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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}Treeis composed of nodes of the form{Key,Value,Smaller,Bigger}and the "empty tree" nodenil. 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 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.

**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)->Tree2Types: Tree1 = Tree2 =tree(Key, Value) RebalancesTree1. 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)->Tree2Types: Tree1 = Tree2 =tree(Key, Value) Removes the node with keyKeyfromTree1and returns the new tree. Assumes that the key is present in the tree, crashes otherwise.delete_any(Key,Tree1)->Tree2Types: Tree1 = Tree2 =tree(Key, Value) Removes the node with keyKeyfromTree1if 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 valueValuefrom node with keyKeyand newTree2without the node with this value. Assumes that the node with key is present in the tree, crashes otherwise.take_any(Key,Tree1)->{Value,Tree2}|errorTypes: Tree1 = Tree2 =tree(Key, term()) Key = Value = term() Returns a valueValuefrom node with keyKeyand newTree2without the node with this value. Returnserrorif the node with the key is not present in the tree.empty()->tree()Returns a new empty tree.enter(Key,Value,Tree1)->Tree2Types: Tree1 = Tree2 =tree(Key, Value) InsertsKeywith valueValueintoTree1if the key is not present in the tree, otherwise updatesKeyto valueValueinTree1. Returns the new tree.from_orddict(List)->TreeTypes: List = [{Key, Value}] Tree =tree(Key, Value) Turns an ordered listListof key-value tuples into a tree. The list must not contain duplicate keys.get(Key,Tree)->ValueTypes: Tree =tree(Key, Value) Retrieves the value stored withKeyinTree. Assumes that the key is present in the tree, crashes otherwise.insert(Key,Value,Tree1)->Tree2Types: Tree1 = Tree2 =tree(Key, Value) InsertsKeywith valueValueintoTree1and 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()) ReturnstrueifKeyis present inTree, otherwisefalse.is_empty(Tree)->boolean()Types: Tree =tree()ReturnstrueifTreeis an empty tree, othwewisefalse.iterator(Tree)->IterTypes: Tree =tree(Key, Value) Iter =iter(Key, Value) 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.iterator_from(Key,Tree)->IterTypes: Tree =tree(Key, Value) Iter =iter(Key, Value) Returns an iterator that can be used for traversing the entries ofTree; seenext/1. The difference as compared to the iterator returned byiterator/1is that the first key greater than or equal toKeyis returned.keys(Tree)->[Key]Types: Tree =tree(Key, Value :: term()) Returns the keys inTreeas an ordered list.largest(Tree)->{Key,Value}Types: Tree =tree(Key, Value) Returns{Key,Value}, whereKeyis the largest key inTree, andValueis 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 upKeyinTree. Returns{value,Value}, ornoneifKeyis not present.map(Function,Tree1)->Tree2Types: 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 treeTree1. Returns a new treeTree2with the same set of keys asTree1and the new set of valuesV2.next(Iter1)->none|{Key,Value,Iter2}Types: Iter1 = Iter2 =iter(Key, Value) Returns{Key,Value,Iter2}, whereKeyis the smallest key referred to by iteratorIter1, andIter2is the new iterator to be used for traversing the remaining nodes, or the atomnoneif no nodes remain.size(Tree)->integer()>=0Types: Tree =tree()Returns the number of nodes inTree.smallest(Tree)->{Key,Value}Types: Tree =tree(Key, Value) Returns{Key,Value}, whereKeyis the smallest key inTree, andValueis 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}, whereKeyis the largest key inTree1,Valueis the value associated with this key, andTree2is 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}, whereKeyis the smallest key inTree1,Valueis the value associated with this key, andTree2is 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)->Tree2Types: Tree1 = Tree2 =tree(Key, Value) UpdatesKeyto valueValueinTree1and 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 inTreeas an ordered list, sorted by their corresponding keys. Duplicates are not removed.

**SEE** **ALSO**

dict(3erl),gb_sets(3erl)