# gb_sets

gb_sets
General balanced trees.

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 (==).

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.

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.

A general balanced set.

A general balanced set iterator.

### Types

Set1 = Set2 = set(Element)

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

### Types

Set1 = Set2 = set(Element)

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.

### Types

Set1 = Set2 = set(Element)

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

### Types

Set1 = Set2 = set(Element)

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

### Types

Set1 = Set2 = set(Element)

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

### Types

Set1 = Set2 = Set3 = set(Element)

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

### Types

Set = set()

Returns a new empty set.

### Types

Pred = fun((Element) -> boolean())
Set1 = Set2 = set(Element)

Filters elements in Set1 using predicate function Pred.

### Types

Function = fun((Element, AccIn) -> AccOut)
Acc0 = Acc1 = AccIn = AccOut = Acc
Set = set(Element)

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

### Types

List = [Element]
Set = set(Element)

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

### Types

List = [Element]
Set = set(Element)

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

### Types

Set1 = Set2 = set(Element)

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

### Types

SetList = [set(Element), ...]
Set = set(Element)

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

### Types

Set1 = Set2 = Set3 = set(Element)

Returns the intersection of Set1 and Set2.

### Types

Set1 = Set2 = set(Element)

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

### Types

Set = set(Element)

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

### Types

Set = set()

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

### Types

Set = set(Element)

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

### Types

Term = term()

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

### Types

Set1 = Set2 = set(Element)

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

### Types

Set = set(Element)
Iter = iter(Element)

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.

### Types

Set = set(Element)
Iter = iter(Element)

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.

### Types

Set = set(Element)

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

### Types

Set = set()

Returns a new empty set.

### Types

Iter1 = Iter2 = iter(Element)

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.

Returns a set containing only element Element.

### Types

Set = set()

Returns the number of elements in Set.

### Types

Set = set(Element)

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

### Types

Set1 = Set2 = Set3 = set(Element)

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

### Types

Set1 = Set2 = set(Element)

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.

### Types

Set1 = Set2 = set(Element)

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.

### Types

Set = set(Element)
List = [Element]

Returns the elements of Set as a list.

### Types

SetList = [set(Element), ...]
Set = set(Element)

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

### Types

Set1 = Set2 = Set3 = set(Element)

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