Add tree creation and mutation functions

lib/mb_binary_tree.ex

@@ -3,16 +3,98 @@ defmodule MbBinaryTree do
   Documentation for `MbBinaryTree`.
   """
 
+  @type t :: nil | nonempty_maybe_improper_list()
+
+  @spec new(any) :: t
   @doc """
-  Hello world.
+  Create a new tree with a root node.
 
   ## Examples
 
-      iex> MbBinaryTree.hello()
+      iex> MbBinaryTree.new(4)
-      :world
+      [4, nil, nil]
 
   """
-  def hello do
+  def new(root) do
-    :world
+    [root, nil, nil]
   end
+
+  @spec is_tree?(any) :: boolean
+  @doc """
+  Test whether argument is a valid binary tree.
+
+  ## Examples
+
+    iex> MbBinaryTree.new(19) |> MbBinaryTree.is_tree?()
+    true
+    iex> MbBinaryTree.is_tree?([12])
+    false
+    iex> MbBinaryTree.is_tree?(12)
+    false
+    iex> MbBinaryTree.is_tree?([12, [4, MbBinaryTree.new(2), MbBinaryTree.new(5)], [26, MbBinaryTree.new(14), [28, MbBinaryTree.new(27), MbBinaryTree.new(30)]]])
+  """
+  def is_tree?(nil), do: true
+  def is_tree?([_, nil, nil]), do: true
+  def is_tree?([_, nil, right]), do: is_tree?(right)
+  def is_tree?([_, left, nil]), do: is_tree?(left)
+  def is_tree?([_, left, right]), do: is_tree?(left) && is_tree?(right)
+  def is_tree?(_), do: false
+
+  @spec left(t) :: t
+  @doc """
+  Get the left child of a tree.
+
+  ## Examples
+
+      iex> MbBinaryTree.left([1, MbBinaryTree.new(2), MbBinaryTree.new(3)])
+      [2, nil, nil]
+      iex> MbBinaryTree.new(12) |> MbBinaryTree.left()
+      nil
+      iex> MbBinaryTree.left([12, [4, MbBinaryTree.new(2), MbBinaryTree.new(5)], [26, MbBinaryTree.new(14), [28, MbBinaryTree.new(27), MbBinaryTree.new(30)]]])
+      [4, [2, nil, nil], [5, nil, nil]]
+  """
+  def left([_, left | _]), do: left
+  def left(_), do: nil
+
+  @spec right(t) :: t
+  @doc """
+  Get the right child of a tree.
+
+  ## Examples
+
+      iex> MbBinaryTree.right([1, MbBinaryTree.new(2), MbBinaryTree.new(3)])
+      [3, nil, nil]
+      iex> MbBinaryTree.new(12) |> MbBinaryTree.right()
+      nil
+      iex> MbBinaryTree.right([12, [4, MbBinaryTree.new(2), MbBinaryTree.new(5)], [26, MbBinaryTree.new(14), [28, MbBinaryTree.new(27), MbBinaryTree.new(30)]]])
+      [26, [14, nil, nil], [28, [27, nil, nil], [30, nil, nil]]]
+  """
+  def right([_, _, right]), do: right
+  def right(_), do: nil
+
+  @spec update_left(t, t) :: t
+  @doc """
+  Update the left child of a tree.
+
+  ## Examples
+
+      iex> MbBinaryTree.update_left([1, MbBinaryTree.new(2), MbBinaryTree.new(3)], MbBinaryTree.new(4))
+      [1, [4, nil, nil], [3, nil, nil]]
+      iex> MbBinaryTree.new(12) |> MbBinaryTree.update_left(MbBinaryTree.new(4))
+      [12, [4, nil, nil], nil]
+  """
+  def update_left([node, _left, right], new_left), do: [node, new_left, right]
+
+  @spec update_right(t, t) :: t
+  @doc """
+  Update the right child of a tree.
+
+  ## Examples
+
+      iex> MbBinaryTree.update_right([1, MbBinaryTree.new(2), MbBinaryTree.new(3)], MbBinaryTree.new(4))
+      [1, [2, nil, nil], [4, nil, nil]]
+      iex> MbBinaryTree.new(12) |> MbBinaryTree.update_right(MbBinaryTree.new(4))
+      [12, nil, [4, nil, nil]]
+  """
+  def update_right([node, left, _right], new_right), do: [node, left, new_right]
 end

test/mb_binary_tree_test.exs

@@ -1,8 +1,4 @@
 defmodule MbBinaryTreeTest do
   use ExUnit.Case
   doctest MbBinaryTree
-
-  test "greets the world" do
-    assert MbBinaryTree.hello() == :world
-  end
 end