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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¶
{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.
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)stdlib 3.2 | Ericsson AB |