Module `Base__List`

Immutable, singly-linked lists, giving fast access to the front of the list, and slow (i.e., O(n)) access to the back of the list. The comparison functions on lists are lexicographic.

type 'a t = 'a list

val compare : ('a -> 'a -> int) -> 'a t -> 'a t -> int
val hash_fold_t : (Base.Hash.state -> 'a -> Base.Hash.state) -> Base.Hash.state -> 'a t -> Base.Hash.state

include Base.Sexpable.S1 with type 'a t := 'a t

type 'a t

val t_of_sexp : (Base.Sexp.t -> 'a) -> Base.Sexp.t -> 'a t
val sexp_of_t : ('a -> Base.Sexp.t) -> 'a t -> Base.Sexp.t

include Base.Container.S1 with type 'a t := 'a t

type 'a t

val mem : 'a t -> 'a -> equal:('a -> 'a -> bool) -> bool: Checks whether the provided element is there, using equal.

val length : 'a t -> int
val is_empty : 'a t -> bool
val iter : 'a t -> f:('a -> unit) -> unit
val fold : 'a t -> init:'accum -> f:('accum -> 'a -> 'accum) -> 'accum: fold t ~init ~f returns f (... f (f (f init e1) e2) e3 ...) en, where e1..en are the elements of t

val fold_result : 'a t -> init:'accum -> f:('accum -> 'a -> ('accum, 'e) Base.Result.t) -> ('accum, 'e) Base.Result.t: fold_result t ~init ~f is a short-circuiting version of fold that runs in the Result monad. If f returns an Error _, that value is returned without any additional invocations of f.

val fold_until : 'a t -> init:'accum -> f:('accum -> 'a -> ('accum, 'final) Base__.Container_intf.Continue_or_stop.t) -> finish:('accum -> 'final) -> 'final

fold_until t ~init ~f ~finish is a short-circuiting version of fold. If f returns Stop _ the computation ceases and results in that value. If f returns Continue _, the fold will proceed. If f never returns Stop _, the final result is computed by finish.

Example:

type maybe_negative =
  | Found_negative of int
  | All_nonnegative of { sum : int }

(** [first_neg_or_sum list] returns the first negative number in [list], if any,
    otherwise returns the sum of the list. *)
let first_neg_or_sum =
  List.fold_until ~init:0
    ~f:(fun sum x ->
      if x < 0
      then Stop (Found_negative x)
      else Continue (sum + x))
    ~finish:(fun sum -> All_nonnegative { sum })
;;

let x = first_neg_or_sum [1; 2; 3; 4; 5]
val x : maybe_negative = All_nonnegative {sum = 15}

let y = first_neg_or_sum [1; 2; -3; 4; 5]
val y : maybe_negative = Found_negative -3

val exists : 'a t -> f:('a -> bool) -> bool: Returns true if and only if there exists an element for which the provided function evaluates to true. This is a short-circuiting operation.

val for_all : 'a t -> f:('a -> bool) -> bool: Returns true if and only if the provided function evaluates to true for all elements. This is a short-circuiting operation.

val count : 'a t -> f:('a -> bool) -> int: Returns the number of elements for which the provided function evaluates to true.

val sum : (module Base__.Container_intf.Summable with type t = 'sum) -> 'a t -> f:('a -> 'sum) -> 'sum: Returns the sum of f i for all i in the container.

val find : 'a t -> f:('a -> bool) -> 'a option: Returns as an option the first element for which f evaluates to true.

val find_map : 'a t -> f:('a -> 'b option) -> 'b option: Returns the first evaluation of f that returns Some, and returns None if there is no such element.

val to_list : 'a t -> 'a list
val to_array : 'a t -> 'a array
val min_elt : 'a t -> compare:('a -> 'a -> int) -> 'a option: Returns a minimum (resp maximum) element from the collection using the provided compare function, or None if the collection is empty. In case of a tie, the first element encountered while traversing the collection is returned. The implementation uses fold so it has the same complexity as fold.

val max_elt : 'a t -> compare:('a -> 'a -> int) -> 'a option

include Base.Monad.S with type 'a t := 'a t

type 'a t

include Base__.Monad_intf.S_without_syntax with type 'a t := 'a t

type 'a t

include Base__.Monad_intf.Infix with type 'a t := 'a t

type 'a t

val (>>=) : 'a t -> ('a -> 'b t) -> 'b t: t >>= f returns a computation that sequences the computations represented by two monad elements. The resulting computation first does t to yield a value v, and then runs the computation returned by f v.

val (>>|) : 'a t -> ('a -> 'b) -> 'b t: t >>| f is t >>= (fun a -> return (f a)).

module Monad_infix : Base__.Monad_intf.Infix with type 'a t := 'a t

val bind : 'a t -> f:('a -> 'b t) -> 'b t: bind t ~f = t >>= f

val return : 'a -> 'a t: return v returns the (trivial) computation that returns v.

val map : 'a t -> f:('a -> 'b) -> 'b t: map t ~f is t >>| f.

val join : 'a t t -> 'a t: join t is t >>= (fun t' -> t').

val ignore_m : 'a t -> unit t: ignore_m t is map t ~f:(fun _ -> ()). ignore_m used to be called ignore, but we decided that was a bad name, because it shadowed the widely used Caml.ignore. Some monads still do let ignore = ignore_m for historical reasons.

val all : 'a t list -> 'a list t
val all_unit : unit t list -> unit t: Like all, but ensures that every monadic value in the list produces a unit value, all of which are discarded rather than being collected into a list.

val all_ignore : unit t list -> unit t

include Base__.Monad_intf.Syntax with type 'a t := 'a t

type 'a t

module Let_syntax : sig ... end

module Or_unequal_lengths : sig ... end: Or_unequal_lengths is used for functions that take multiple lists and that only make sense if all the lists have the same length, e.g., iter2, map3. Such functions check the list lengths prior to doing anything else, and return Unequal_lengths if not all the lists have the same length.

val of_list : 'a t -> 'a t

of_list is the identity function. It is useful so that the List module matches the same signature that other container modules do, namely:

val of_list : 'a List.t -> 'a t

val nth : 'a t -> int -> 'a option
val nth_exn : 'a t -> int -> 'a: Return the n-th element of the given list. The first element (head of the list) is at position 0. Raise if the list is too short or n is negative.

val rev : 'a t -> 'a t: List reversal.

val rev_append : 'a t -> 'a t -> 'a t: rev_append l1 l2 reverses l1 and concatenates it to l2. This is equivalent to (List.rev l1) @ l2, but rev_append is more efficient.

val unordered_append : 'a t -> 'a t -> 'a t: unordered_append l1 l2 has the same elements as l1 @ l2, but in some unspecified order. Generally takes time proportional to length of first list, but is O(1) if either list is empty.

val rev_map : 'a t -> f:('a -> 'b) -> 'b t: rev_map l ~f gives the same result as List.rev (ListLabels.map f l), but is more efficient.

val iter2_exn : 'a t -> 'b t -> f:('a -> 'b -> unit) -> unit: iter2 [a1; ...; an] [b1; ...; bn] ~f calls in turn f a1 b1; ...; f an bn. The exn version will raise if the two lists have different lengths.

val iter2 : 'a t -> 'b t -> f:('a -> 'b -> unit) -> unit Or_unequal_lengths.t
val rev_map2_exn : 'a t -> 'b t -> f:('a -> 'b -> 'c) -> 'c t: rev_map2_exn l1 l2 ~f gives the same result as List.rev (List.map2_exn l1 l2 ~f), but is more efficient.

val rev_map2 : 'a t -> 'b t -> f:('a -> 'b -> 'c) -> 'c t Or_unequal_lengths.t
val fold2_exn : 'a t -> 'b t -> init:'c -> f:('c -> 'a -> 'b -> 'c) -> 'c: fold2 ~f ~init:a [b1; ...; bn] [c1; ...; cn] is f (... (f (f a b1 c1) b2 c2) ...) bn cn. The exn version will raise if the two lists have different lengths.

val fold2 : 'a t -> 'b t -> init:'c -> f:('c -> 'a -> 'b -> 'c) -> 'c Or_unequal_lengths.t
val for_alli : 'a t -> f:(int -> 'a -> bool) -> bool: Like List.for_all, but passes the index as an argument.

val for_all2_exn : 'a t -> 'b t -> f:('a -> 'b -> bool) -> bool: Like List.for_all, but for a two-argument predicate. The exn version will raise if the two lists have different lengths.

val for_all2 : 'a t -> 'b t -> f:('a -> 'b -> bool) -> bool Or_unequal_lengths.t
val existsi : 'a t -> f:(int -> 'a -> bool) -> bool: Like List.exists, but passes the index as an argument.

val exists2_exn : 'a t -> 'b t -> f:('a -> 'b -> bool) -> bool: Like List.exists, but for a two-argument predicate. The exn version will raise if the two lists have different lengths.

val exists2 : 'a t -> 'b t -> f:('a -> 'b -> bool) -> bool Or_unequal_lengths.t
val filter : 'a t -> f:('a -> bool) -> 'a t: filter l ~f returns all the elements of the list l that satisfy the predicate p. The order of the elements in the input list is preserved.

val rev_filter : 'a t -> f:('a -> bool) -> 'a t: Like filter, but reverses the order of the input list.

val filteri : 'a t -> f:(int -> 'a -> bool) -> 'a t
val partition_map : 'a t -> f:('a -> [ `Fst of 'b | `Snd of 'c ]) -> 'b t * 'c t: partition_map t ~f partitions t according to f.

val partition3_map : 'a t -> f:('a -> [ `Fst of 'b | `Snd of 'c | `Trd of 'd ]) -> 'b t * 'c t * 'd t
val partition_tf : 'a t -> f:('a -> bool) -> 'a t * 'a t: partition_tf l ~f returns a pair of lists (l1, l2), where l1 is the list of all the elements of l that satisfy the predicate p, and l2 is the list of all the elements of l that do not satisfy p. The order of the elements in the input list is preserved. The "tf" suffix is mnemonic to remind readers at a call that the result is (trues, falses).

val partition_result : ('ok, 'error) Base.Result.t t -> 'ok t * 'error t: partition_result l returns a pair of lists (l1, l2), where l1 is the list of all Ok elements in l and l2 is the list of all Error elements. The order of elements in the input list is preserved.

val split_n : 'a t -> int -> 'a t * 'a t

split_n [e1; ...; em] n is ([e1; ...; en], [en+1; ...; em]).

If n > m, ([e1; ...; em], []) is returned.
If n < 0, ([], [e1; ...; em]) is returned.

val sort : 'a t -> compare:('a -> 'a -> int) -> 'a t

Sort a list in increasing order according to a comparison function. The comparison function must return 0 if its arguments compare as equal, a positive integer if the first is greater, and a negative integer if the first is smaller (see Array.sort for a complete specification). For example, Poly.compare is a suitable comparison function.

The current implementation uses Merge Sort. It runs in linear heap space and logarithmic stack space.

Presently, the sort is stable, meaning that two equal elements in the input will be in the same order in the output.

val stable_sort : 'a t -> compare:('a -> 'a -> int) -> 'a t: Like sort, but guaranteed to be stable.

val merge : 'a t -> 'a t -> compare:('a -> 'a -> int) -> 'a t: Merges two lists: assuming that l1 and l2 are sorted according to the comparison function compare, merge compare l1 l2 will return a sorted list containing all the elements of l1 and l2. If several elements compare equal, the elements of l1 will be before the elements of l2.

val hd : 'a t -> 'a option
val tl : 'a t -> 'a t option
val hd_exn : 'a t -> 'a: Returns the first element of the given list. Raises if the list is empty.

val tl_exn : 'a t -> 'a t: Returns the given list without its first element. Raises if the list is empty.

val findi : 'a t -> f:(int -> 'a -> bool) -> (int * 'a) option
val find_exn : 'a t -> f:('a -> bool) -> 'a: find_exn t ~f returns the first element of t that satisfies f. It raises Caml.Not_found or Not_found_s if there is no such element.

val find_map_exn : 'a t -> f:('a -> 'b option) -> 'b: Returns the first evaluation of f that returns Some. Raises Caml.Not_found or Not_found_s if f always returns None.

val find_mapi : 'a t -> f:(int -> 'a -> 'b option) -> 'b option
val find_mapi_exn : 'a t -> f:(int -> 'a -> 'b option) -> 'b
val append : 'a t -> 'a t -> 'a t: E.g., append [1; 2] [3; 4; 5] is [1; 2; 3; 4; 5]

val map : 'a t -> f:('a -> 'b) -> 'b t: map f [a1; ...; an] applies function f to a1, a2, ..., an, in order, and builds the list [f a1; ...; f an] with the results returned by f.

val folding_map : 'a t -> init:'b -> f:('b -> 'a -> 'b * 'c) -> 'c t
val folding_mapi : 'a t -> init:'b -> f:(int -> 'b -> 'a -> 'b * 'c) -> 'c t

val fold_map : 'a t -> init:'b -> f:('b -> 'a -> 'b * 'c) -> 'b * 'c t
val fold_mapi : 'a t -> init:'b -> f:(int -> 'b -> 'a -> 'b * 'c) -> 'b * 'c t
val concat_map : 'a t -> f:('a -> 'b t) -> 'b t: concat_map t ~f is concat (map t ~f), except that there is no guarantee about the order in which f is applied to the elements of t.

val concat_mapi : 'a t -> f:(int -> 'a -> 'b t) -> 'b t: concat_mapi t ~f is like concat_map, but passes the index as an argument

val map2_exn : 'a t -> 'b t -> f:('a -> 'b -> 'c) -> 'c t: map2 [a1; ...; an] [b1; ...; bn] ~f is [f a1 b1; ...; f an bn]. The exn version will raise if the two lists have different lengths.

val map2 : 'a t -> 'b t -> f:('a -> 'b -> 'c) -> 'c t Or_unequal_lengths.t

val rev_map3_exn : 'a t -> 'b t -> 'c t -> f:('a -> 'b -> 'c -> 'd) -> 'd t
val rev_map3 : 'a t -> 'b t -> 'c t -> f:('a -> 'b -> 'c -> 'd) -> 'd t Or_unequal_lengths.t

val map3_exn : 'a t -> 'b t -> 'c t -> f:('a -> 'b -> 'c -> 'd) -> 'd t
val map3 : 'a t -> 'b t -> 'c t -> f:('a -> 'b -> 'c -> 'd) -> 'd t Or_unequal_lengths.t
val rev_map_append : 'a t -> 'b t -> f:('a -> 'b) -> 'b t: rev_map_append l1 l2 ~f reverses l1 mapping f over each element, and appends the result to the front of l2.

val fold_right : 'a t -> f:('a -> 'b -> 'b) -> init:'b -> 'b: fold_right [a1; ...; an] ~f ~init:b is f a1 (f a2 (... (f an b) ...)).

val fold_left : 'a t -> init:'b -> f:('b -> 'a -> 'b) -> 'b: fold_left is the same as Container.S1.fold, and one should always use fold rather than fold_left, except in functors that are parameterized over a more general signature where this equivalence does not hold.

val unzip : ('a * 'b) t -> 'a t * 'b t
val unzip3 : ('a * 'b * 'c) t -> 'a t * 'b t * 'c t

val zip : 'a t -> 'b t -> ('a * 'b) t Or_unequal_lengths.t
val zip_exn : 'a t -> 'b t -> ('a * 'b) t
val mapi : 'a t -> f:(int -> 'a -> 'b) -> 'b t: mapi is just like map, but it also passes in the index of each element as the first argument to the mapped function. Tail-recursive.

val rev_mapi : 'a t -> f:(int -> 'a -> 'b) -> 'b t
val iteri : 'a t -> f:(int -> 'a -> unit) -> unit: iteri is just like iter, but it also passes in the index of each element as the first argument to the iter'd function. Tail-recursive.

val foldi : 'a t -> init:'b -> f:(int -> 'b -> 'a -> 'b) -> 'b: foldi is just like fold, but it also passes in the index of each element as the first argument to the folded function. Tail-recursive.

val reduce_exn : 'a t -> f:('a -> 'a -> 'a) -> 'a: reduce_exn [a1; ...; an] ~f is f (... (f (f a1 a2) a3) ...) an. It fails on the empty list. Tail recursive.

val reduce : 'a t -> f:('a -> 'a -> 'a) -> 'a option

val reduce_balanced : 'a t -> f:('a -> 'a -> 'a) -> 'a option

reduce_balanced returns the same value as reduce when f is associative, but differs in that the tree of nested applications of f has logarithmic depth.

This is useful when your 'a grows in size as you reduce it and f becomes more expensive with bigger inputs. For example, reduce_balanced ~f:(^) takes n*log(n) time, while reduce ~f:(^) takes quadratic time.

val reduce_balanced_exn : 'a t -> f:('a -> 'a -> 'a) -> 'a

val group : 'a t -> break:('a -> 'a -> bool) -> 'a t t

group l ~break returns a list of lists (i.e., groups) whose concatenation is equal to the original list. Each group is broken where break returns true on a pair of successive elements.

Example:

group ~break:(<>) ['M';'i';'s';'s';'i';'s';'s';'i';'p';'p';'i'] ->

[['M'];['i'];['s';'s'];['i'];['s';'s'];['i'];['p';'p'];['i']]

val groupi : 'a t -> break:(int -> 'a -> 'a -> bool) -> 'a t t

This is just like group, except that you get the index in the original list of the current element along with the two elements.

Example, group the chars of "Mississippi" into triples:

groupi ~break:(fun i _ _ -> i mod 3 = 0)
  ['M';'i';'s';'s';'i';'s';'s';'i';'p';'p';'i'] ->

[['M'; 'i'; 's']; ['s'; 'i'; 's']; ['s'; 'i'; 'p']; ['p'; 'i']]

val chunks_of : 'a t -> length:int -> 'a t t: chunks_of l ~length returns a list of lists whose concatenation is equal to the original list. Every list has length elements, except for possibly the last list, which may have fewer. chunks_of raises if length <= 0.

val last : 'a t -> 'a option: The final element of a list. The _exn version raises on the empty list.

val last_exn : 'a t -> 'a
val is_prefix : 'a t -> prefix:'a t -> equal:('a -> 'a -> bool) -> bool: is_prefix xs ~prefix returns true if xs starts with prefix.

val find_consecutive_duplicate : 'a t -> equal:('a -> 'a -> bool) -> ('a * 'a) option: find_consecutive_duplicate t ~equal returns the first pair of consecutive elements (a1, a2) in t such that equal a1 a2. They are returned in the same order as they appear in t. equal need not be an equivalence relation; it is simply used as a predicate on consecutive elements.

val remove_consecutive_duplicates : ?⁠which_to_keep:[ `First | `Last ] -> 'a t -> equal:('a -> 'a -> bool) -> 'a t: Returns the given list with consecutive duplicates removed. The relative order of the other elements is unaffected. The element kept from a run of duplicates is determined by which_to_keep.

val dedup_and_sort : compare:('a -> 'a -> int) -> 'a t -> 'a t: Returns the given list with duplicates removed and in sorted order.

val dedup : compare:('a -> 'a -> int) -> 'a t -> 'a t
val find_a_dup : compare:('a -> 'a -> int) -> 'a t -> 'a option: find_a_dup returns a duplicate from the list (with no guarantees about which duplicate you get), or None if there are no dups.

val contains_dup : compare:('a -> 'a -> int) -> 'a t -> bool: Returns true if there are any two elements in the list which are the same. O(n log n) time complexity.

val find_all_dups : compare:('a -> 'a -> int) -> 'a t -> 'a list: find_all_dups returns a list of all elements that occur more than once, with no guarantees about order. O(n log n) time complexity.

val count : 'a t -> f:('a -> bool) -> int: count l ~f is the number of elements in l that satisfy the predicate f.

val counti : 'a t -> f:(int -> 'a -> bool) -> int
val range : ?⁠stride:int -> ?⁠start:[ `inclusive | `exclusive ] -> ?⁠stop:[ `inclusive | `exclusive ] -> int -> int -> int t: range ?stride ?start ?stop start_i stop_i is the list of integers from start_i to stop_i, stepping by stride. If stride < 0 then we need start_i > stop_i for the result to be nonempty (or start_i = stop_i in the case where both bounds are inclusive).

val range' : compare:('a -> 'a -> int) -> stride:('a -> 'a) -> ?⁠start:[ `inclusive | `exclusive ] -> ?⁠stop:[ `inclusive | `exclusive ] -> 'a -> 'a -> 'a t: range' is analogous to range for general start/stop/stride types. range' raises if stride x returns x or if the direction that stride x moves x changes from one call to the next.

val init : int -> f:(int -> 'a) -> 'a t: init n ~f is [(f 0); (f 1); ...; (f (n-1))]. It is an error if n < 0. init applies f to values in decreasing order; starting with n - 1, and ending with 0. This is the opposite order to Array.init.

val rev_filter_map : 'a t -> f:('a -> 'b option) -> 'b t: rev_filter_map l ~f is the reversed sublist of l containing only elements for which f returns Some e.

val rev_filter_mapi : 'a t -> f:(int -> 'a -> 'b option) -> 'b t: rev_filter_mapi is just like rev_filter_map, but it also passes in the index of each element as the first argument to the mapped function. Tail-recursive.

val filter_map : 'a t -> f:('a -> 'b option) -> 'b t: filter_map l ~f is the sublist of l containing only elements for which f returns Some e.

val filter_mapi : 'a t -> f:(int -> 'a -> 'b option) -> 'b t: filter_mapi is just like filter_map, but it also passes in the index of each element as the first argument to the mapped function. Tail-recursive.

val filter_opt : 'a option t -> 'a t: filter_opt l is the sublist of l containing only elements which are Some e. In other words, filter_opt l = filter_map ~f:ident l.

module Assoc : sig ... end: Interpret a list of (key, value) pairs as a map in which only the first occurrence of a key affects the semantics, i.e.:

val sub : 'a t -> pos:int -> len:int -> 'a t: sub pos len l is the len-element sublist of l, starting at pos.

val take : 'a t -> int -> 'a t: take l n returns the first n elements of l, or all of l if n > length l. take l n = fst (split_n l n).

val drop : 'a t -> int -> 'a t: drop l n returns l without the first n elements, or the empty list if n > length l. drop l n is equivalent to snd (split_n l n).

val take_while : 'a t -> f:('a -> bool) -> 'a t: take_while l ~f returns the longest prefix of l for which f is true.

val drop_while : 'a t -> f:('a -> bool) -> 'a t: drop_while l ~f drops the longest prefix of l for which f is true.

val split_while : 'a t -> f:('a -> bool) -> 'a t * 'a t: split_while xs ~f = (take_while xs ~f, drop_while xs ~f).

val concat : 'a t t -> 'a t: Concatenates a list of lists. The elements of the argument are all concatenated together (in the same order) to give the result. Tail recursive over outer and inner lists.

val concat_no_order : 'a t t -> 'a t: Like concat, but faster and without preserving any ordering (i.e., for lists that are essentially viewed as multi-sets).

val cons : 'a -> 'a t -> 'a t
val cartesian_product : 'a t -> 'b t -> ('a * 'b) t: Returns a list with all possible pairs -- if the input lists have length len1 and len2, the resulting list will have length len1 * len2.

val permute : ?⁠random_state:Base.Random.State.t -> 'a t -> 'a t

permute ?random_state t returns a permutation of t.

permute side-effects random_state by repeated calls to Random.State.int. If random_state is not supplied, permute uses Random.State.default.

val random_element : ?⁠random_state:Base.Random.State.t -> 'a t -> 'a option

random_element ?random_state t is None if t is empty, else it is Some x for some x chosen uniformly at random from t.

random_element side-effects random_state by calling Random.State.int. If random_state is not supplied, random_element uses Random.State.default.

val random_element_exn : ?⁠random_state:Base.Random.State.t -> 'a t -> 'a

val is_sorted : 'a t -> compare:('a -> 'a -> int) -> bool

is_sorted t ~compare returns true iff for all adjacent a1; a2 in t, compare a1 a2 <= 0.

is_sorted_strictly is similar, except it uses < instead of <=.

val is_sorted_strictly : 'a t -> compare:('a -> 'a -> int) -> bool
val equal : ('a -> 'a -> bool) -> 'a t -> 'a t -> bool

module Infix : sig ... end

val transpose : 'a t t -> 'a t t option

transpose m transposes the rows and columns of the matrix m, considered as either a row of column lists or (dually) a column of row lists.

Example:

transpose [[1;2;3];[4;5;6]] = [[1;4];[2;5];[3;6]]

On non-empty rectangular matrices, transpose is an involution (i.e., transpose (transpose m) = m). Transpose returns None when called on lists of lists with non-uniform lengths.

val transpose_exn : 'a t t -> 'a t t: transpose_exn transposes the rows and columns of its argument, throwing an exception if the list is not rectangular.

val intersperse : 'a t -> sep:'a -> 'a t: intersperse xs ~sep places sep between adjacent elements of xs. For example, intersperse [1;2;3] ~sep:0 = [1;0;2;0;3].