list.ml

(**************************************************************************)
(*                                                                        *)
(*                                 OCaml                                  *)
(*                                                                        *)
(*             Xavier Leroy, projet Cristal, INRIA Rocquencourt           *)
(*                                                                        *)
(*   Copyright 1996 Institut National de Recherche en Informatique et     *)
(*     en Automatique.                                                    *)
(*                                                                        *)
(*   All rights reserved.  This file is distributed under the terms of    *)
(*   the GNU Lesser General Public License version 2.1, with the          *)
(*   special exception on linking described in the file LICENSE.          *)
(*                                                                        *)
(**************************************************************************)

(* An alias for the type of lists. *)
type 'a t = 'a list = [] | (::) of 'a * 'a list

(* List operations *)

let rec length_aux len = function
    [] -> len
  | _::l -> length_aux (len + 1) l

let length l = length_aux 0 l

let cons a l = a::l

let hd = function
    [] -> failwith "hd"
  | a::_ -> a

let tl = function
    [] -> failwith "tl"
  | _::l -> l

let nth l n =
  if n < 0 then invalid_arg "List.nth" else
  let rec nth_aux l n =
    match l with
    | [] -> failwith "nth"
    | a::l -> if n = 0 then a else nth_aux l (n-1)
  in nth_aux l n

let nth_opt l n =
  if n < 0 then invalid_arg "List.nth" else
  let rec nth_aux l n =
    match l with
    | [] -> None
    | a::l -> if n = 0 then Some a else nth_aux l (n-1)
  in nth_aux l n

let append = (@)

let rec rev_append l1 l2 =
  match l1 with
    [] -> l2
  | a :: l -> rev_append l (a :: l2)

let rev l = rev_append l []

let[@tail_mod_cons] rec init i last f =
  if i > last then []
  else if i = last then [f i]
  else
    let r1 = f i in
    let r2 = f (i+1) in
    r1 :: r2 :: init (i+2) last f

let init len f =
  if len < 0 then invalid_arg "List.init" else
  init 0 (len - 1) f

let rec flatten = function
    [] -> []
  | l::r -> l @ flatten r

let concat = flatten

let[@tail_mod_cons] rec map f = function
    [] -> []
  | [a1] ->
      let r1 = f a1 in
      [r1]
  | a1::a2::l ->
      let r1 = f a1 in
      let r2 = f a2 in
      r1::r2::map f l

let[@tail_mod_cons] rec mapi i f = function
    [] -> []
  | [a1] ->
      let r1 = f i a1 in
      [r1]
  | a1::a2::l ->
      let r1 = f i a1 in
      let r2 = f (i+1) a2 in
      r1::r2::mapi (i+2) f l

let mapi f l = mapi 0 f l

let rev_map f l =
  let rec rmap_f accu = function
    | [] -> accu
    | a::l -> rmap_f (f a :: accu) l
  in
  rmap_f [] l


let rec iter f = function
    [] -> ()
  | a::l -> f a; iter f l

let rec iteri i f = function
    [] -> ()
  | a::l -> f i a; iteri (i + 1) f l

let iteri f l = iteri 0 f l

let rec fold_left f accu l =
  match l with
    [] -> accu
  | a::l -> fold_left f (f accu a) l

let rec fold_right f l accu =
  match l with
    [] -> accu
  | a::l -> f a (fold_right f l accu)

let[@tail_mod_cons] rec map2 f l1 l2 =
  match (l1, l2) with
    ([], []) -> []
  | ([a1], [b1]) ->
      let r1 = f a1 b1 in
      [r1]
  | (a1::a2::l1, b1::b2::l2) ->
      let r1 = f a1 b1 in
      let r2 = f a2 b2 in
      r1::r2::map2 f l1 l2
  | (_, _) -> invalid_arg "List.map2"

let rev_map2 f l1 l2 =
  let rec rmap2_f accu l1 l2 =
    match (l1, l2) with
    | ([], []) -> accu
    | (a1::l1, a2::l2) -> rmap2_f (f a1 a2 :: accu) l1 l2
    | (_, _) -> invalid_arg "List.rev_map2"
  in
  rmap2_f [] l1 l2


let rec iter2 f l1 l2 =
  match (l1, l2) with
    ([], []) -> ()
  | (a1::l1, a2::l2) -> f a1 a2; iter2 f l1 l2
  | (_, _) -> invalid_arg "List.iter2"

let rec fold_left2 f accu l1 l2 =
  match (l1, l2) with
    ([], []) -> accu
  | (a1::l1, a2::l2) -> fold_left2 f (f accu a1 a2) l1 l2
  | (_, _) -> invalid_arg "List.fold_left2"

let rec fold_right2 f l1 l2 accu =
  match (l1, l2) with
    ([], []) -> accu
  | (a1::l1, a2::l2) -> f a1 a2 (fold_right2 f l1 l2 accu)
  | (_, _) -> invalid_arg "List.fold_right2"

let rec for_all p = function
    [] -> true
  | a::l -> p a && for_all p l

let rec exists p = function
    [] -> false
  | a::l -> p a || exists p l

let rec for_all2 p l1 l2 =
  match (l1, l2) with
    ([], []) -> true
  | (a1::l1, a2::l2) -> p a1 a2 && for_all2 p l1 l2
  | (_, _) -> invalid_arg "List.for_all2"

let rec exists2 p l1 l2 =
  match (l1, l2) with
    ([], []) -> false
  | (a1::l1, a2::l2) -> p a1 a2 || exists2 p l1 l2
  | (_, _) -> invalid_arg "List.exists2"

let rec mem x = function
    [] -> false
  | a::l -> compare a x = 0 || mem x l

let rec memq x = function
    [] -> false
  | a::l -> a == x || memq x l

let rec assoc x = function
    [] -> raise Not_found
  | (a,b)::l -> if compare a x = 0 then b else assoc x l

let rec assoc_opt x = function
    [] -> None
  | (a,b)::l -> if compare a x = 0 then Some b else assoc_opt x l

let rec assq x = function
    [] -> raise Not_found
  | (a,b)::l -> if a == x then b else assq x l

let rec assq_opt x = function
    [] -> None
  | (a,b)::l -> if a == x then Some b else assq_opt x l

let rec mem_assoc x = function
  | [] -> false
  | (a, _) :: l -> compare a x = 0 || mem_assoc x l

let rec mem_assq x = function
  | [] -> false
  | (a, _) :: l -> a == x || mem_assq x l

let rec remove_assoc x = function
  | [] -> []
  | (a, _ as pair) :: l ->
      if compare a x = 0 then l else pair :: remove_assoc x l

let rec remove_assq x = function
  | [] -> []
  | (a, _ as pair) :: l -> if a == x then l else pair :: remove_assq x l

let rec find p = function
  | [] -> raise Not_found
  | x :: l -> if p x then x else find p l

let rec find_opt p = function
  | [] -> None
  | x :: l -> if p x then Some x else find_opt p l

let find_index p =
  let rec aux i = function
    [] -> None
    | a::l -> if p a then Some i else aux (i+1) l in
  aux 0

let rec find_map f = function
  | [] -> None
  | x :: l ->
     begin match f x with
       | Some _ as result -> result
       | None -> find_map f l
     end

let find_mapi f =
  let rec aux i = function
  | [] -> None
  | x :: l ->
     begin match f i x with
       | Some _ as result -> result
       | None -> aux (i+1) l
     end in
  aux 0

let[@tail_mod_cons] rec find_all p = function
  | [] -> []
  | x :: l -> if p x then x :: find_all p l else find_all p l

let filter = find_all

let[@tail_mod_cons] rec filteri p i = function
  | [] -> []
  | x::l ->
      let i' = i + 1 in
      if p i x then x :: filteri p i' l else filteri p i' l

let filteri p l = filteri p 0 l

let[@tail_mod_cons] rec filter_map f = function
  | [] -> []
  | x :: l ->
      match f x with
      | None -> filter_map f l
      | Some v -> v :: filter_map f l

let[@tail_mod_cons] rec concat_map f = function
  | [] -> []
  | x::xs -> prepend_concat_map (f x) f xs
and[@tail_mod_cons] prepend_concat_map ys f xs =
  match ys with
  | [] -> concat_map f xs
  | y :: ys -> y :: prepend_concat_map ys f xs

let fold_left_map f accu l =
  let rec aux accu l_accu = function
    | [] -> accu, rev l_accu
    | x :: l ->
        let accu, x = f accu x in
        aux accu (x :: l_accu) l in
  aux accu [] l

let partition p l =
  let rec part yes no = function
  | [] -> (rev yes, rev no)
  | x :: l -> if p x then part (x :: yes) no l else part yes (x :: no) l in
  part [] [] l

let partition_map p l =
  let rec part left right = function
  | [] -> (rev left, rev right)
  | x :: l ->
     begin match p x with
       | Either.Left v -> part (v :: left) right l
       | Either.Right v -> part left (v :: right) l
     end
  in
  part [] [] l

let rec split = function
    [] -> ([], [])
  | (x,y)::l ->
      let (rx, ry) = split l in (x::rx, y::ry)

let rec combine l1 l2 =
  match (l1, l2) with
    ([], []) -> []
  | (a1::l1, a2::l2) -> (a1, a2) :: combine l1 l2
  | (_, _) -> invalid_arg "List.combine"

(** sorting *)

let rec merge cmp l1 l2 =
  match l1, l2 with
  | [], l2 -> l2
  | l1, [] -> l1
  | h1 :: t1, h2 :: t2 ->
      if cmp h1 h2 <= 0
      then h1 :: merge cmp t1 l2
      else h2 :: merge cmp l1 t2


let stable_sort cmp l =
  let rec rev_merge l1 l2 accu =
    match l1, l2 with
    | [], l2 -> rev_append l2 accu
    | l1, [] -> rev_append l1 accu
    | h1::t1, h2::t2 ->
        if cmp h1 h2 <= 0
        then rev_merge t1 l2 (h1::accu)
        else rev_merge l1 t2 (h2::accu)
  in
  let rec rev_merge_rev l1 l2 accu =
    match l1, l2 with
    | [], l2 -> rev_append l2 accu
    | l1, [] -> rev_append l1 accu
    | h1::t1, h2::t2 ->
        if cmp h1 h2 > 0
        then rev_merge_rev t1 l2 (h1::accu)
        else rev_merge_rev l1 t2 (h2::accu)
  in
  let rec sort n l =
    match n, l with
    | 2, x1 :: x2 :: tl ->
        let s = if cmp x1 x2 <= 0 then [x1; x2] else [x2; x1] in
        (s, tl)
    | 3, x1 :: x2 :: x3 :: tl ->
        let s =
          if cmp x1 x2 <= 0 then
            if cmp x2 x3 <= 0 then [x1; x2; x3]
            else if cmp x1 x3 <= 0 then [x1; x3; x2]
            else [x3; x1; x2]
          else if cmp x1 x3 <= 0 then [x2; x1; x3]
          else if cmp x2 x3 <= 0 then [x2; x3; x1]
          else [x3; x2; x1]
        in
        (s, tl)
    | n, l ->
        let n1 = n asr 1 in
        let n2 = n - n1 in
        let s1, l2 = rev_sort n1 l in
        let s2, tl = rev_sort n2 l2 in
        (rev_merge_rev s1 s2 [], tl)
  and rev_sort n l =
    match n, l with
    | 2, x1 :: x2 :: tl ->
        let s = if cmp x1 x2 > 0 then [x1; x2] else [x2; x1] in
        (s, tl)
    | 3, x1 :: x2 :: x3 :: tl ->
        let s =
          if cmp x1 x2 > 0 then
            if cmp x2 x3 > 0 then [x1; x2; x3]
            else if cmp x1 x3 > 0 then [x1; x3; x2]
            else [x3; x1; x2]
          else if cmp x1 x3 > 0 then [x2; x1; x3]
          else if cmp x2 x3 > 0 then [x2; x3; x1]
          else [x3; x2; x1]
        in
        (s, tl)
    | n, l ->
        let n1 = n asr 1 in
        let n2 = n - n1 in
        let s1, l2 = sort n1 l in
        let s2, tl = sort n2 l2 in
        (rev_merge s1 s2 [], tl)
  in
  let len = length l in
  if len < 2 then l else fst (sort len l)


let sort = stable_sort
let fast_sort = stable_sort

(* Note: on a list of length between about 100000 (depending on the minor
   heap size and the type of the list) and Sys.max_array_size, it is
   actually faster to use the following, but it might also use more memory
   because the argument list cannot be deallocated incrementally.

   Also, there seems to be a bug in this code or in the
   implementation of obj_truncate.

external obj_truncate : 'a array -> int -> unit = "caml_obj_truncate"

let array_to_list_in_place a =
  let l = Array.length a in
  let rec loop accu n p =
    if p <= 0 then accu else begin
      if p = n then begin
        obj_truncate a p;
        loop (a.(p-1) :: accu) (n-1000) (p-1)
      end else begin
        loop (a.(p-1) :: accu) n (p-1)
      end
    end
  in
  loop [] (l-1000) l


let stable_sort cmp l =
  let a = Array.of_list l in
  Array.stable_sort cmp a;
  array_to_list_in_place a

*)


(** sorting + removing duplicates *)

let sort_uniq cmp l =
  let rec rev_merge l1 l2 accu =
    match l1, l2 with
    | [], l2 -> rev_append l2 accu
    | l1, [] -> rev_append l1 accu
    | h1::t1, h2::t2 ->
        let c = cmp h1 h2 in
        if c = 0 then rev_merge t1 t2 (h1::accu)
        else if c < 0
        then rev_merge t1 l2 (h1::accu)
        else rev_merge l1 t2 (h2::accu)
  in
  let rec rev_merge_rev l1 l2 accu =
    match l1, l2 with
    | [], l2 -> rev_append l2 accu
    | l1, [] -> rev_append l1 accu
    | h1::t1, h2::t2 ->
        let c = cmp h1 h2 in
        if c = 0 then rev_merge_rev t1 t2 (h1::accu)
        else if c > 0
        then rev_merge_rev t1 l2 (h1::accu)
        else rev_merge_rev l1 t2 (h2::accu)
  in
  let rec sort n l =
    match n, l with
    | 2, x1 :: x2 :: tl ->
        let s =
          let c = cmp x1 x2 in
          if c = 0 then [x1] else if c < 0 then [x1; x2] else [x2; x1]
        in
        (s, tl)
    | 3, x1 :: x2 :: x3 :: tl ->
        let s =
          let c = cmp x1 x2 in
          if c = 0 then
            let c = cmp x2 x3 in
            if c = 0 then [x2] else if c < 0 then [x2; x3] else [x3; x2]
          else if c < 0 then
            let c = cmp x2 x3 in
            if c = 0 then [x1; x2]
            else if c < 0 then [x1; x2; x3]
            else
              let c = cmp x1 x3 in
              if c = 0 then [x1; x2]
              else if c < 0 then [x1; x3; x2]
              else [x3; x1; x2]
          else
            let c = cmp x1 x3 in
            if c = 0 then [x2; x1]
            else if c < 0 then [x2; x1; x3]
            else
              let c = cmp x2 x3 in
              if c = 0 then [x2; x1]
              else if c < 0 then [x2; x3; x1]
              else [x3; x2; x1]
        in
        (s, tl)
    | n, l ->
        let n1 = n asr 1 in
        let n2 = n - n1 in
        let s1, l2 = rev_sort n1 l in
        let s2, tl = rev_sort n2 l2 in
        (rev_merge_rev s1 s2 [], tl)
  and rev_sort n l =
    match n, l with
    | 2, x1 :: x2 :: tl ->
        let s =
          let c = cmp x1 x2 in
          if c = 0 then [x1] else if c > 0 then [x1; x2] else [x2; x1]
        in
        (s, tl)
    | 3, x1 :: x2 :: x3 :: tl ->
        let s =
          let c = cmp x1 x2 in
          if c = 0 then
            let c = cmp x2 x3 in
            if c = 0 then [x2] else if c > 0 then [x2; x3] else [x3; x2]
          else if c > 0 then
            let c = cmp x2 x3 in
            if c = 0 then [x1; x2]
            else if c > 0 then [x1; x2; x3]
            else
              let c = cmp x1 x3 in
              if c = 0 then [x1; x2]
              else if c > 0 then [x1; x3; x2]
              else [x3; x1; x2]
          else
            let c = cmp x1 x3 in
            if c = 0 then [x2; x1]
            else if c > 0 then [x2; x1; x3]
            else
              let c = cmp x2 x3 in
              if c = 0 then [x2; x1]
              else if c > 0 then [x2; x3; x1]
              else [x3; x2; x1]
        in
        (s, tl)
    | n, l ->
        let n1 = n asr 1 in
        let n2 = n - n1 in
        let s1, l2 = sort n1 l in
        let s2, tl = sort n2 l2 in
        (rev_merge s1 s2 [], tl)
  in
  let len = length l in
  if len < 2 then l else fst (sort len l)


let rec compare_lengths l1 l2 =
  match l1, l2 with
  | [], [] -> 0
  | [], _ -> -1
  | _, [] -> 1
  | _ :: l1, _ :: l2 -> compare_lengths l1 l2

let rec compare_length_with l n =
  match l with
  | [] ->
    if n = 0 then 0 else
      if n > 0 then -1 else 1
  | _ :: l ->
    if n <= 0 then 1 else
      compare_length_with l (n-1)

let is_empty = function
  | [] -> true
  | _ :: _ -> false

(** {1 Comparison} *)

(* Note: we are *not* shortcutting the list by using
   [List.compare_lengths] first; this may be slower on long lists
   immediately start with distinct elements. It is also incorrect for
   [compare] below, and it is better (principle of least surprise) to
   use the same approach for both functions. *)
let rec equal eq l1 l2 =
  match l1, l2 with
  | [], [] -> true
  | [], _::_ | _::_, [] -> false
  | a1::l1, a2::l2 -> eq a1 a2 && equal eq l1 l2

let rec compare cmp l1 l2 =
  match l1, l2 with
  | [], [] -> 0
  | [], _::_ -> -1
  | _::_, [] -> 1
  | a1::l1, a2::l2 ->
    let c = cmp a1 a2 in
    if c <> 0 then c
    else compare cmp l1 l2

(** {1 Iterators} *)

let to_seq l =
  let rec aux l () = match l with
    | [] -> Seq.Nil
    | x :: tail -> Seq.Cons (x, aux tail)
  in
  aux l

let[@tail_mod_cons] rec of_seq seq =
  match seq () with
  | Seq.Nil -> []
  | Seq.Cons (x1, seq) ->
      begin match seq () with
      | Seq.Nil -> [x1]
      | Seq.Cons (x2, seq) -> x1 :: x2 :: of_seq seq
      end