# Module BatISet

    module BatISet: sig .. end

DIET : Discrete Interval Encoding Trees

Sets of integers represented as ranges

This data structure is efficient for large sets of integers where many adjacent integers are all part of the set. This will have higher overhead for sets with lots of point elements, but will be much more efficient for sets containing mostly ranges.

    type t = (int * int) BatAvlTree.tree

the underlying representation is a balanced tree of ranges

    type elt = int

This kind of set only holds ints

    val empty : t

The empty set

    val is_empty : t -> bool

Test whether a set is empty, returns `true` if the set is empty.

    val mem : int -> t -> bool

test whether a given int is a member of the set

    val add : int -> t -> t

Add the given int to the set, returning a new set

    val add_range : int -> int -> t -> t

`add_range lo hi t` adds the range of integers `lo, hi` (including both endpoints) to the given set, returning a new set
Raises `Invalid_argument` if `lo` > `hi`

    val singleton : int -> t

Return the singleton set containing only the given element

    val remove : int -> t -> t

Remove an element from the given set, returning a new set

    val remove_range : int -> int -> t -> t

`remove_range lo hi t` removes a range of elements from the given set, returning a new set
Raises `Invalid_argument` if `lo` > `hi`

    val union : t -> t -> t

Compute the union of two sets. This is the set whose elements are those elements in either input set.

    val inter : t -> t -> t

Compute the intersection of two sets. This is the set whose elements are those in *both* of the input sets.

    val diff : t -> t -> t

Compute the difference between two sets. This is the set of elements that are in the first but not in the second. Unlike `union` and `inter`, order matters here.

    val compl : t -> t

Create the complement of the given set - i.e. the set of all values not in the input set.

    val compare : t -> t -> int

Compare two sets. It is not safe to use the polymorphic (<) and related functions to compare these sets, as the tree representation used can balance in multiple ways.

    val equal : t -> t -> bool

Test whether two sets are equal. It is not safe to use the polymorphic (=) on these sets, as the same set can have multiple representations depending on how it was built.

    val ord : t -> t -> BatOrd.order

Same as `compare` but returns `BatOrd.Lt | BatOrd.Eq | BatOrd.Gt` instead of an int.

    val subset : t -> t -> bool

`subset t u` returns `true` if `t` is a subset of `u`

    val from : int -> t -> t

`from x t` returns the portion of `t` in the range `x, max_int`

    val after : int -> t -> t

`after x t` returns the portion of `t` in the range `x+1, max_int`

    val until : int -> t -> t

`until x t` returns the portion of `t` in the range `min_int, x`

    val before : int -> t -> t

`before x t` returns the portion of `t` in the range `min_int, x-1`

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

`iter f t` calls `f` once for each element of `t`

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

`iter_range f t` calls `f` once for each contiguous range of `t`. The contiguous ranges of a set are sequences of adjacent integers all part of the set.

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

`fold f t x0` returns the final result of merging each element of `t` into `x0` using merge function `f`

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

As fold, but operates on contiguous ranges

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

Tests whether a predicate applies to all elements of the set

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

Test whether some element of a set satisfies a predicate

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

Builds the subset of those elements that satisfy the predicate

    val partition : (int -> bool) -> t -> t * t

partitions the input set into two sets with elements that satisfy the predicate and those that don't

    val cardinal : t -> int

Returns the number of elements in the set

    val elements : t -> int list

Returns a list of all elements in the set

    val ranges : t -> (int * int) list

Returns a list of all contiguous ranges in the set

    val min_elt : t -> int

Returns the minimum element in the set

    val max_elt : t -> int

Returns the maximum element in the set

    val choose : t -> int

Returns some element in the set

    val enum : t -> (int * int) BatEnum.t

Enumerates all contiguous ranges in the set

    val of_enum : (int * int) BatEnum.t -> t

    val of_list : (int * int) list -> t

Build a ISet.t out of a list or enum of ranges

    val print : 'a BatIO.output -> t -> unit