Module Vect

module Vect: 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 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

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 : int -> 'a t -> 'a

get n r returns the (n+1)th element from the vect r; i.e. get 0 r 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 set : int -> 'a -> 'a t -> 'a t

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

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

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 : ('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 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 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 id_map : ('a -> 'a) -> 'a t -> 'a t

id_map f v returns a vect isomorphic to v where each element of index i equals f (get v i). It is very similar to map, but tries to share as much data as possible with the original vect; for example, id_map (fun x -> x) v == v. This can lead to significative space savings if f leaves many values unmodified. For each element, the new value f x and the old one x are compared with <>. Operates in O(n) time.

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.

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