20012016
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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 (==).
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_set/1
- is_subset/2
- new/0
- size/1
- subtract/2
- to_list/1
- union/1
- union/2
A general balanced set.
A general balanced set iterator.
Add a (possibly existing) element to a set.
Returns a new set formed from Set1 with
Element inserted. If Element
is already an
element in Set1, nothing is changed.
Rebalance tree representation of a set.
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.
Remove a (possibly non-existing) element from a set.
Returns a new set formed from Set1 with
Element removed. If Element
is not an element
in Set1, nothing is changed.
Remove an element from a set.
Returns a new set formed from Set1 with
Element removed. Assumes that
Element is present
in Set1.
Remove a (possibly non-existing) element from a set.
Returns a new set formed from Set1 with
Element removed. If Element
is not an element
in Set1, nothing is changed.
Return the difference of two sets.
Returns only the elements of Set1 that are not
also elements of Set2.
Return an empty set.
Returns a new empty set.
Filter set elements.
Filters elements in Set1 using predicate function
Pred.
Fold over set elements.
Folds Function over every element in
Set
returning the final value of the accumulator.
Convert a list into a set.
Returns a set of the elements in List, where
List can be unordered and contain duplicates.
Make a set from an ordset list.
Turns an ordered-set list List into a set.
The list must not contain duplicates.
Add a new element to a set.
Returns a new set formed from Set1 with
Element inserted. Assumes that
Element is not
present in Set1.
Return the intersection of a list of sets.
Returns the intersection of the non-empty list of sets.
Return the intersection of two sets.
Returns the intersection of Set1 and
Set2.
Check whether two sets are disjoint.
Returns true if Set1 and
Set2 are disjoint (have no elements in common),
otherwise false.
Test for membership of a set.
Returns true if Element is an element of
Set, otherwise false.
Test for empty set.
Returns true if Set is an empty set,
otherwise false.
Test for membership of a set.
Returns true if Element is an element of
Set, otherwise false.
Test for a set.
Returns true if Term appears to be a set,
otherwise false.
Test for subset.
Returns true when every element of Set1 is
also a member of Set2, otherwise false.
Return an iterator for a set.
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.
Return an iterator for a set starting from a specified 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.
Return largest element.
Returns the largest element in Set. Assumes that
Set is not empty.
Return an empty set.
Returns a new empty set.
Traverse a set with an iterator.
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.
Return a set with one element.
Returns a set containing only element Element.
Return the number of elements in a set.
Returns the number of elements in Set.
Return smallest element.
Returns the smallest element in Set. Assumes that
Set is not empty.
Return the difference of two sets.
Returns only the elements of Set1 that are not
also elements of Set2.
Extract largest 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.
Extract smallest 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.
Convert a set into a list.
Returns the elements of Set as a list.
Return the union of a list of sets.
Returns the merged (union) set of the list of sets.
Return the union of two sets.
Returns the merged (union) set of Set1 and
Set2.
See Also
gb_trees(3),
ordsets(3),
sets(3)