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## man page of gb_trees

### gb_trees: General Balanced Trees

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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.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## 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() -> TreeTypes Tree = 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, Val}] Key = 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 = Val = term() Tree = gb_tree() Retrieves the value stored withKeyinTree. Assumes that the key is present in the tree, crashes otherwise.lookup(Key, Tree) -> {value, Val} | noneTypes Key = Val = term() Tree = gb_tree() Looks upKeyinTree; returns{value, Val}, ornoneifKeyis not present.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) -> bool()Types Tree = gb_tree() ReturnstrueifKeyis present inTree, otherwisefalse.is_empty(Tree) -> bool()Types Tree = gb_tree() ReturnstrueifTreeis an empty tree, andfalseotherwise.iterator(Tree) -> IterTypes Tree = gb_tree() Iter = term() 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.map(Function, Tree1) -> Tree2Types Function = fun(K, V1) -> V2 Tree1 = Tree2 = gb_tree() 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) -> {Key, Val, Iter2} | noneTypes Iter1 = Iter2 = 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) -> int()Types 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) GB_TREES(3)

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