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.
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
set(Element)
A general balanced set.
set() = set(term())
iter(Element)
A general balanced set iterator.
iter() = iter(term())
Returns a new set formed from Set1
with Element
inserted. If Element
is already an element in Set1
, nothing is changed.
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.
Returns a new set formed from Set1
with Element
removed. If Element
is not an element in Set1
, nothing is changed.
Returns a new set formed from Set1
with Element
removed. Assumes that Element
is present in Set1
.
Returns a new set formed from Set1
with Element
removed. If Element
is not an element in Set1
, nothing is changed.
Returns only the elements of Set1
that are not also elements of Set2
.
Returns a new empty set.
Filters elements in Set1
using predicate function Pred
.
Folds Function
over every element in Set
returning the final value of the accumulator.
Returns a set of the elements in List
, where List
can be unordered and contain duplicates.
Turns an ordered-set list List
into a set. The list must not contain duplicates.
Returns a new set formed from Set1
with Element
inserted. Assumes that Element
is not present in Set1
.
Returns the intersection of the non-empty list of sets.
Returns the intersection of Set1
and Set2
.
Returns true
if Set1
and Set2
are disjoint (have no elements in common), otherwise false
.
Returns true
if Element
is an element of Set
, otherwise false
.
Returns true
if Set
is an empty set, otherwise false
.
Returns true
if Element
is an element of Set
, otherwise false
.
Returns true
if Term
appears to be a set, otherwise false
.
Returns true
when every element of Set1
is also a member of Set2
, otherwise false
.
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.
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.
Returns the largest element in Set
. Assumes that Set
is not empty.
Returns a new empty set.
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.
set
(Element)Returns a set containing only element Element
.
Returns the number of elements in Set
.
Returns the smallest element in Set
. Assumes that Set
is not empty.
Returns only the elements of Set1
that are not also elements of Set2
.
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.
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.
Returns the elements of Set
as a list.
Returns the merged (union) set of the list of sets.
Returns the merged (union) set of Set1
and Set2
.
gb_trees(3)
, ordsets(3)
, sets(3)
© 2010–2017 Ericsson AB
Licensed under the Apache License, Version 2.0.