# gb_trees

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Module

gb_trees

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Module Summary

General balanced trees.

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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 (==).

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Data Structure

Trees and iterators are built using opaque data structures that should not be pattern-matched from outside this module.

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 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.

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Data Types

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tree(Key, Value)

A general balanced tree.

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tree() = tree(term(), term())

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iter(Key, Value)

A general balanced tree iterator.

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iter() = iter(term(), term())

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Exports

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balance(Tree1) -> Tree2

### Types

Tree1 = Tree2 = tree(Key, Value)

Rebalances Tree1. 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.

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delete(Key, Tree1) -> Tree2

### Types

Tree1 = Tree2 = tree(Key, Value)

Removes the node with key Key from Tree1 and returns the new tree. Assumes that the key is present in the tree, crashes otherwise.

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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 the new tree.

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take(Key, Tree1) -> {Value, Tree2}
OTP 20.0

### Types

Tree1 = Tree2 = tree(Key, term())
Key = Value = term()

Returns a value Value from node with key Key and new Tree2 without the node with this value. Assumes that the node with key is present in the tree, crashes otherwise.

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take_any(Key, Tree1) -> {Value, Tree2} | error
OTP 20.0

### Types

Tree1 = Tree2 = tree(Key, term())
Key = Value = term()

Returns a value Value from node with key Key and new Tree2 without the node with this value. Returns error if the node with the key is not present in the tree.

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empty() -> tree()

Returns a new empty tree.

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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.

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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.

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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.

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insert(Key, Value, Tree1) -> Tree2

### Types

Tree1 = Tree2 = tree(Key, Value)

Inserts Key with value Value into Tree1 and returns the new tree. Assumes that the key is not present in the tree, crashes otherwise.

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is_defined(Key, Tree) -> boolean()

### Types

Tree = tree(Key, Value :: term())

Returns true if Key is present in Tree, otherwise false.

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is_empty(Tree) -> boolean()

### Types

Tree = tree()

Returns true if Tree is an empty tree, othwewise false.

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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.

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iterator_from(Key, Tree) -> Iter
OTP 18.0

### 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 difference as compared to the iterator returned by iterator/1 is that the first key greater than or equal to Key is returned.

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keys(Tree) -> [Key]

### Types

Tree = tree(Key, Value :: term())

Returns the keys in Tree as an ordered list.

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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 not empty.

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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.

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map(Function, Tree1) -> Tree2

### Types

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 tree Tree1. Returns a new tree Tree2 with the same set of keys as Tree1 and the new set of values V2.

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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 iterator Iter1, and Iter2 is the new iterator to be used for traversing the remaining nodes, or the atom none if no nodes remain.

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size(Tree) -> integer() >= 0

### Types

Tree = tree()

Returns the number of nodes in Tree.

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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 not empty.

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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 not empty.

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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 not empty.

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to_list(Tree) -> [{Key, Value}]

### Types

Tree = tree(Key, Value)

Converts a tree into an ordered list of key-value tuples.

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update(Key, Value, Tree1) -> Tree2

### Types

Tree1 = Tree2 = tree(Key, Value)

Updates Key to value Value in Tree1 and returns the new tree. Assumes that the key is present in the tree.

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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.

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See Also

dict(3), gb_sets(3)