Polish merge sort challenge and solution

Add None input test case.  Update space complexity discussion.

sorting_searching/merge_sort/merge_sort_challenge.ipynb

@@ -44,6 +44,7 @@
    "source": [
     "## Test Cases\n",
     "\n",
+    "* None -> None\n",
     "* Empty input -> []\n",
     "* One element -> [element]\n",
     "* Two or more elements\n",
@@ -104,6 +105,11 @@
     "\n",
     "class TestMergeSort(object):\n",
     "    def test_merge_sort(self):\n",
+    "        print('None input')\n",
+    "        data = None\n",
+    "        sorted_data = merge_sort(data)\n",
+    "        assert_equal(sorted_data, None)\n",
+    "\n",
     "        print('Empty input')\n",
     "        data = []\n",
     "        sorted_data = merge_sort(data)\n",
@@ -143,21 +149,21 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 2",
+   "display_name": "Python 3",
    "language": "python",
-   "name": "python2"
+   "name": "python3"
   },
   "language_info": {
    "codemirror_mode": {
     "name": "ipython",
-    "version": 2
+    "version": 3
    },
    "file_extension": ".py",
    "mimetype": "text/x-python",
    "name": "python",
    "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython2",
-   "version": "2.7.10"
+   "pygments_lexer": "ipython3",
+   "version": "3.4.3"
   }
  },
  "nbformat": 4,

sorting_searching/merge_sort/merge_sort_solution.ipynb

@@ -43,6 +43,7 @@
    "source": [
     "## Test Cases\n",
     "\n",
+    "* None -> None\n",
     "* Empty input -> []\n",
     "* One element -> [element]\n",
     "* Two or more elements\n",
@@ -68,7 +69,9 @@
     "\n",
     "Complexity:\n",
     "* Time: O(n log(n))\n",
-    "* Space: O(n), stable"
+    "* Space: O(n+m), n = number of elements, m = recursion depth\n",
+    "\n",
+    "Most implementations are stable."
    ]
   },
   {
@@ -112,11 +115,11 @@
     "\n",
     "\n",
     "def merge_sort(data):\n",
-    "    if len(data) < 2:\n",
+    "    if data is None or len(data) < 2:\n",
     "        return data\n",
     "    mid = len(data) // 2\n",
     "    left = data[0:mid]\n",
-    "    right = data[mid:len(data)]\n",
+    "    right = data[mid:]\n",
     "    left = merge_sort(left)\n",
     "    right = merge_sort(right)\n",
     "    return merge(left, right)"
@@ -152,6 +155,11 @@
     "\n",
     "class TestMergeSort(object):\n",
     "    def test_merge_sort(self):\n",
+    "        print('None input')\n",
+    "        data = None\n",
+    "        sorted_data = merge_sort(data)\n",
+    "        assert_equal(sorted_data, None)\n",
+    "\n",
     "        print('Empty input')\n",
     "        data = []\n",
     "        sorted_data = merge_sort(data)\n",
@@ -190,6 +198,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
+      "None input\n",
       "Empty input\n",
       "One element\n",
       "Two or more elements\n",
@@ -204,21 +213,21 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 2",
+   "display_name": "Python 3",
    "language": "python",
-   "name": "python2"
+   "name": "python3"
   },
   "language_info": {
    "codemirror_mode": {
     "name": "ipython",
-    "version": 2
+    "version": 3
    },
    "file_extension": ".py",
    "mimetype": "text/x-python",
    "name": "python",
    "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython2",
-   "version": "2.7.10"
+   "pygments_lexer": "ipython3",
+   "version": "3.4.3"
   }
  },
  "nbformat": 4,

sorting_searching/merge_sort/test_merge_sort.py

@@ -3,6 +3,11 @@ from nose.tools import assert_equal
 
 class TestMergeSort(object):
     def test_merge_sort(self):
+        print('None input')
+        data = None
+        sorted_data = merge_sort(data)
+        assert_equal(sorted_data, None)
+
         print('Empty input')
         data = []
         sorted_data = merge_sort(data)