# Module BatVect

    module BatVect: sig .. end

Extensible vectors with constant-time append/prepend.

This module implements extensible arrays which work very much like ropes as described in Boehm, H., Atkinson, R., and Plass, M. 1995. Ropes: an alternative to strings. Softw. Pract. Exper. 25, 12 (Dec. 1995), 1315-1330.

These vectors have some interesting properties:

- lower space overhead than other structures based on balanced trees such as Vec. The overhead can be adjusted, allowing to make get faster at the expense of set and viceversa.
- appending or prepending a small vector to an arbitrarily large one in amortized constant time
- concat, substring, insert, remove operations in amortized logarithmic time
- access to and modification of vectors in logarithmic time

Functional nature and persistence

All operations but `destructive_set` (provided for efficient ephemeral usage) are non-destructive: the original vect is never modified. When a new vect is returned as the result of an operation, it will share as much data as possible with its "parent". For instance, if a vect of length `n` undergoes `m` operations (assume `n >> m`) like set, append or prepend, the modified vector will only require `O(m)` space in addition to that taken by the original vect.

However, Vect is an amortized data structure, and its use in a persistent setting can easily degrade its amortized time bounds. It is thus mainly intended to be used ephemerally. In some cases, it is possible to use Vect persistently with the same amortized bounds by explicitly rebalancing vects to be reused using `balance`. Special care must be taken to avoid calling `balance` too frequently; in the limit, calling `balance` after each modification would defeat the purpose of amortization.

This module is not thread-safe.
Author(s): Mauricio Fernandez

    type 'a t

The type of a polymorphic vect.

    exception Out_of_bounds

Raised when an operation violates the bounds of the vect.

    val max_length : int

Maximum length of the vect.

###### Creation and conversions

    val empty : 'a t

The empty vect.

    val singleton : 'a -> 'a t

Returns a vect of length 1 holding only the given element.

    val of_array : 'a array -> 'a t

`of_array s` returns a vect corresponding to the array `s`. Operates in `O(n)` time.

    val to_array : 'a t -> 'a array

`to_array r` returns an array corresponding to the vect `r`.

    val to_list : 'a t -> 'a list

Returns a list with the elements contained in the vect.

    val of_list : 'a list -> 'a t

    val make : int -> 'a -> 'a t

`make i c` returns a vect of length `i` whose elements are all equal to `c`; it is similar to Array.make

    val init : int -> (int -> 'a) -> 'a t

`init n f` returns a fresh vect of length `n`, with element number `i` initialized to the result of `f i`. In other terms, `init n f` tabulates the results of `f` applied to the integers `0` to `n-1`.
Raises `Invalid_argument` if `n < 0` or `n > max_length`.

###### Properties

    val is_empty : 'a t -> bool

Returns whether the vect is empty or not.

    val height : 'a t -> int

Returns the height (depth) of the vect.

    val length : 'a t -> int

Returns the length of the vect (`O(1)`).

###### Operations

    val balance : 'a t -> 'a t

`balance r` returns a balanced copy of the `r` vect. Note that vects are automatically rebalanced when their height exceeds a given threshold, but `balance` allows to invoke that operation explicity.

    val concat : 'a t -> 'a t -> 'a t

`concat r u` concatenates the `r` and `u` vects. In general, it operates in `O(log(min n1 n2))` amortized time. Small vects are treated specially and can be appended/prepended in amortized `O(1)` time.

    val append : 'a -> 'a t -> 'a t

`append c r` returns a new vect with the `c` element at the end in amortized `O(1)` time.

    val prepend : 'a -> 'a t -> 'a t

`prepend c r` returns a new vect with the `c` character at the beginning in amortized `O(1)` time.

    val get : 'a t -> int -> 'a

`get v n` returns the (n+1)th element from the vect `v`; i.e. `get v 0` returns the first element. Operates in worst-case `O(log size)` time.
Raises `Out_of_bounds` if a character out of bounds is requested.

    val at : 'a t -> int -> 'a

as `get`

    val set : 'a t -> int -> 'a -> 'a t

`set v n c` returns a copy of the `v` vect where the (n+1)th element (see also `get`) has been set to `c`. Operates in worst-case `O(log size)` time.

    val modify : 'a t -> int -> ('a -> 'a) -> 'a t

`modify v n f` is equivalent to `set v n (f (get v n))`, but more efficient. Operates in worst-case `O(log size)` time.

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

`destructive_set n e v` sets the element of index `n` in the `v` vect to `e`. This operation is destructive, and will also affect vects sharing the modified leaf with `v`. Use with caution.

    val sub : 'a t -> int -> int -> 'a t

`sub m n r` returns a sub-vect of `r` containing all the elements whose indexes range from `m` to `m + n - 1` (included).
Raises `Out_of_bounds` in the same cases as Array.sub. Operates in worst-case `O(log size)` time.

    val insert : int -> 'a t -> 'a t -> 'a t

`insert n r u` returns a copy of the `u` vect where `r` has been inserted between the elements with index `n` and `n + 1` in the original vect. The length of the new vect is `length u + length r`. Operates in amortized `O(log(size r) + log(size u))` time.

    val remove : int -> int -> 'a t -> 'a t

`remove m n r` returns the vect resulting from deleting the elements with indexes ranging from `m` to `m + n - 1` (included) from the original vect `r`. The length of the new vect is `length r - n`. Operates in amortized `O(log(size r))` time.

###### Conversion

    val enum : 'a t -> 'a BatEnum.t

Returns an enumeration of the elements of the vector. Behavior of the enumeration is undefined if the contents of the vector changes afterwards.

    val of_enum : 'a BatEnum.t -> 'a t

Build a vector from an enumeration.

    val backwards : 'a t -> 'a BatEnum.t

Returns an enumeration of the elements of a vector, from last to first. Behavior of the enumeration is undefined if the contents of the vector changes afterwards.

    val of_backwards : 'a BatEnum.t -> 'a t

Build a vector from an enumeration, from last to first.

###### Iteration and higher-order functions

    val iter : ('a -> unit) -> 'a t -> unit

`iter f r` applies `f` to all the elements in the `r` vect, in order.

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

Operates like iter, but also passes the index of the character to the given function.

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

`rangeiter f m n r` applies `f` to all the elements whose indices `k` satisfy `m` <= `k` < `m + n`. It is thus equivalent to `iter f (sub m n r)`, but does not create an intermediary vect. `rangeiter` operates in worst-case `O(n + log m)` time, which improves on the `O(n log m)` bound from an explicit loop using `get`.
Raises `Out_of_bounds` in the same cases as `sub`.

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

`fold_left f a r` computes `f (... (f (f a r0) r1)...) rN-1` where `rn = Vect.get n r` and `N = length r`.

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

An alias for `BatVect.fold_left`

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

as `BatVect.fold_left`, but no initial value - just applies reducing function to elements from left to right.

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

`fold_right f r a` computes `f (r0 ... (f rN-2 (f rN-1 a)) ...))` where `rn = Vect.get n r` and `N = length r`.

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

As `BatVect.fold`, but with the position of each value passed to the folding function

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

`map f v` returns a vect isomorphic to `v` where each element of index `i` equals `f (get v i)`. Therefore, the height of the returned vect is the same as that of the original one. Operates in `O(n)` time.

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

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

###### Predicates

    val for_all : ('a -> bool) -> 'a t -> bool

`for_all p [a0; a1; ...; an]` checks if all elements of the vect satisfy the predicate `p`. That is, it returns `(p a0) && (p a1) && ... && (p an)`.

    val exists : ('a -> bool) -> 'a t -> bool

`exists p [a0; a1; ...; an]` checks if at least one element of the vect satisfies the predicate `p`. That is, it returns `(p a0) || (p a1) || ... || (p an)`.

    val find : ('a -> bool) -> 'a t -> 'a

`find p a` returns the first element of vect `a` that satisfies the predicate `p`.
Raises `Not_found` if there is no value that satisfies `p` in the vect `a`.

    val mem : 'a -> 'a t -> bool

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

    val memq : 'a -> 'a t -> bool

Same as `Vect.mem` but uses physical equality instead of structural equality to compare vect elements.

    val findi : ('a -> bool) -> 'a t -> int

`findi p a` returns the index of the first element of vect `a` that satisfies the predicate `p`.
Raises `Not_found` if there is no value that satisfies `p` in the vect `a`.

    val filter : ('a -> bool) -> 'a t -> 'a t

`filter f v` returns a vect with the elements `x` from `v` such that `f x` returns `true`. Operates in `O(n)` time.

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

`filter_map f e` returns a vect consisting of all elements `x` such that `f y` returns `Some x` , where `y` is an element of `e`.

    val find_all : ('a -> bool) -> 'a t -> 'a t

`find_all` is another name for `Vect.filter`.

    val partition : ('a -> bool) -> 'a t -> 'a t * 'a t

`partition p v` returns a pair of vects `(v1, v2)`, where `v1` is the vect of all the elements of `v` that satisfy the predicate `p`, and `v2` is the vect of all the elements of `v` that do not satisfy `p`. The order of the elements in the input vect is preserved.

###### Convenience Functions

    val first : 'a t -> 'a

    val last : 'a t -> 'a

These return the first and last values in the vector

    val shift : 'a t -> 'a * 'a t

Return the first element of a vector and its last `n-1` elements.

    val pop : 'a t -> 'a * 'a t

Return the last element of a vector and its first `n-1` elements.

###### Boilerplate code

    val print : ?first:string ->
           ?last:string ->
           ?sep:string ->
           ('a BatInnerIO.output -> 'b -> unit) ->
           'a BatInnerIO.output -> 'b t -> unit

    val compare : 'a BatOrd.comp -> 'a t BatOrd.comp

    val equal : 'a BatOrd.eq -> 'a t BatOrd.eq

    val ord : 'a BatOrd.ord -> 'a t BatOrd.ord

###### Functorial interface

    module type RANDOMACCESS = sig .. end

    module Make: functor (R : RANDOMACCESS) -> functor (PARAM : sig
    val max_height : int
    val leaf_size : intend) -> sig .. end