[Sync Iteration] elixir/binary-search/1

solutions/elixir/binary-search/1/lib/binary_search.ex

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+defmodule BinarySearch do
+  @doc """
+    Searches for a key in the tuple using the binary search algorithm.
+    It returns :not_found if the key is not in the tuple.
+    Otherwise returns {:ok, index}.
+
+    ## Examples
+
+      iex> BinarySearch.search({}, 2)
+      :not_found
+
+      iex> BinarySearch.search({1, 3, 5}, 2)
+      :not_found
+
+      iex> BinarySearch.search({1, 3, 5}, 5)
+      {:ok, 2}
+
+  """
+
+  @spec search(tuple, integer) :: {:ok, integer} | :not_found
+  def search(numbers, key) do
+    delta = numbers |> tuple_size() |> div(2)
+    get_index(numbers, key, delta, delta)
+  end
+
+  defp get_index(numbers, key, index, delta, checked \\ [])
+  defp get_index(numbers, key, index, _, _) when elem(numbers, index) == key, do: {:ok, index}
+  defp get_index(_, _, _, 0, _), do: :not_found
+
+  defp get_index(numbers, key, index, delta, checked) when elem(numbers, index) > key do
+    if index in checked do
+      :not_found
+    else
+      half = div(delta + 1, 2)
+      get_index(numbers, key, index - half, half, [index | checked])
+    end
+  end
+
+  defp get_index(numbers, key, index, delta, checked) when elem(numbers, index) < key do
+    if index in checked do
+      :not_found
+    else
+      half = div(delta + 1, 2)
+      get_index(numbers, key, index + half, half, [index | checked])
+    end
+  end
+
+  defp get_index(_, _, _, _, _), do: :not_found
+end