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.
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 : int -> int -> 'a t -> '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 : ('a -> 'b -> 'a) -> 'a -> 'b t -> 'a

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

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

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 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 -> 'a -> 'b -> 'a) -> 'a -> 'b t -> 'a

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

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

find p a returns the first element of array a that satisfies the predicate p.
Raises Not_found if there is no value that satisfies p in the array 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 Array.mem but uses physical equality instead of structural equality to compare array elements.

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

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

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

partition p a returns a pair of arrays (a1, a2), where a1 is the array of all the elements of a that satisfy the predicate p, and a2 is the array of all the elements of a that do not satisfy p. The order of the elements in the input array is preserved.

val first : 'a t -> 'a

Convenience Functions

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

Printing

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

Functorial interface

module type RANDOMACCESS = sig .. end

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