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gb_trees(3erl) | Erlang Module Definition | gb_trees(3erl) |

# 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¶

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.

# 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) -> Tree2

Types:

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.

delete(Key, Tree1) -> Tree2

Types:

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

delete_any(Key, Tree1) -> Tree2

Types:

Removes the node with key *Key* from *Tree1* if the key
is present in the tree, otherwise does nothing. Returns the new tree.

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

Types:

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.

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

Types:

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.

empty() -> tree()

Returns a new empty tree.

enter(Key, Value, Tree1) -> Tree2

Types:

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.

from_orddict(List) -> Tree

Types:

Tree = tree(Key, Value)

Turns an ordered list *List* of key-value tuples into a tree.
The list must not contain duplicate keys.

get(Key, Tree) -> Value

Types:

Retrieves the value stored with *Key* in *Tree*. Assumes
that the key is present in the tree, crashes otherwise.

insert(Key, Value, Tree1) -> Tree2

Types:

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

is_defined(Key, Tree) -> boolean()

Types:

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

is_empty(Tree) -> boolean()

Types:

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

iterator(Tree) -> Iter

Types:

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.

iterator_from(Key, Tree) -> Iter

Types:

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.

keys(Tree) -> [Key]

Types:

Returns the keys in *Tree* as an ordered list.

largest(Tree) -> {Key, Value}

Types:

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.

lookup(Key, Tree) -> none | {value, Value}

Types:

Looks up *Key* in *Tree*. Returns *{value, Value}*,
or *none* if *Key* is not present.

map(Function, Tree1) -> Tree2

Types:

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*.

next(Iter1) -> none | {Key, Value, Iter2}

Types:

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.

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

Types:

Returns the number of nodes in *Tree*.

smallest(Tree) -> {Key, Value}

Types:

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.

take_largest(Tree1) -> {Key, Value, Tree2}

Types:

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.

take_smallest(Tree1) -> {Key, Value, Tree2}

Types:

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.

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

Types:

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

update(Key, Value, Tree1) -> Tree2

Types:

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

values(Tree) -> [Value]

Types:

Returns the values in *Tree* as an ordered list, sorted by
their corresponding keys. Duplicates are not removed.

# SEE ALSO¶

*dict(3erl)*, *gb_sets(3erl)*

stdlib 4.0.1 | Ericsson AB |