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

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 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.

       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) -> Tree2

	      Types  Tree1 = Tree2 = gb_tree()

	      Rebalances Tree1 . 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) -> Tree2

	      Types  Key = term()
		     Tree1 = Tree2 = gb_tree()

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

       delete_any(Key, Tree1) -> Tree2

	      Types  Key = term()
		     Tree1 = Tree2 = gb_tree()

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

       empty() -> Tree

	      Types  Tree = gb_tree()

	      Returns a new empty tree

       enter(Key, Val, Tree1) -> Tree2

	      Types  Key = Val = term()
		     Tree1 = Tree2 = gb_tree()

	      Inserts Key with value Val into Tree1 if the key is not present in the tree, otherwise updates Key to value Val in Tree1	.  Returns
	      the new tree.

       from_orddict(List) -> Tree

	      Types  List = [{Key, Val}]
		     Key = Val = term()
		     Tree = gb_tree()

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

       get(Key, Tree) -> Val

	      Types  Key = Val = term()
		     Tree = gb_tree()

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

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

	      Types  Key = Val = term()
		     Tree = gb_tree()

	      Looks up Key in Tree ; returns {value, Val} , or none if Key is not present.

       insert(Key, Val, Tree1) -> Tree2

	      Types  Key = Val = term()
		     Tree1 = Tree2 = gb_tree()

	      Inserts Key with value Val into Tree1 ; 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()

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

       is_empty(Tree) -> bool()

	      Types  Tree = gb_tree()

	      Returns true if Tree is an empty tree, and false otherwise.

       iterator(Tree) -> Iter

	      Types  Tree = gb_tree()
		     Iter = term()

	      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 mem-
	      ory at one time.

       keys(Tree) -> [Key]

	      Types  Tree = gb_tree()
		     Key = term()

	      Returns the keys in Tree as an ordered list.

       largest(Tree) -> {Key, Val}

	      Types  Tree = gb_tree()
		     Key = Val = term()

	      Returns {Key, Val} , where Key is the largest key in Tree , and Val is the value associated with this key. Assumes that the tree	is
	      nonempty.

       map(Function, Tree1) -> Tree2

	      Types  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} | none

	      Types  Iter1 = Iter2 = Key = Val = term()

	      Returns {Key, Val, Iter2} where Key is the smallest key referred to by the 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) -> int()

	      Types  Tree = gb_tree()

	      Returns the number of nodes in Tree .

       smallest(Tree) -> {Key, Val}

	      Types  Tree = gb_tree()
		     Key = Val = term()

	      Returns {Key, Val} , where Key is the smallest key in Tree , and Val is 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} , where Key is the largest key in Tree1 , Val is the value associated with this key,  and  Tree2  is  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} , where Key is the smallest key in Tree1 , Val is the value associated with this key, and Tree2 is 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) -> Tree2

	      Types  Key = Val = term()
		     Tree1 = Tree2 = gb_tree()

	      Updates Key to value Val in Tree1 ; 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 in Tree as an ordered list, sorted by their corresponding keys. Duplicates are not removed.

SEE ALSO

       gb_sets(3erl) , dict(3erl)

Ericsson AB							   stdlib 1.17.3						    gb_trees(3erl)