gb_trees(3erl) Erlang Module Definition gb_trees(3erl)
NAME
gb_trees - General balanced trees.
DESCRIPTION
This module provides Prof. Arne Andersson's General Balanced Trees.
These have no storage overhead compared to unbalanced binary trees, and
their performance is better than AVL trees.
This module considers two keys as different if and only if they do not
compare equal (==).
DATA STRUCTURE
Trees and iterators are built using opaque data structures that should
not be pattern-matched from outside this module.
There is no attempt to balance trees after deletions. As deletions do
not increase the height of a tree, this should be OK.
The 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.
DATA TYPES
tree(Key, Value)
A general balanced tree.
tree() = tree(term(), term())
iter(Key, Value)
A general balanced tree iterator.
iter() = iter(term(), term())
EXPORTS
balance(Tree1) -> Tree2
Types:
Tree1 = Tree2 = tree(Key, Value)
Rebalances Tree1. Notice that this is rarely necessary, but can
be motivated when many nodes have been deleted from the tree
without further insertions. Rebalancing can then be forced to
minimize lookup times, as deletion does not rebalance the tree.
delete(Key, Tree1) -> Tree2
Types:
Tree1 = Tree2 = tree(Key, Value)
Removes the node with key Key from Tree1 and returns the new
tree. Assumes that the key is present in the tree, crashes oth-
erwise.
delete_any(Key, Tree1) -> Tree2
Types:
Tree1 = Tree2 = tree(Key, Value)
Removes the node with key Key from Tree1 if the key is present
in the tree, otherwise does nothing. Returns the new tree.
take(Key, Tree1) -> {Value, Tree2}
Types:
Tree1 = Tree2 = tree(Key, term())
Key = Value = term()
Returns a value Value from node with key Key and new Tree2 with-
out the node with this value. Assumes that the node with key is
present in the tree, crashes otherwise.
take_any(Key, Tree1) -> {Value, Tree2} | error
Types:
Tree1 = Tree2 = tree(Key, term())
Key = Value = term()
Returns a value Value from node with key Key and new Tree2 with-
out the node with this value. Returns error if the node with the
key is not present in the tree.
empty() -> tree()
Returns a new empty tree.
enter(Key, Value, Tree1) -> Tree2
Types:
Tree1 = Tree2 = tree(Key, Value)
Inserts Key with value Value into Tree1 if the key is not
present in the tree, otherwise updates Key to value Value in
Tree1. Returns the new tree.
from_orddict(List) -> Tree
Types:
List = [{Key, Value}]
Tree = tree(Key, Value)
Turns an ordered list List of key-value tuples into a tree. The
list must not contain duplicate keys.
get(Key, Tree) -> Value
Types:
Tree = tree(Key, Value)
Retrieves the value stored with Key in Tree. Assumes that the
key is present in the tree, crashes otherwise.
insert(Key, Value, Tree1) -> Tree2
Types:
Tree1 = Tree2 = tree(Key, Value)
Inserts Key with value Value into Tree1 and returns the new
tree. Assumes that the key is not present in the tree, crashes
otherwise.
is_defined(Key, Tree) -> boolean()
Types:
Tree = tree(Key, Value :: term())
Returns true if Key is present in Tree, otherwise false.
is_empty(Tree) -> boolean()
Types:
Tree = tree()
Returns true if Tree is an empty tree, othwewise false.
iterator(Tree) -> Iter
Types:
Tree = tree(Key, Value)
Iter = iter(Key, Value)
Returns an iterator that can be used for traversing the entries
of Tree; see next/1. The implementation of this is very effi-
cient; 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.
iterator_from(Key, Tree) -> Iter
Types:
Tree = tree(Key, Value)
Iter = iter(Key, Value)
Returns an iterator that can be used for traversing the entries
of Tree; see next/1. The difference as compared to the iterator
returned by iterator/1 is that the first key greater than or
equal to Key is returned.
keys(Tree) -> [Key]
Types:
Tree = tree(Key, Value :: term())
Returns the keys in Tree as an ordered list.
largest(Tree) -> {Key, Value}
Types:
Tree = tree(Key, Value)
Returns {Key, Value}, where Key is the largest key in Tree, and
Value is the value associated with this key. Assumes that the
tree is not empty.
lookup(Key, Tree) -> none | {value, Value}
Types:
Tree = tree(Key, Value)
Looks up Key in Tree. Returns {value, Value}, or none if Key is
not present.
map(Function, Tree1) -> Tree2
Types:
Function = fun((K :: Key, V1 :: Value1) -> V2 :: Value2)
Tree1 = tree(Key, Value1)
Tree2 = tree(Key, Value2)
Maps function F(K, V1) -> V2 to all key-value pairs of tree
Tree1. Returns a new tree Tree2 with the same set of keys as
Tree1 and the new set of values V2.
next(Iter1) -> none | {Key, Value, Iter2}
Types:
Iter1 = Iter2 = iter(Key, Value)
Returns {Key, Value, Iter2}, where Key is the smallest key re-
ferred to by iterator Iter1, and Iter2 is the new iterator to be
used for traversing the remaining nodes, or the atom none if no
nodes remain.
size(Tree) -> integer() >= 0
Types:
Tree = tree()
Returns the number of nodes in Tree.
smallest(Tree) -> {Key, Value}
Types:
Tree = tree(Key, Value)
Returns {Key, Value}, where Key is the smallest key in Tree, and
Value is the value associated with this key. Assumes that the
tree is not empty.
take_largest(Tree1) -> {Key, Value, Tree2}
Types:
Tree1 = Tree2 = tree(Key, Value)
Returns {Key, Value, Tree2}, where Key is the largest key in
Tree1, Value is the value associated with this key, and Tree2 is
this tree with the corresponding node deleted. Assumes that the
tree is not empty.
take_smallest(Tree1) -> {Key, Value, Tree2}
Types:
Tree1 = Tree2 = tree(Key, Value)
Returns {Key, Value, Tree2}, where Key is the smallest key in
Tree1, Value is the value associated with this key, and Tree2 is
this tree with the corresponding node deleted. Assumes that the
tree is not empty.
to_list(Tree) -> [{Key, Value}]
Types:
Tree = tree(Key, Value)
Converts a tree into an ordered list of key-value tuples.
update(Key, Value, Tree1) -> Tree2
Types:
Tree1 = Tree2 = tree(Key, Value)
Updates Key to value Value in Tree1 and returns the new tree.
Assumes that the key is present in the tree.
values(Tree) -> [Value]
Types:
Tree = tree(Key :: term(), Value)
Returns the values in Tree as an ordered list, sorted by their
corresponding keys. Duplicates are not removed.
SEE ALSO
dict(3erl), gb_sets(3erl)
Ericsson AB stdlib 3.13 gb_trees(3erl)