$R
  let q = of_list [1;2;3] in
  assert_equal 1 (take_front q);
  assert_equal 3 (take_back q);
  assert_equal 2 (take_front q);
  assert_equal true (is_empty q)
*)

let to_rev_list q = fold (fun l x -> x::l) [] q

let to_list q = List.rev (to_rev_list q)

let rec gen_iter_ f g = match g() with
  | None -> ()
  | Some x -> f x; gen_iter_ f g

let of_gen g =
  let q = create () in
  gen_iter_ (fun x -> push_back q x) g;
  q

let to_gen q =
  let first = q.cur in
  let cell = ref q.cur.cell in
  let cur = ref q.cur in
  let rec next () = match !cell with
    | Zero when (!cur).next == first -> None
    | Zero ->
      (* go to next node *)
      let n = !cur in
      cur := n.next;
      cell := n.next.cell;
      next ()
    | One x -> cell := Zero; Some x
    | Two (x,y) -> cell := One y; Some x
    | Three (x,y,z) -> cell := Two (y,z); Some x
  in
  next

(*$T
  of_list [1;2;3] |> to_gen |> of_gen |> to_list = [1;2;3]
*)

(*$Q
  Q.(list int) (fun l -> \
    of_list l |> to_gen |> of_gen |> to_list = l)
*)

(* naive implem of copy, for now *)
let copy d =
  let d' = create () in
  iter (fun x -> push_back d' x) d;
  d'

(*$R
  let q = of_list [1;2;3;4] in
  assert_equal 4 (length q);
  let q' = copy q in
  let cmp = equal ?eq:None in
  assert_equal 4 (length q');
  assert_equal ~cmp q q';
  push_front q 0;
  assert_bool "not equal" (not (cmp q q'));
  assert_equal 5 (length q);
  push_front q' 0;
  assert_equal ~cmp q q'
*)

let equal ?(eq=(=)) a b =
  let rec aux eq a b = match a() , b() with
    | None, None -> true
    | None, Some _
    | Some _, None -> false
    | Some x, Some y -> eq x y && aux eq a b
  in aux eq (to_gen a) (to_gen b)

let compare ?(cmp=Pervasives.compare) a b =
  let rec aux cmp a b = match a() , b() with
    | None, None -> 0
    | None, Some _ -> -1
    | Some _, None -> 1
    | Some x, Some y ->
        let c = cmp x y in
        if c=0 then aux cmp a b else c
  in aux cmp (to_gen a) (to_gen b)

(*$Q
   Q.(pair (list int) (list int)) (fun (l1,l2) -> \
    CCOrd.equiv (compare (of_list l1) (of_list l2)) \
      (CCList.compare Pervasives.compare l1 l2))
  *)

type 'a printer = Format.formatter -> 'a -> unit

let print pp_x out d =
  let first = ref true in
  Format.fprintf out "@[<hov2>deque {";
  iter
    (fun x ->
      if !first then first:= false else Format.fprintf out ";@ ";
      pp_x out x
    ) d;
  Format.fprintf out "}@]"