/Erlang 21

# gb_sets

gb_sets

## Module Summary

General balanced trees.

## Description

This module provides ordered sets using Prof. Arne Andersson's General Balanced Trees. Ordered sets can be much more efficient than using ordered lists, for larger sets, but depends on the application.

This module considers two elements as different if and only if they do not compare equal (`==`).

## Complexity Note

The complexity on set operations is bounded by either O(|S|) or O(|T| * log(|S|)), where S is the largest given set, depending on which is fastest for any particular function call. For operating on sets of almost equal size, this implementation is about 3 times slower than using ordered-list sets directly. For sets of very different sizes, however, this solution can be arbitrarily much faster; in practical cases, often 10-100 times. This implementation is particularly suited for accumulating elements a few at a time, building up a large set (> 100-200 elements), and repeatedly testing for membership in the current set.

As with normal tree structures, lookup (membership testing), insertion, and deletion have logarithmic complexity.

## Compatibility

The following functions in this module also exist and provides the same functionality in the `sets(3)` and `ordsets(3)` modules. That is, by only changing the module name for each call, you can try out different set representations.

• `add_element/2`
• `del_element/2`
• `filter/2`
• `fold/3`
• `from_list/1`
• `intersection/1`
• `intersection/2`
• `is_element/2`
• `is_empty/1`
• `is_set/1`
• `is_subset/2`
• `new/0`
• `size/1`
• `subtract/2`
• `to_list/1`
• `union/1`
• `union/2`

## Data Types

`set(Element)`

A general balanced set.

`set() = set(term())`
`iter(Element)`

A general balanced set iterator.

`iter() = iter(term())`

## Types

Returns a new set formed from `Set1` with `Element` inserted. If `Element` is already an element in `Set1`, nothing is changed.

balance(Set1) -> Set2

## Types

Rebalances the tree representation of `Set1`. Notice that this is rarely necessary, but can be motivated when a large number of elements have been deleted from the tree without further insertions. Rebalancing can then be forced to minimise lookup times, as deletion does not rebalance the tree.

del_element(Element, Set1) -> Set2

## Types

Returns a new set formed from `Set1` with `Element` removed. If `Element` is not an element in `Set1`, nothing is changed.

delete(Element, Set1) -> Set2

## Types

Returns a new set formed from `Set1` with `Element` removed. Assumes that `Element` is present in `Set1`.

delete_any(Element, Set1) -> Set2

## Types

Returns a new set formed from `Set1` with `Element` removed. If `Element` is not an element in `Set1`, nothing is changed.

difference(Set1, Set2) -> Set3

## Types

Returns only the elements of `Set1` that are not also elements of `Set2`.

empty() -> Set

## Types

Returns a new empty set.

filter(Pred, Set1) -> Set2

## Types

Filters elements in `Set1` using predicate function `Pred`.

fold(Function, Acc0, Set) -> Acc1

## Types

Folds `Function` over every element in `Set` returning the final value of the accumulator.

from_list(List) -> Set

## Types

Returns a set of the elements in `List`, where `List` can be unordered and contain duplicates.

from_ordset(List) -> Set

## Types

Turns an ordered-set list `List` into a set. The list must not contain duplicates.

insert(Element, Set1) -> Set2

## Types

Returns a new set formed from `Set1` with `Element` inserted. Assumes that `Element` is not present in `Set1`.

intersection(SetList) -> Set

## Types

Returns the intersection of the non-empty list of sets.

intersection(Set1, Set2) -> Set3

## Types

Returns the intersection of `Set1` and `Set2`.

is_disjoint(Set1, Set2) -> boolean()

## Types

Returns `true` if `Set1` and `Set2` are disjoint (have no elements in common), otherwise `false`.

is_element(Element, Set) -> boolean()

## Types

Returns `true` if `Element` is an element of `Set`, otherwise `false`.

is_empty(Set) -> boolean()

## Types

Returns `true` if `Set` is an empty set, otherwise `false`.

is_member(Element, Set) -> boolean()

## Types

Returns `true` if `Element` is an element of `Set`, otherwise `false`.

is_set(Term) -> boolean()

## Types

Returns `true` if `Term` appears to be a set, otherwise `false`.

is_subset(Set1, Set2) -> boolean()

## Types

Returns `true` when every element of `Set1` is also a member of `Set2`, otherwise `false`.

iterator(Set) -> Iter

## Types

Returns an iterator that can be used for traversing the entries of `Set`; see `next/1`. The implementation of this is very efficient; traversing the whole set using `next/1` is only slightly slower than getting the list of all elements using `to_list/1` and traversing that. The main advantage of the iterator approach is that it does not require the complete list of all elements to be built in memory at one time.

iterator_from(Element, Set) -> Iter

## Types

Returns an iterator that can be used for traversing the entries of `Set`; see `next/1`. The difference as compared to the iterator returned by `iterator/1` is that the first element greater than or equal to `Element` is returned.

largest(Set) -> Element

## Types

Returns the largest element in `Set`. Assumes that `Set` is not empty.

new() -> Set

## Types

Returns a new empty set.

next(Iter1) -> {Element, Iter2} | none

## Types

Returns `{Element, Iter2}`, where `Element` is the smallest element referred to by iterator `Iter1`, and `Iter2` is the new iterator to be used for traversing the remaining elements, or the atom `none` if no elements remain.

singleton(Element) -> `set`(Element)

Returns a set containing only element `Element`.

size(Set) -> integer() >= 0

## Types

Returns the number of elements in `Set`.

smallest(Set) -> Element

## Types

Returns the smallest element in `Set`. Assumes that `Set` is not empty.

subtract(Set1, Set2) -> Set3

## Types

Returns only the elements of `Set1` that are not also elements of `Set2`.

take_largest(Set1) -> {Element, Set2}

## Types

Returns `{Element, Set2}`, where `Element` is the largest element in `Set1`, and `Set2` is this set with `Element` deleted. Assumes that `Set1` is not empty.

take_smallest(Set1) -> {Element, Set2}

## Types

Returns `{Element, Set2}`, where `Element` is the smallest element in `Set1`, and `Set2` is this set with `Element` deleted. Assumes that `Set1` is not empty.

to_list(Set) -> List

## Types

Returns the elements of `Set` as a list.

union(SetList) -> Set

## Types

Returns the merged (union) set of the list of sets.

union(Set1, Set2) -> Set3

## Types

Returns the merged (union) set of `Set1` and `Set2`.

`gb_trees(3)`, `ordsets(3)`, `sets(3)`