From f1e458239266dac1d18120c6c3b092a67a739577 Mon Sep 17 00:00:00 2001
From: William Carroll <wpcarro@gmail.com>
Date: Fri, 11 Dec 2020 22:43:26 +0000
Subject: [PATCH] Define Math module

Support `Math.factor` and cover it with tests.
---
 assessments/semiprimes/server/lib/math.ex     | 26 +++++++++++++++
 .../semiprimes/server/test/math_test.exs      | 32 +++++++++++++++++++
 2 files changed, 58 insertions(+)
 create mode 100644 assessments/semiprimes/server/lib/math.ex
 create mode 100644 assessments/semiprimes/server/test/math_test.exs

diff --git a/assessments/semiprimes/server/lib/math.ex b/assessments/semiprimes/server/lib/math.ex
new file mode 100644
index 000000000..8a33be475
--- /dev/null
+++ b/assessments/semiprimes/server/lib/math.ex
@@ -0,0 +1,26 @@
+defmodule Math do
+  @moduledoc """
+  Math utilities.
+  """
+  alias Extras
+
+  @doc """
+  Returns the prime factors for `n`.
+
+  ## Examples
+
+      iex> Math.factor(15)
+      [3, 5]
+
+  """
+  def factor(1), do: []
+
+  def factor(n) do
+    Extras.range(2, n - 1)
+    |> Enum.find(&(rem(n, &1) == 0))
+    |> case do
+      nil -> [n]
+      x -> [x | factor(div(n, x))]
+    end
+  end
+end
diff --git a/assessments/semiprimes/server/test/math_test.exs b/assessments/semiprimes/server/test/math_test.exs
new file mode 100644
index 000000000..81c60e406
--- /dev/null
+++ b/assessments/semiprimes/server/test/math_test.exs
@@ -0,0 +1,32 @@
+defmodule MathTest do
+  use ExUnit.Case
+  doctest Math
+
+  describe "factor" do
+    test "returns the prime factors for an input" do
+      [
+        {15, [3, 5]},
+        {12, [2, 2, 3]},
+        {9, [3, 3]},
+        {21, [3, 7]}
+      ]
+      |> Enum.map(fn {input, expected} ->
+        Math.factor(input) == expected
+      end)
+      |> Enum.all?()
+      |> assert
+    end
+
+    test "handles large numbers" do
+      assert Math.factor(104_023) == [17, 29, 211]
+    end
+
+    test "returns an empty list for 1" do
+      assert Math.factor(1) == []
+    end
+
+    test "returns the prime number itself when the input is prime" do
+      assert Math.factor(7) == [7]
+    end
+  end
+end