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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
{Size, Tree}
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. 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)