
gb_trees(3erl) Erlang Module Definition gb_trees(3erl)
NAME
gb_trees  General Balanced Trees
DESCRIPTION
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 gen
eral 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
gb_tree() = a GB tree
EXPORTS
balance(Tree1) > Tree2
Types Tree1 = Tree2 = gb_tree()
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 Key = term()
Tree1 = Tree2 = gb_tree()
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 Key = term()
Tree1 = Tree2 = gb_tree()
Removes the node with key Key from Tree1 if the key is present in the tree, other
wise does nothing; returns new tree.
empty() > Tree
Types Tree = gb_tree()
Returns a new empty tree
enter(Key, Val, Tree1) > Tree2
Types Key = Val = term()
Tree1 = Tree2 = gb_tree()
Inserts Key with value Val into Tree1 if the key is not present in the tree, other
wise updates Key to value Val in Tree1 . Returns the new tree.
from_orddict(List) > Tree
Types List = [{Key, Val}]
Key = Val = term()
Tree = gb_tree()
Turns an ordered list List of keyvalue tuples into a tree. The list must not con
tain duplicate keys.
get(Key, Tree) > Val
Types Key = Val = term()
Tree = gb_tree()
Retrieves the value stored with Key in Tree . Assumes that the key is present in
the tree, crashes otherwise.
lookup(Key, Tree) > {value, Val}  none
Types Key = Val = term()
Tree = gb_tree()
Looks up Key in Tree ; returns {value, Val} , or none if Key is not present.
insert(Key, Val, Tree1) > Tree2
Types Key = Val = term()
Tree1 = Tree2 = gb_tree()
Inserts Key with value Val into Tree1 ; returns the new tree. Assumes that the key
is not present in the tree, crashes otherwise.
is_defined(Key, Tree) > bool()
Types Tree = gb_tree()
Returns true if Key is present in Tree , otherwise false .
is_empty(Tree) > bool()
Types Tree = gb_tree()
Returns true if Tree is an empty tree, and false otherwise.
iterator(Tree) > Iter
Types Tree = gb_tree()
Iter = term()
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 = gb_tree()
Key = term()
Returns the keys in Tree as an ordered list.
largest(Tree) > {Key, Val}
Types Tree = gb_tree()
Key = Val = term()
Returns {Key, Val} , where Key is the largest key in Tree , and Val is the value
associated with this key. Assumes that the tree is nonempty.
map(Function, Tree1) > Tree2
Types Function = fun(K, V1) > V2
Tree1 = Tree2 = gb_tree()
maps the function F(K, V1) > V2 to all keyvalue pairs of the tree Tree1 and
returns a new tree Tree2 with the same set of keys as Tree1 and the new set of val
ues V2.
next(Iter1) > {Key, Val, Iter2}  none
Types Iter1 = Iter2 = Key = Val = term()
Returns {Key, Val, 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) > int()
Types Tree = gb_tree()
Returns the number of nodes in Tree .
smallest(Tree) > {Key, Val}
Types Tree = gb_tree()
Key = Val = term()
Returns {Key, Val} , where Key is the smallest key in Tree , and Val is the value
associated with this key. Assumes that the tree is nonempty.
take_largest(Tree1) > {Key, Val, Tree2}
Types Tree1 = Tree2 = gb_tree()
Key = Val = term()
Returns {Key, Val, Tree2} , where Key is the largest key in Tree1 , Val 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, Val, Tree2}
Types Tree1 = Tree2 = gb_tree()
Key = Val = term()
Returns {Key, Val, Tree2} , where Key is the smallest key in Tree1 , Val 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, Val}]
Types Tree = gb_tree()
Key = Val = term()
Converts a tree into an ordered list of keyvalue tuples.
update(Key, Val, Tree1) > Tree2
Types Key = Val = term()
Tree1 = Tree2 = gb_tree()
Updates Key to value Val in Tree1 ; returns the new tree. Assumes that the key is
present in the tree.
values(Tree) > [Val]
Types Tree = gb_tree()
Val = term()
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)
Ericsson AB stdlib 1.17.3 gb_trees(3erl) 
