= Ruby/RBTree

== Description

A RBTree is a sorted associative collection that is implemented with a
Red-Black Tree. It maps keys to values like a Hash, but maintains its
elements in ascending key order. The interface is the almost identical
to that of Hash.

A Red-Black Tree is a kind of binary tree that automatically balances
by itself when a node is inserted or deleted. Lookup, insertion, and
deletion are performed in O(log N) time in the expected and worst
cases. On the other hand, the average case complexity of
lookup/insertion/deletion on a Hash is constant time. A Hash is
usually faster than a RBTree where ordering is unimportant.

The elements of a RBTree are sorted using the <=> method of their keys
or a Proc set by the readjust method. It means all keys should be
comparable with each other or a Proc that takes two keys should return
a negative integer, 0, or a positive integer as the first argument is
less than, equal to, or greater than the second one.

RBTree also provides a few additional methods to take advantage of the
ordering:

* lower_bound, upper_bound, bound
* first, last
* shift, pop
* reverse_each

== Example

A RBTree cannot contain duplicate keys. Use MultiRBTree that is the
parent class of RBTree to store duplicate keys.

  require "rbtree"
  
  rbtree = RBTree["c", 10, "a", 20]
  rbtree["b"] = 30
  p rbtree["b"]              # => 30
  rbtree.each do |k, v|
    p [k, v]
  end                        # => ["a", 20] ["b", 30] ["c", 10]
  
  mrbtree = MultiRBTree["c", 10, "a", 20, "e", 30, "a", 40]
  p mrbtree.lower_bound("b") # => ["c", 10]
  mrbtree.bound("a", "d") do |k, v|
    p [k, v]
  end                        # => ["a", 20] ["a", 40] ["c", 10]

Note: a RBTree cannot be modified during iteration.

== Installation

Run the following command.

  $ sudo gem install rbtree

== Changes
=== 0.4.5
* Support Ruby 3.2.0-dev (development branch).

=== 0.4.4
* Remove the rb_safe_level warning on Ruby 2.7.

=== 0.4.3
* Quick bug fixes for Ruby 3.

== License

MIT License. Copyright (c) 2002-2013 OZAWA Takuma.

dict.c and dict.h are modified copies that are originally in Kazlib
1.20 written by Kaz Kylheku. Its license is similar to the MIT
license. See dict.c and dict.h for the details. The web page of Kazlib
is at http://www.kylheku.com/~kaz/kazlib.html.
