20012015
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gb_sets
gb_sets
General Balanced Trees
An implementation of ordered sets using Prof. Arne Andersson's
General Balanced Trees. This 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 between 10
and 100 times. This implementation is particularly suited for
accumulating elements a few at a time, building up a large set
(more than 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
All of the following functions in this module also exist
and do the same thing in the sets and ordsets
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 GB set.
A GB 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. Note that
this is rarely necessary, but may be motivated when a large
number of elements have been deleted from the tree without
further insertions. Rebalancing could then be forced in order
to minimise lookup times, since deletion only does not
rebalance the tree.
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 which 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 may 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 two sets
Returns the intersection of Set1 and Set2.
Return the intersection of a list of sets
Returns the intersection of the non-empty list of sets.
Check whether two sets are disjoint
Returns true if Set1 and
Set2 are disjoint (have no elements in common),
and false otherwise.
Test for empty set
Returns true if Set is an empty set, and
false otherwise.
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 nonempty.
Traverse a set with an iterator
Returns {Element, Iter2} where Element is the
smallest element referred to by the 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 the 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 nonempty.
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
nonempty.
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
nonempty.
Convert a set into a list
Returns the elements of Set as a list.
Return the union of two sets
Returns the merged (union) set of Set1 and
Set2.
Return the union of a list of sets
Returns the merged (union) set of the list of sets.
SEE ALSO
gb_trees(3),
ordsets(3),
sets(3)