Source file CCArray.ml

(* This file is free software, part of containers. See file "license" for more details. *)

(** {1 Array utils} *)

type 'a iter = ('a -> unit) -> unit
type 'a gen = unit -> 'a option
type 'a equal = 'a -> 'a -> bool
type 'a ord = 'a -> 'a -> int
type 'a random_gen = Random.State.t -> 'a
type 'a printer = Format.formatter -> 'a -> unit

(** {2 Arrays} *)

include Array

let empty = [||]

let get_safe a i =
  if i >= 0 && i < Array.length a then
    Some (Array.unsafe_get a i)
  else
    None

let map_inplace f a = Array.iteri (fun i e -> Array.unsafe_set a i (f e)) a
let mapi_inplace f a = Array.iteri (fun i e -> Array.unsafe_set a i (f i e)) a
let fold = Array.fold_left

let foldi f acc a =
  let rec aux acc i =
    if i = Array.length a then
      acc
    else
      aux (f acc i a.(i)) (i + 1)
  in
  aux acc 0

let fold_while f acc a =
  let rec fold_while_i f acc i =
    if i < Array.length a then (
      let acc, cont = f acc a.(i) in
      match cont with
      | `Stop -> acc
      | `Continue -> fold_while_i f acc (i + 1)
    ) else
      acc
  in
  fold_while_i f acc 0

let fold_map f acc a =
  let n = length a in
  (* need special case for initializing the result *)
  if n = 0 then
    acc, [||]
  else (
    let acc, b0 = f acc a.(0) in
    let res = Array.make n b0 in
    let acc = ref acc in
    for i = 1 to n - 1 do
      let new_acc, b = f !acc a.(i) in
      acc := new_acc;
      res.(i) <- b
    done;
    !acc, res
  )

let scan_left f acc a =
  let n = length a in
  let res = Array.make (n + 1) acc in
  Array.iteri
    (fun i x ->
      let new_acc = f res.(i) x in
      res.(i + 1) <- new_acc)
    a;
  res

let reverse_in_place a =
  let len = Array.length a in
  if len > 0 then
    for k = 0 to (len - 1) / 2 do
      let t = a.(k) in
      a.(k) <- a.(len - 1 - k);
      a.(len - 1 - k) <- t
    done

let sorted cmp a =
  let b = Array.copy a in
  Array.sort cmp b;
  b

let sort_indices cmp a =
  let len = Array.length a in
  let b = Array.init len (fun k -> k) in
  Array.sort (fun k1 k2 -> cmp a.(k1) a.(k2)) b;
  b

let sort_ranking cmp a = sort_indices compare (sort_indices cmp a)

let rev a =
  let b = Array.copy a in
  reverse_in_place b;
  b

exception Found

let mem ?(eq = Stdlib.( = )) elt a =
  try
    Array.iter (fun e -> if eq e elt then raise_notrace Found) a;
    false
  with Found -> true

let rec find_aux f a i =
  if i >= Array.length a then
    None
  else (
    match f i a.(i) with
    | Some _ as res -> res
    | None -> find_aux f a (i + 1)
  )

[@@@ocaml.warning "-32"]

let find_map f a = find_aux (fun _ -> f) a 0
let find = find_map
let find_map_i f a = find_aux f a 0
let findi = find_map_i

[@@@ocaml.warning "+32"]

let find_idx p a =
  find_aux
    (fun i x ->
      if p x then
        Some (i, x)
      else
        None)
    a 0

let max cmp a =
  if Array.length a = 0 then
    None
  else
    Some
      (fold
         (fun acc elt ->
           if cmp acc elt < 0 then
             elt
           else
             acc)
         a.(0) a)

let max_exn cmp a =
  match max cmp a with
  | None -> invalid_arg "CCArray.max_exn"
  | Some elt -> elt

let argmax cmp a =
  if Array.length a = 0 then
    None
  else
    Some
      (foldi
         (fun acc i elt ->
           if cmp a.(acc) elt < 0 then
             i
           else
             acc)
         0 a)

let argmax_exn cmp a =
  match argmax cmp a with
  | None -> invalid_arg "CCArray.argmax_exn"
  | Some elt -> elt

let min cmp a =
  if Array.length a = 0 then
    None
  else
    Some
      (fold
         (fun acc elt ->
           if cmp acc elt > 0 then
             elt
           else
             acc)
         a.(0) a)

let min_exn cmp a =
  match min cmp a with
  | None -> invalid_arg "CCArray.min_exn"
  | Some elt -> elt

let argmin cmp a =
  if Array.length a = 0 then
    None
  else
    Some
      (foldi
         (fun acc i elt ->
           if cmp a.(acc) elt > 0 then
             i
           else
             acc)
         0 a)

let argmin_exn cmp a =
  match argmin cmp a with
  | None -> invalid_arg "CCArray.argmin_exn"
  | Some elt -> elt

let filter_map f a =
  let rec aux acc i =
    if i = Array.length a then (
      let a' = Array.of_list acc in
      reverse_in_place a';
      a'
    ) else (
      match f a.(i) with
      | None -> aux acc (i + 1)
      | Some x -> aux (x :: acc) (i + 1)
    )
  in
  aux [] 0

let filter p a =
  filter_map
    (fun x ->
      if p x then
        Some x
      else
        None)
    a

(* append [rev a] in front of [acc] *)
let rec __rev_append_list a acc i =
  if i = Array.length a then
    acc
  else
    __rev_append_list a (a.(i) :: acc) (i + 1)

let flat_map f a =
  let rec aux acc i =
    if i = Array.length a then (
      let a' = Array.of_list acc in
      reverse_in_place a';
      a'
    ) else (
      let a' = f a.(i) in
      aux (__rev_append_list a' acc 0) (i + 1)
    )
  in
  aux [] 0

let monoid_product f a1 a2 =
  let na1 = length a1 in
  init
    (na1 * length a2)
    (fun i_prod ->
      let i = i_prod mod na1 in
      let j = i_prod / na1 in
      f a1.(i) a2.(j))

let rec _lookup_rec ~cmp k a i j =
  if i > j then
    raise Not_found
  else if i = j then
    if cmp k a.(i) = 0 then
      i
    else
      raise Not_found
  else (
    let middle = (j + i) / 2 in
    match cmp k a.(middle) with
    | 0 -> middle
    | n when n < 0 -> _lookup_rec ~cmp k a i (middle - 1)
    | _ -> _lookup_rec ~cmp k a (middle + 1) j
  )

let _lookup_exn ~cmp k a i j =
  if i > j then raise Not_found;
  match cmp k a.(i) with
  | 0 -> i
  | n when n < 0 -> raise Not_found (* too low *)
  | _ when i = j -> raise Not_found (* too high *)
  | _ ->
    (match cmp k a.(j) with
    | 0 -> j
    | n when n < 0 -> _lookup_rec ~cmp k a (i + 1) (j - 1)
    | _ -> raise Not_found)
(* too high *)

let lookup_exn ~cmp k a = _lookup_exn ~cmp k a 0 (Array.length a - 1)

let lookup ~cmp k a =
  try Some (_lookup_exn ~cmp k a 0 (Array.length a - 1))
  with Not_found -> None

let bsearch ~cmp k a =
  let rec aux i j =
    if i > j then
      `Just_after j
    else (
      let middle = i + ((j - i) / 2) in
      (* avoid overflow *)
      match cmp k a.(middle) with
      | 0 -> `At middle
      | n when n < 0 -> aux i (middle - 1)
      | _ -> aux (middle + 1) j
    )
  in
  let n = Array.length a in
  if n = 0 then
    `Empty
  else (
    match cmp a.(0) k, cmp a.(n - 1) k with
    | c, _ when c > 0 -> `All_bigger
    | _, c when c < 0 -> `All_lower
    | _ -> aux 0 (n - 1)
  )

let rec _for_all2 p a1 a2 i1 i2 ~len =
  len = 0
  || (p a1.(i1) a2.(i2) && _for_all2 p a1 a2 (i1 + 1) (i2 + 1) ~len:(len - 1))

let for_all2 p a b =
  Array.length a = Array.length b && _for_all2 p a b 0 0 ~len:(Array.length a)

let rec _exists2 p a1 a2 i1 i2 ~len =
  len > 0
  && (p a1.(i1) a2.(i2) || _exists2 p a1 a2 (i1 + 1) (i2 + 1) ~len:(len - 1))

let exists2 p a b =
  _exists2 p a b 0 0 ~len:(Stdlib.min (Array.length a) (Array.length b))

let _fold2 f acc a b i j ~len =
  let rec aux acc o =
    if o = len then
      acc
    else (
      let acc = f acc (Array.get a (i + o)) (Array.get b (j + o)) in
      aux acc (o + 1)
    )
  in
  aux acc 0

let fold2 f acc a b =
  if length a <> length b then invalid_arg "fold2";
  _fold2 f acc a b 0 0 ~len:(Array.length a)

let ( -- ) i j =
  if i <= j then
    Array.init (j - i + 1) (fun k -> i + k)
  else
    Array.init (i - j + 1) (fun k -> i - k)

let ( --^ ) i j =
  if i = j then
    [||]
  else if i > j then
    Array.init (i - j) (fun k -> i - k)
  else
    Array.init (j - i) (fun k -> i + k)

(** all the elements of a, but the i-th, into a list *)
let except_idx a i =
  foldi
    (fun acc j elt ->
      if i = j then
        acc
      else
        elt :: acc)
    [] a

let equal eq a b =
  let rec aux i =
    if i = Array.length a then
      true
    else
      eq a.(i) b.(i) && aux (i + 1)
  in
  Array.length a = Array.length b && aux 0

let compare cmp a b =
  let rec aux i =
    if i = Array.length a then
      if i = Array.length b then
        0
      else
        -1
    else if i = Array.length b then
      1
    else (
      let c = cmp a.(i) b.(i) in
      if c = 0 then
        aux (i + 1)
      else
        c
    )
  in
  aux 0

(* swap elements of array *)
let swap a i j =
  if i <> j then (
    let tmp = a.(i) in
    a.(i) <- a.(j);
    a.(j) <- tmp
  )

(* shuffle a[i … j] using the given int random generator
   See http://en.wikipedia.org/wiki/Fisher-Yates_shuffle *)
let _shuffle _rand_int a i j =
  for k = j - 1 downto i + 1 do
    let l = _rand_int (k + 1) in
    let tmp = a.(l) in
    a.(l) <- a.(k);
    a.(k) <- tmp
  done

let shuffle a = _shuffle Random.int a 0 (Array.length a)
let shuffle_with st a = _shuffle (Random.State.int st) a 0 (Array.length a)

let random_choose a =
  let n = Array.length a in
  if n = 0 then invalid_arg "Array.random_choose";
  fun st -> a.(Random.State.int st n)

let random_len n g st = Array.init n (fun _ -> g st)

let random g st =
  let n = Random.State.int st 1_000 in
  random_len n g st

let random_non_empty g st =
  let n = 1 + Random.State.int st 1_000 in
  random_len n g st

let pp ?(pp_start = fun _ () -> ()) ?(pp_stop = fun _ () -> ())
    ?(pp_sep = fun out () -> Format.fprintf out ",@ ") pp_item out a =
  pp_start out ();
  for k = 0 to Array.length a - 1 do
    if k > 0 then pp_sep out ();
    pp_item out a.(k)
  done;
  pp_stop out ()

let pp_i ?(pp_start = fun _ () -> ()) ?(pp_stop = fun _ () -> ())
    ?(pp_sep = fun out () -> Format.fprintf out ",@ ") pp_item out a =
  pp_start out ();
  for k = 0 to Array.length a - 1 do
    if k > 0 then pp_sep out ();
    pp_item k out a.(k)
  done;
  pp_stop out ()

let to_string ?(sep = ", ") item_to_string a =
  Array.to_list a |> List.map item_to_string |> String.concat sep

let to_seq a =
  let rec aux i () =
    if i >= length a then
      Seq.Nil
    else
      Seq.Cons (a.(i), aux (i + 1))
  in
  aux 0

let to_iter a k = iter k a

let to_gen a =
  let k = ref 0 in
  fun () ->
    if !k < Array.length a then (
      let x = a.(!k) in
      incr k;
      Some x
    ) else
      None

(** {2 Generic Functions} *)

module type MONO_ARRAY = sig
  type elt
  type t

  val length : t -> int
  val get : t -> int -> elt
  val set : t -> int -> elt -> unit
end

(* Dual Pivot Quicksort (Yaroslavskiy)
   from "average case analysis of Java 7's Dual Pivot Quicksort" *)
module SortGeneric (A : MONO_ARRAY) = struct
  module Rand = Random.State

  let seed_ = [| 123456 |]

  type state = {
    mutable l: int; (* left pointer *)
    mutable g: int; (* right pointer *)
    mutable k: int;
  }

  let rand_idx_ rand i j = i + Rand.int rand (j - i)

  let swap_ a i j =
    if i = j then
      ()
    else (
      let tmp = A.get a i in
      A.set a i (A.get a j);
      A.set a j tmp
    )

  let sort ~cmp a =
    let rec insert_ a i k =
      if k < i then
        ()
      else if cmp (A.get a k) (A.get a (k + 1)) > 0 then (
        swap_ a k (k + 1);
        insert_ a i (k - 1)
      )
    in
    (* recursive part of insertion sort *)
    let rec sort_insertion_rec a i j k =
      if k < j then (
        insert_ a i (k - 1);
        sort_insertion_rec a i j (k + 1)
      )
    in
    (* insertion sort, for small slices *)
    let sort_insertion a i j =
      if j - i > 1 then sort_insertion_rec a i j (i + 1)
    in
    let rand = Rand.make seed_ in
    (* sort slice.
       There is a chance that the two pivots are equal, but it's unlikely. *)
    let rec sort_slice_ ~st a i j =
      if j - i > 10 then (
        st.l <- i;
        st.g <- j - 1;
        st.k <- i;
        (* choose pivots *)
        let p = A.get a (rand_idx_ rand i j) in
        let q = A.get a (rand_idx_ rand i j) in
        (* invariant: st.p <= st.q, swap them otherwise *)
        let p, q =
          if cmp p q > 0 then
            q, p
          else
            p, q
        in
        while st.k <= st.g do
          let cur = A.get a st.k in
          if cmp cur p < 0 then (
            (* insert in leftmost band *)
            if st.k <> st.l then swap_ a st.k st.l;
            st.l <- st.l + 1
          ) else if cmp cur q > 0 then (
            (* insert in rightmost band *)
            while st.k < st.g && cmp (A.get a st.g) q > 0 do
              st.g <- st.g - 1
            done;
            swap_ a st.k st.g;
            st.g <- st.g - 1;
            (* the element swapped from the right might be in the first situation.
               that is, < p  (we know it's <= q already) *)
            if cmp (A.get a st.k) p < 0 then (
              if st.k <> st.l then swap_ a st.k st.l;
              st.l <- st.l + 1
            )
          );
          st.k <- st.k + 1
        done;
        (* save values before recursing *)
        let l = st.l and g = st.g and sort_middle = cmp p q < 0 in
        sort_slice_ ~st a i l;
        if sort_middle then sort_slice_ ~st a l (g + 1);
        sort_slice_ ~st a (g + 1) j
      ) else
        sort_insertion a i j
    in
    if A.length a > 0 then (
      let st = { l = 0; g = A.length a; k = 0 } in
      sort_slice_ ~st a 0 (A.length a)
    )
end

let sort_generic (type arr elt)
    (module A : MONO_ARRAY with type t = arr and type elt = elt) ~cmp a =
  let module S = SortGeneric (A) in
  S.sort ~cmp a

module Infix = struct
  let ( >>= ) a f = flat_map f a
  let ( >>| ) a f = map f a
  let ( >|= ) a f = map f a
  let ( -- ) = ( -- )
  let ( --^ ) = ( --^ )

  type 'a t = 'a array

  let ( let* ) = ( >>= )
  let ( let+ ) = ( >|= )
  let[@inline] ( and+ ) a1 a2 = monoid_product (fun x y -> x, y) a1 a2
  let ( and* ) = ( and+ )
end

include Infix