yoavlt / red_black_tree

Red-black tree implementation for Elixir.

RedBlackTree

Red-black tree implementation for Elixir.

Install

Add the following to your mix.exs deps:

{:red_black_tree, "~> 1.0"}

About

Provides an ordered key-value store with O(log(N)) lookup, insert, and delete performance and O(1) size performance.

Implements the Dict behavior, Enumerable protocol, and the Collectable protocol.

Comparison

By default, keys are compared using strict equality (see note below), allowing for polymorphic keys in the same tree:

RedBlackTree.new()
|> RedBlackTree.insert(:a, 1)
|> RedBlackTree.insert({:compound, :key}, 2)

A custom comparator may be provided at initialization via the :comparator option.

For example, let's say we want to store maps containing order information, sorted by the revenue generated and unique by id. We'll use the RedBlackTree.compare_terms function for comparisions since it takes care of weird cases (see note below.)

order_revenue = RedBlackTree.new([], comparator: fn (value1, value2) ->
  # If the ids are the same, they are the same
  if value1.id === value2.id do
    0
  else
    case RedBlackTree.compare_terms(value1.revenue, value2.revenue) do
      # If the revenues are the same but the ids are different, fall back to id comparison for ordering
      0 -> RedBlackTree.compare_terms(value1.id, value2.id)
      # otherwise return the comparison
      revenue_comparison -> revenue_comparison
    end
  end
end)

updated_tree = order_revenue
  |> RedBlackTree.insert(%{id: 3, revenue: 40}, 40)
  |> RedBlackTree.insert(%{id: 50, revenue: 10}, 10)
  |> RedBlackTree.insert(%{id: 1, revenue: 50}, 50)
  |> RedBlackTree.insert(%{id: 2, revenue: 40}, 40)
# => #RedBlackTree<[{%{id: 50, revenue: 10}, 10}, {%{id: 2, revenue: 40}, 40},
 {%{id: 3, revenue: 40}, 40}, {%{id: 1, revenue: 50}, 50}]>

# Notice how changing the revenue of order 2 bumps it all the way to the end,
# since its revenue now equals order 1 but it loses the tie-breaker

RedBlackTree.insert(updated_tree, %{id: 2, revenue: 50}, 50)
# #RedBlackTree<[{%{id: 50, revenue: 10}, 10}, {%{id: 2, revenue: 40}, 40},
 {%{id: 3, revenue: 40}, 40}, {%{id: 1, revenue: 50}, 50},
 {%{id: 2, revenue: 50}, 50}]>

Note

Due to the way Erlang, and therefore Elixir, implement comparisons for floats and integers, it is possible for a two keys to be equal (key == other_key) but not strictly equal (key !== other_key).

To guarantee consistent ordering, the default :comparator function must fallback to hashing keys that exhibit this property on comparison. In these rare cases, there will be a small performance penalty.

Example:

tree = RedBlackTree.new([1 => :bubbles])

# Hashing necessary since 1 != 1.0 and 1 == 1.0
updated = RedBlackTree.insert(tree, 1.0, :walrus)

# No hashing necessary, no performance impact
RedBlackTree.insert(updated, 0.5, :frank)
|> RedBlackTree.insert(1.5, :suzie)