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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 otherwise.
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 without 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 without 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 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.
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 referred 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)