gb_trees
General Balanced Trees
An efficient implementation of Prof. Arne Andersson's General Balanced Trees. These have no storage overhead compared to unbalanced binary trees, and their performance is in general better than AVL trees.
This module considers two keys as different if and only if
they do not compare equal (==
).
Data structure
Data structure:
- {Size, Tree}, where `Tree' is composed of nodes of the form: - {Key, Value, Smaller, Bigger}, and the "empty tree" node: - nil.
There is no attempt to balance trees after deletions. Since deletions do not increase the height of a tree, this should be OK.
Original balance condition h(T) <= ceil(c * log(|T|)) has been changed to the similar (but not quite equivalent) condition 2 ^ h(T) <= |T| ^ c. This should also be OK.
Performance is comparable to the AVL trees in the Erlang book (and faster in general due to less overhead); the difference is that deletion works for these trees, but not for the book's trees. Behaviour is logarithmic (as it should be).
A GB tree.
A GB tree iterator.
Functions
balance(Tree1) -> Tree2
Rebalances
. Note that this is rarely necessary,
but may be motivated when a large number of nodes 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.
delete(Key, Tree1) -> Tree2
Removes the node with key
from
;
returns new tree. Assumes that the key is present in the tree,
crashes otherwise.
delete_any(Key, Tree1) -> Tree2
Removes the node with key
from
if
the key is present in the tree, otherwise does nothing;
returns new tree.
empty() -> gb_tree()
Returns a new empty tree
enter(Key, Val, Tree1) -> Tree2
Inserts
with value
into
if
the key is not present in the tree, otherwise updates
to value
in
. Returns the
new tree.
from_orddict(List) -> Tree
Turns an ordered list
of key-value tuples into a
tree. The list must not contain duplicate keys.
get(Key, Tree) -> Val
Retrieves the value stored with
in
.
Assumes that the key is present in the tree, crashes
otherwise.
lookup(Key, Tree) -> none | {value, Val}
Looks up
in
; returns
{value,
, or none
if
is not
present.
insert(Key, Val, Tree1) -> Tree2
Inserts
with value
into
;
returns the new tree. Assumes that the key is not present in
the tree, crashes otherwise.
is_defined(Key, Tree) -> boolean()
Returns true
if
is present in
,
otherwise false
.
is_empty(Tree) -> boolean()
Returns true
if
is an empty tree, and
false
otherwise.
iterator(Tree) -> Iter
Returns an iterator that can be used for traversing the
entries of
; see next/1
. The implementation
of this is very efficient; traversing the whole tree 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.
keys(Tree) -> [Key]
Returns the keys in
as an ordered list.
largest(Tree) -> {Key, Val}
Returns {
, where
is the largest
key in
, and
is the value associated
with this key. Assumes that the tree is nonempty.
map(Function, Tree1) -> Tree2
Maps the function F(
and returns a new tree
with the same set of keys
as
and the new set of values
.
next(Iter1) -> none | {Key, Val, Iter2}
Returns {
where
is the
smallest key referred to by the iterator
, and
is the new iterator to be used for
traversing the remaining nodes, or the atom none
if no
nodes remain.
size(Tree) -> integer() >= 0
Returns the number of nodes in
.
smallest(Tree) -> {Key, Val}
Returns {
, where
is the smallest
key in
, and
is the value associated
with this key. Assumes that the tree is nonempty.
take_largest(Tree1) -> {Key, Val, Tree2}
Returns {
, where
is the
largest key in
,
is the value
associated with this key, and
is this tree with
the corresponding node deleted. Assumes that the tree is
nonempty.
take_smallest(Tree1) -> {Key, Val, Tree2}
Returns {
, where
is the
smallest key in
,
is the value
associated with this key, and
is this tree with
the corresponding node deleted. Assumes that the tree is
nonempty.
to_list(Tree) -> [{Key, Val}]
Converts a tree into an ordered list of key-value tuples.
update(Key, Val, Tree1) -> Tree2
Updates
to value
in
;
returns the new tree. Assumes that the key is present in the
tree.
values(Tree) -> [Val]
Returns the values in
as an ordered list, sorted
by their corresponding keys. Duplicates are not removed.