package containers

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package containers
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Array utils

type 'a sequence = ('a -> unit) -> unit
type 'a klist = unit -> [ `Nil | `Cons of 'a * 'a klist ]
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

Arrays

include module type of Array
val make : int -> 'a -> 'a array

Array.make n x returns a fresh array of length n, initialized with x. All the elements of this new array are initially physically equal to x (in the sense of the == predicate). Consequently, if x is mutable, it is shared among all elements of the array, and modifying x through one of the array entries will modify all other entries at the same time.

Raise Invalid_argument if n < 0 or n > Sys.max_array_length. If the value of x is a floating-point number, then the maximum size is only Sys.max_array_length / 2.

val create : int -> 'a -> 'a array
  • deprecated

    Array.create is an alias for Array.make.

val create_float : int -> float array

Array.create_float n returns a fresh float array of length n, with uninitialized data.

  • since 4.03
val make_float : int -> float array
val init : int -> (int -> 'a) -> 'a array

Array.init n f returns a fresh array of length n, with element number i initialized to the result of f i. In other terms, Array.init n f tabulates the results of f applied to the integers 0 to n-1.

Raise Invalid_argument if n < 0 or n > Sys.max_array_length. If the return type of f is float, then the maximum size is only Sys.max_array_length / 2.

val make_matrix : int -> int -> 'a -> 'a array array

Array.make_matrix dimx dimy e returns a two-dimensional array (an array of arrays) with first dimension dimx and second dimension dimy. All the elements of this new matrix are initially physically equal to e. The element (x,y) of a matrix m is accessed with the notation m.(x).(y).

Raise Invalid_argument if dimx or dimy is negative or greater than Sys.max_array_length. If the value of e is a floating-point number, then the maximum size is only Sys.max_array_length / 2.

val create_matrix : int -> int -> 'a -> 'a array array
val append : 'a array -> 'a array -> 'a array

Array.append v1 v2 returns a fresh array containing the concatenation of the arrays v1 and v2.

val concat : 'a array list -> 'a array

Same as Array.append, but concatenates a list of arrays.

val sub : 'a array -> int -> int -> 'a array

Array.sub a start len returns a fresh array of length len, containing the elements number start to start + len - 1 of array a.

Raise Invalid_argument "Array.sub" if start and len do not designate a valid subarray of a; that is, if start < 0, or len < 0, or start + len > Array.length a.

val copy : 'a array -> 'a array

Array.copy a returns a copy of a, that is, a fresh array containing the same elements as a.

val fill : 'a array -> int -> int -> 'a -> unit

Array.fill a ofs len x modifies the array a in place, storing x in elements number ofs to ofs + len - 1.

Raise Invalid_argument "Array.fill" if ofs and len do not designate a valid subarray of a.

val to_list : 'a array -> 'a list

Array.to_list a returns the list of all the elements of a.

val of_list : 'a list -> 'a array

Array.of_list l returns a fresh array containing the elements of l.

Iterators

val mapi : (int -> 'a -> 'b) -> 'a array -> 'b array

Same as Array.map, but the function is applied to the index of the element as first argument, and the element itself as second argument.

val fold_left : ('a -> 'b -> 'a) -> 'a -> 'b array -> 'a

Array.fold_left f x a computes f (... (f (f x a.(0)) a.(1)) ...) a.(n-1), where n is the length of the array a.

val fold_right : ('b -> 'a -> 'a) -> 'b array -> 'a -> 'a

Array.fold_right f a x computes f a.(0) (f a.(1) ( ... (f a.(n-1) x) ...)), where n is the length of the array a.

Iterators on two arrays

Array scanning

val mem : 'a -> 'a array -> bool

mem a l is true if and only if a is equal to an element of l.

  • since 4.03.0
val memq : 'a -> 'a array -> bool

Same as Array.mem, but uses physical equality instead of structural equality to compare array elements.

  • since 4.03.0

Sorting

val sort : ('a -> 'a -> int) -> 'a array -> unit

Sort an array 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 below for a complete specification). For example, Pervasives.compare is a suitable comparison function, provided there are no floating-point NaN values in the data. After calling Array.sort, the array is sorted in place in increasing order. Array.sort is guaranteed to run in constant heap space and (at most) logarithmic stack space.

The current implementation uses Heap Sort. It runs in constant stack space.

Specification of the comparison function: Let a be the array and cmp the comparison function. The following must be true for all x, y, z in a :

  • cmp x y > 0 if and only if cmp y x < 0
  • if cmp x y >= 0 and cmp y z >= 0 then cmp x z >= 0

When Array.sort returns, a contains the same elements as before, reordered in such a way that for all i and j valid indices of a :

  • cmp a.(i) a.(j) >= 0 if and only if i >= j
val stable_sort : ('a -> 'a -> int) -> 'a array -> unit

Same as Array.sort, but the sorting algorithm is stable (i.e. elements that compare equal are kept in their original order) and not guaranteed to run in constant heap space.

The current implementation uses Merge Sort. It uses n/2 words of heap space, where n is the length of the array. It is usually faster than the current implementation of Array.sort.

val fast_sort : ('a -> 'a -> int) -> 'a array -> unit

Same as Array.sort or Array.stable_sort, whichever is faster on typical input.

Iterators
val to_seqi : 'a array -> (int * 'a) Seq.t

Iterate on the array, in increasing order, yielding indices along elements. Modifications of the array during iteration will be reflected in the iterator.

  • since 4.07
val of_seq : 'a Seq.t -> 'a array

Create an array from the generator

  • since 4.07
type 'a t = 'a array
val empty : 'a t

The empty array, physically equal to ||.

val equal : 'a equal -> 'a t equal

Hoist an equality test for elements to arrays. Arrays are only equal if their lengths are the same and corresponding elements test equal.

val compare : 'a ord -> 'a t ord
val swap : 'a t -> int -> int -> unit

swap arr i j swaps elements at indices i and j.

  • since 1.4
val get : 'a t -> int -> 'a

get a n returns the element number n of array a. The first element has number 0. The last element has number length a - 1. You can also write a.(n) instead of get a n.

Raise Invalid_argument "index out of bounds" if n is outside the range 0 to (length a - 1).

val get_safe : 'a t -> int -> 'a option

get_safe a i returns Some a.(i) if i is a valid index.

  • since 0.18
val set : 'a t -> int -> 'a -> unit

set a n x modifies array a in place, replacing element number n with x. You can also write a.(n) <- x instead of set a n x.

Raise Invalid_argument "index out of bounds" if n is outside the range 0 to length a - 1.

val length : _ t -> int

Return the length (number of elements) of the given array.

val fold : ('a -> 'b -> 'a) -> 'a -> 'b t -> 'a

fold f x a computes f (... (f (f x a.(0)) a.(1)) ...) a.(n-1), where n is the length of the array a.

val foldi : ('a -> int -> 'b -> 'a) -> 'a -> 'b t -> 'a

Fold left on array, with index.

val fold_while : ('a -> 'b -> 'a * [ `Stop | `Continue ]) -> 'a -> 'b t -> 'a

Fold left on array until a stop condition via ('a, `Stop) is indicated by the accumulator.

  • since 0.8
val fold_map : ('acc -> 'a -> 'acc * 'b) -> 'acc -> 'a t -> 'acc * 'b t

fold_map f acc a is a fold_left-like function, but it also maps the array to another array.

  • since 1.2
val scan_left : ('acc -> 'a -> 'acc) -> 'acc -> 'a t -> 'acc t

scan_left f acc a returns the array [|acc; f acc x0; f (f acc a.(0)) a.(1); …|] .

  • since 1.2
val iter : ('a -> unit) -> 'a t -> unit

iter f a applies function f in turn to all the elements of a. It is equivalent to f a.(0); f a.(1); ...; f a.(length a - 1); ().

val iteri : (int -> 'a -> unit) -> 'a t -> unit

Like Array.iter, but the function is applied to the index of the element as first argument, and the element itself as second argument.

val blit : 'a t -> int -> 'a t -> int -> int -> unit

blit v1 o1 v2 o2 len copies len elements from array v1, starting at element number o1, to array v2, starting at element number o2. It works correctly even if v1 and v2 are the same array, and the source and destination chunks overlap.

Raise Invalid_argument "Array.blit" if o1 and len do not designate a valid subarray of v1, or if o2 and len do not designate a valid subarray of v2.

val reverse_in_place : 'a t -> unit

Reverse the array in place.

val sorted : ('a -> 'a -> int) -> 'a t -> 'a array

sorted cmp a makes a copy of a and sorts it with cmp.

  • since 1.0
val sort_indices : ('a -> 'a -> int) -> 'a t -> int array

sort_indices cmp a returns a new array b, with the same length as a, such that b.(i) is the index at which the i-th element of sorted cmp a appears in a. a is not modified.

In other words, map (fun i -> a.(i)) (sort_indices cmp a) = sorted cmp a. sort_indices yields the inverse permutation of sort_ranking.

  • since 1.0
val sort_ranking : ('a -> 'a -> int) -> 'a t -> int array

sort_ranking cmp a returns a new array b, with the same length as a, such that b.(i) is the index at which the i-the element of a appears in sorted cmp a. a is not modified.

In other words, map (fun i -> (sorted cmp a).(i)) (sort_ranking cmp a) = a. sort_ranking yields the inverse permutation of sort_indices.

In the absence of duplicate elements in a, we also have lookup_exn a.(i) (sorted a) = (sorted_ranking a).(i).

  • since 1.0
val find_map : ('a -> 'b option) -> 'a t -> 'b option

find_map f a returns Some y if there is an element x such that f x = Some y, else it returns None.

  • since 1.3
val find : ('a -> 'b option) -> 'a t -> 'b option

Alias to find_map.

  • deprecated

    since 1.3

val find_map_i : (int -> 'a -> 'b option) -> 'a t -> 'b option

Like find_map, but also pass the index to the predicate function.

  • since 1.3
val findi : (int -> 'a -> 'b option) -> 'a t -> 'b option

Alias to find_map_i.

  • since 0.3.4
  • deprecated

    since 1.3

val find_idx : ('a -> bool) -> 'a t -> (int * 'a) option

find_idx p x returns Some (i,x) where x is the i-th element of l, and p x holds. Otherwise returns None.

  • since 0.3.4
val lookup : cmp:'a ord -> 'a -> 'a t -> int option

Lookup the index of some value in a sorted array. Undefined behavior if the array is not sorted wrt cmp. Complexity: O(log (n)) (dichotomic search).

  • returns

    None if the key is not present, or Some i (i the index of the key) otherwise.

val lookup_exn : cmp:'a ord -> 'a -> 'a t -> int

Like lookup, but

  • raises Not_found

    if the key is not present.

val bsearch : cmp:('a -> 'a -> int) -> 'a -> 'a t -> [ `All_lower | `All_bigger | `Just_after of int | `Empty | `At of int ]

bsearch ?cmp x arr finds the index of the object x in the array arr, provided arr is sorted using cmp. If the array is not sorted, the result is not specified (may

  • raises Invalid_argument).

    Complexity: O(log n) where n is the length of the array (dichotomic search).

  • returns
    • `At i if cmp arr.(i) x = 0 (for some i).
    • `All_lower if all elements of arr are lower than x.
    • `All_bigger if all elements of arr are bigger than x.
    • `Just_after i if arr.(i) < x < arr.(i+1).
    • `Empty if the array is empty.
  • raises Invalid_argument

    if the array is found to be unsorted w.r.t cmp.

  • since 0.13
val for_all : ('a -> bool) -> 'a t -> bool

for_all p [|a1; ...; an|] checks if all elements of the array satisfy the predicate p. That is, it returns (p a1) && (p a2) && ... && (p an).

val for_all2 : ('a -> 'b -> bool) -> 'a t -> 'b t -> bool

Forall on pairs of arrays.

  • raises Invalid_argument

    if they have distinct lengths. Allow different types.

  • since 0.20
val exists : ('a -> bool) -> 'a t -> bool

exists p [|a1; ...; an|] checks if at least one element of the array satisfies the predicate p. That is, it returns (p a1) || (p a2) || ... || (p an).

val exists2 : ('a -> 'b -> bool) -> 'a t -> 'b t -> bool

Exists on pairs of arrays.

  • raises Invalid_argument

    if they have distinct lengths. Allow different types.

  • since 0.20
val fold2 : ('acc -> 'a -> 'b -> 'acc) -> 'acc -> 'a t -> 'b t -> 'acc

Fold on two arrays stepwise.

  • raises Invalid_argument

    if they have distinct lengths.

  • since 0.20
val iter2 : ('a -> 'b -> unit) -> 'a t -> 'b t -> unit

Iterate on two arrays stepwise.

  • raises Invalid_argument

    if they have distinct lengths.

  • since 0.20
val shuffle : 'a t -> unit

Shuffle randomly the array, in place.

val shuffle_with : Random.State.t -> 'a t -> unit

Like shuffle but using a specialized random state.

val random_choose : 'a t -> 'a random_gen

Choose an element randomly.

  • raises Not_found

    if the array/slice is empty.

val to_seq : 'a t -> 'a sequence

Return a sequence of the elements of an array. The input array is shared with the sequence and modifications of it will result in modification of the sequence.

val to_gen : 'a t -> 'a gen

Return a gen of the elements of an array.

val to_klist : 'a t -> 'a klist

Return a klist of the elements of an array.

IO

val pp : ?sep:string -> 'a printer -> 'a t printer

Print an array of items with printing function.

val pp_i : ?sep:string -> (int -> 'a printer) -> 'a t printer

Print an array, giving the printing function both index and item.

val map : ('a -> 'b) -> 'a t -> 'b t

map f a applies function f to all the elements of a, and builds an array with the results returned by f: [| f a.(0); f a.(1); ...; f a.(length a - 1) |].

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

map2 f a b applies function f to all the elements of a and b, and builds an array with the results returned by f: [| f a.(0) b.(0); ...; f a.(length a - 1) b.(length b - 1)|].

  • raises Invalid_argument

    if they have distinct lengths.

  • since 0.20
val rev : 'a t -> 'a t

Copy + reverse in place.

  • since 0.20
val filter : ('a -> bool) -> 'a t -> 'a t

Filter elements out of the array. Only the elements satisfying the given predicate will be kept.

val filter_map : ('a -> 'b option) -> 'a t -> 'b t

Map each element into another value, or discard it.

val flat_map : ('a -> 'b t) -> 'a t -> 'b array

Transform each element into an array, then flatten.

val (>>=) : 'a t -> ('a -> 'b t) -> 'b t

Infix version of flat_map.

val (>>|) : 'a t -> ('a -> 'b) -> 'b t

Infix version of map.

  • since 0.8
val (>|=) : 'a t -> ('a -> 'b) -> 'b t

Infix version of map.

  • since 0.8
val except_idx : 'a t -> int -> 'a list

Remove given index, obtaining the list of the other elements.

val (--) : int -> int -> int t

Range array. Bounds included.

val (--^) : int -> int -> int t

Range array, excluding right bound.

  • since 0.17
val random : 'a random_gen -> 'a t random_gen
val random_non_empty : 'a random_gen -> 'a t random_gen
val random_len : int -> 'a random_gen -> 'a t random_gen

Generic Functions

module type MONO_ARRAY = sig ... end
val sort_generic : (module MONO_ARRAY with type elt = 'elt and type t = 'arr) -> cmp:('elt -> 'elt -> int) -> 'arr -> unit

Sort the array, without allocating (eats stack space though). Performance might be lower than Array.sort.

  • since 0.14
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