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gb_trees(3erl) | Erlang Module Definition | gb_trees(3erl) |
NAME¶
gb_trees - General Balanced TreesDESCRIPTION¶
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).
DATA TYPES¶
tree(Key, Value)
A GB tree.
tree()
tree() is equivalent to tree(term(), term()).
iter(Key, Value)
A GB tree iterator.
iter()
iter() is equivalent to iter(term(), term()).
EXPORTS¶
balance(Tree1) -> Tree2
Types:
Tree1 = Tree2 = tree(Key, Value)
Rebalances Tree1. 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
Types:
Tree1 = Tree2 = tree(Key, Value)
Removes the node with key Key from Tree1; returns 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 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; 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, and false
otherwise.
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.
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 nonempty.
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 the function F(K, V1) -> V2 to all key-value pairs of the tree
Tree1 and 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 the 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 nonempty.
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 nonempty.
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 nonempty.
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; 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¶
gb_sets(3erl), dict(3erl)stdlib 2.2 | Ericsson AB |