Add Binary Search

lib/search/binary_search.ex

@@ -0,0 +1,29 @@
+defmodule Algorithms.Search.BinarySearch do
+  @moduledoc """
+  Performs a binary search on a sorted list and returns the index of the target element.
+  If the target is not found, it returns -1.
+  """
+  def search(list, target) do
+    binary_search(list, target, 0, length(list) - 1)
+  end
+
+  defp binary_search(_list, _target, low, high) when low > high do
+    -1
+  end
+
+  defp binary_search(list, target, low, high) do
+    mid = div(low + high, 2)
+    current = Enum.at(list, mid)
+
+    cond do
+      current == target ->
+        mid
+
+      current > target ->
+        binary_search(list, target, low, mid - 1)
+
+      current < target ->
+        binary_search(list, target, mid + 1, high)
+    end
+  end
+end

test/search/binary_search_test.exs

@@ -0,0 +1,43 @@
+defmodule Algorithms.Search.BinarySearchTest do
+  alias Algorithms.Search.BinarySearch
+
+  use ExUnit.Case
+
+  describe "search/2 - example test cases" do
+    test "finds element in the middle of the list" do
+      assert BinarySearch.search([1, 3, 5, 7, 9], 5) == 2
+    end
+
+    test "finds element at the beginning of the list" do
+      assert BinarySearch.search([1, 3, 5, 7, 9], 1) == 0
+    end
+
+    test "finds element at the end of the list" do
+      assert BinarySearch.search([1, 3, 5, 7, 9], 9) == 4
+    end
+
+    test "returns -1 when element is not in the list" do
+      assert BinarySearch.search([1, 3, 5, 7, 9], 4) == -1
+    end
+
+    test "works with an empty list" do
+      assert BinarySearch.search([], 1) == -1
+    end
+
+    test "works with a single-element list" do
+      assert BinarySearch.search([1], 1) == 0
+      assert BinarySearch.search([1], 2) == -1
+    end
+
+    test "works with a large sorted list" do
+      list = Enum.to_list(1..1000)
+      assert BinarySearch.search(list, 500) == 499
+      assert BinarySearch.search(list, 1001) == -1
+    end
+
+    test "handles duplicate elements" do
+      assert BinarySearch.search([1, 2, 2, 3, 4, 5, 5, 6], 2) in [1, 2]
+      assert BinarySearch.search([1, 2, 2, 3, 4, 5, 5, 6], 5) in [5, 6]
+    end
+  end
+end