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**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 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 conditionh(T)<=ceil(c*log(|T|))has been changed to the similar (but not quite equivalent) condition2^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.iter()A GB tree iterator.

**EXPORTS**

balance(Tree1)->Tree2Types: Tree1 = Tree2 = gb_tree() RebalancesTree1. 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)->Tree2Types: Key = term() Tree1 = Tree2 = gb_tree() Removes the node with keyKeyfromTree1; returns new tree. Assumes that the key is present in the tree, crashes otherwise.delete_any(Key,Tree1)->Tree2Types: Key = term() Tree1 = Tree2 = gb_tree() Removes the node with keyKeyfromTree1if the key is present in the tree, otherwise does nothing; returns new tree.empty()->gb_tree()Returns a new empty treeenter(Key,Val,Tree1)->Tree2Types: Key = Val = term() Tree1 = Tree2 = gb_tree() InsertsKeywith valueValintoTree1if the key is not present in the tree, otherwise updatesKeyto valueValinTree1. Returns the new tree.from_orddict(List)->TreeTypes: List = [{Key :: term(), Val :: term()}] Tree = gb_tree() Turns an ordered listListof key-value tuples into a tree. The list must not contain duplicate keys.get(Key,Tree)->ValTypes: Key = term() Tree = gb_tree() Val = term() Retrieves the value stored withKeyinTree. Assumes that the key is present in the tree, crashes otherwise.insert(Key,Val,Tree1)->Tree2Types: Key = Val = term() Tree1 = Tree2 = gb_tree() InsertsKeywith valueValintoTree1; returns the new tree. Assumes that the key is not present in the tree, crashes otherwise.is_defined(Key,Tree)->boolean()Types: Key = term() Tree = gb_tree() ReturnstrueifKeyis present inTree, otherwisefalse.is_empty(Tree)->boolean()Types: Tree = gb_tree() ReturnstrueifTreeis an empty tree, andfalseotherwise.iterator(Tree)->IterTypes: Tree = gb_tree() Iter =iter()Returns an iterator that can be used for traversing the entries ofTree; seenext/1. The implementation of this is very efficient; traversing the whole tree usingnext/1is only slightly slower than getting the list of all elements usingto_list/1and 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 inTreeas an ordered list.largest(Tree)->{Key,Val}Types: Tree = gb_tree() Key = Val = term() Returns{Key,Val}, whereKeyis the largest key inTree, andValis the value associated with this key. Assumes that the tree is nonempty.lookup(Key,Tree)->none|{value,Val}Types: Key = Val = term() Tree = gb_tree() Looks upKeyinTree; returns{value,Val}, ornoneifKeyis not present.map(Function,Tree1)->Tree2Types: Function = fun((K :: term(), V1 :: term()) -> V2 :: term()) Tree1 = Tree2 = gb_tree() Maps the function F(K, V1) -> V2 to all key-value pairs of the treeTree1and returns a new treeTree2with the same set of keys asTree1and the new set of valuesV2.next(Iter1)->none|{Key,Val,Iter2}Types: Iter1 = Iter2 =iter()Key = Val = term() Returns{Key,Val,Iter2}whereKeyis the smallest key referred to by the iteratorIter1, andIter2is the new iterator to be used for traversing the remaining nodes, or the atomnoneif no nodes remain.size(Tree)->integer()>=0Types: Tree = gb_tree() Returns the number of nodes inTree.smallest(Tree)->{Key,Val}Types: Tree = gb_tree() Key = Val = term() Returns{Key,Val}, whereKeyis the smallest key inTree, andValis 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}, whereKeyis the largest key inTree1,Valis the value associated with this key, andTree2is 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}, whereKeyis the smallest key inTree1,Valis the value associated with this key, andTree2is 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 key-value tuples.update(Key,Val,Tree1)->Tree2Types: Key = Val = term() Tree1 = Tree2 = gb_tree() UpdatesKeyto valueValinTree1; 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 inTreeas an ordered list, sorted by their corresponding keys. Duplicates are not removed.

**SEE** **ALSO**

gb_sets(3erl),dict(3erl)