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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.

       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.

       iter()

              A GB tree iterator.

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() -> 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 :: term(), 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 = term()
                 Tree = gb_tree()
                 Val = term()

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

       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) -> boolean()

              Types:

                 Key = term()
                 Tree = gb_tree()

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

       is_empty(Tree) -> boolean()

              Types:

                 Tree = gb_tree()

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

       iterator(Tree) -> Iter

              Types:

                 Tree = gb_tree()
                 Iter = iter()

              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.

       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.

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

              Types:

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

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

       map(Function, Tree1) -> Tree2

              Types:

                 Function = fun((K :: term(), V1 :: term()) -> V2 :: term())
                 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) -> none | {Key, Val, Iter2}

              Types:

                 Iter1 = Iter2 = iter()
                 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) -> integer() >= 0

              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)