Polish bst challenge and solution

Add root is None input test case.  Update time and space complexity discussion.

graphs_trees/bst/bst.py

@@ -11,6 +11,9 @@ class Node(object):
 
 
 def insert(root, data):
+    if root is None:
+        root = Node(data)
+        return root
     if data <= root.data:
         if root.left is None:
             root.left = Node(data)

graphs_trees/bst/bst_challenge.ipynb

@@ -56,7 +56,9 @@
     "### In-Order Traversal (Provided)\n",
     "\n",
     "* 5, 2, 8, 1, 3 -> 1, 2, 3, 5, 8\n",
-    "* 1, 2, 3, 4, 5 -> 1, 2, 3, 4, 5"
+    "* 1, 2, 3, 4, 5 -> 1, 2, 3, 4, 5\n",
+    "\n",
+    "If the `root` input is `None`, return a tree with the only element being the new root node."
    ]
   },
   {
@@ -158,7 +160,7 @@
     "        assert_equal(str(self.results), '[1, 2, 3, 5, 8]')\n",
     "        self.results.clear_results()\n",
     "\n",
-    "        node = Node(1)\n",
+    "        node = insert(None, 1)\n",
     "        insert(node, 2)\n",
     "        insert(node, 3)\n",
     "        insert(node, 4)\n",
@@ -190,21 +192,21 @@
  ],
  "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",
+   "pygments_lexer": "ipython3",
-   "version": "2.7.10"
+   "version": "3.4.3"
   }
  },
  "nbformat": 4,

graphs_trees/bst/bst_solution.ipynb

@@ -56,7 +56,9 @@
     "### In-Order Traversal (Provided)\n",
     "\n",
     "* 5, 2, 8, 1, 3 -> 1, 2, 3, 5, 8\n",
-    "* 1, 2, 3, 4, 5 -> 1, 2, 3, 4, 5"
+    "* 1, 2, 3, 4, 5 -> 1, 2, 3, 4, 5\n",
+    "\n",
+    "If the `root` input is `None`, return a tree with the only element being the new root node."
    ]
   },
   {
@@ -67,6 +69,7 @@
     "\n",
     "### Insert\n",
     "\n",
+    "* If the root is None, return Node(data)\n",
     "* If the data is <= the current node's data\n",
     "    * If the current node's left child is None, set it to Node(data)\n",
     "    * Else, recursively call insert on the left child\n",
@@ -76,8 +79,10 @@
     "\n",
     "Complexity:\n",
     "\n",
-    "* Time: O(log n)\n",
+    "* Time: O(h), where h is the height of the tree\n",
-    "* Space: O(1)"
+    "    * In a balanced tree, the height is O(nlogn)\n",
+    "    * In the worst case we have a linked list structure with O(n)\n",
+    "* Space: O(m), where m is the recursion depth, or O(1) if using an iterative approach"
    ]
   },
   {
@@ -117,6 +122,9 @@
     "\n",
     "\n",
     "def insert(root, data):\n",
+    "    if root is None:\n",
+    "        root = Node(data)\n",
+    "        return root\n",
     "    if data <= root.data:\n",
     "        if root.left is None:\n",
     "            root.left = Node(data)\n",
@@ -208,7 +216,7 @@
     "        assert_equal(str(self.results), '[1, 2, 3, 5, 8]')\n",
     "        self.results.clear_results()\n",
     "\n",
-    "        node = Node(1)\n",
+    "        node = insert(None, 1)\n",
     "        insert(node, 2)\n",
     "        insert(node, 3)\n",
     "        insert(node, 4)\n",
@@ -250,21 +258,21 @@
  ],
  "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",
+   "pygments_lexer": "ipython3",
-   "version": "2.7.10"
+   "version": "3.4.3"
   }
  },
  "nbformat": 4,

graphs_trees/bst/test_bst.py

@@ -16,7 +16,7 @@ class TestTree(object):
         assert_equal(str(self.results), '[1, 2, 3, 5, 8]')
         self.results.clear_results()
 
-        node = Node(1)
+        node = insert(None, 1)
         insert(node, 2)
         insert(node, 3)
         insert(node, 4)