Polish bst successor challenge and solution (#82)

Update constraints, test cases, tests, algorithm discussion, and code.

graphs_trees/bst_successor/bst_successor_challenge.ipynb

@@ -36,7 +36,11 @@
     "\n",
     "* If there is no successor, do we return None?\n",
     "    * Yes\n",
+    "* If the input is None, should we throw an exception?\n",
+    "    * Yes\n",
     "* Can we assume we already have a Node class that keeps track of parents?\n",
+    "    * Yes\n",
+    "* Can we assume this fits memory?\n",
     "    * Yes"
    ]
   },
@@ -57,10 +61,11 @@
     "               /\n",
     "              9\n",
     "\n",
-    "In: 4  Out: 5\n",
+    "In: None  Out: Exception\n",
-    "In: 5  Out: 6\n",
+    "In: 4     Out: 5\n",
-    "In: 8  Out: 9\n",
+    "In: 5     Out: 6\n",
-    "In: 15 Out: None\n",
+    "In: 8     Out: 9\n",
+    "In: 15    Out: None\n",
     "</pre>"
    ]
   },
@@ -129,10 +134,15 @@
    "source": [
     "# %load test_bst_successor.py\n",
     "from nose.tools import assert_equal\n",
+    "from nose.tools import raises\n",
     "\n",
     "\n",
     "class TestBstSuccessor(object):\n",
     "\n",
+    "    @raises(Exception)\n",
+    "    def test_bst_successor_empty(self):\n",
+    "        bst_successor(None)\n",
+    "\n",
     "    def test_bst_successor(self):\n",
     "        nodes = {}\n",
     "        node = Node(5)\n",
@@ -160,6 +170,7 @@
     "def main():\n",
     "    test = TestBstSuccessor()\n",
     "    test.test_bst_successor()\n",
+    "    test.test_bst_successor_empty()\n",
     "\n",
     "\n",
     "if __name__ == '__main__':\n",
@@ -192,7 +203,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.4.3"
+   "version": "3.5.0"
   }
  },
  "nbformat": 4,

graphs_trees/bst_successor/bst_successor_solution.ipynb

@@ -35,7 +35,11 @@
     "\n",
     "* If there is no successor, do we return None?\n",
     "    * Yes\n",
+    "* If the input is None, should we throw an exception?\n",
+    "    * Yes\n",
     "* Can we assume we already have a Node class that keeps track of parents?\n",
+    "    * Yes\n",
+    "* Can we assume this fits memory?\n",
     "    * Yes"
    ]
   },
@@ -56,10 +60,11 @@
     "               /\n",
     "              9\n",
     "\n",
-    "In: 4  Out: 5\n",
+    "In: None  Out: Exception\n",
-    "In: 5  Out: 6\n",
+    "In: 4     Out: 5\n",
-    "In: 8  Out: 9\n",
+    "In: 5     Out: 6\n",
-    "In: 15 Out: None\n",
+    "In: 8     Out: 9\n",
+    "In: 15    Out: None\n",
     "</pre>"
    ]
   },
@@ -72,11 +77,12 @@
     "* If the node has a right subtree, return the left-most node in the right subtree\n",
     "* Else, go up until you find a node that is its parent's left node\n",
     "    * If you get to the root (ie node.parent is None), return None\n",
+    "        * The original input node must be the largest in the tree\n",
     "    * Else, return the parent\n",
     "    \n",
     "Complexity:\n",
-    "* Time: O(n)\n",
+    "* Time: O(h), where h is the height of the tree\n",
-    "* Space: O(h), where h is the height of the tree"
+    "* Space: O(h), where h is the recursion depth (tree height), or O(1) if using an iterative approach"
    ]
   },
   {
@@ -107,7 +113,7 @@
    "source": [
     "def left_most_node(node):\n",
     "    if node is None:\n",
-    "        return\n",
+    "        return None\n",
     "    if node.left is None:\n",
     "        return node.data\n",
     "    return left_most_node(node.left)\n",
@@ -115,7 +121,7 @@
     "\n",
     "def bst_successor(node):\n",
     "    if node is None:\n",
-    "        return\n",
+    "        raise Exception('Invalid input node')\n",
     "    if node.right is not None:\n",
     "        return left_most_node(node.right)\n",
     "    else:\n",
@@ -124,7 +130,9 @@
     "            node = node.parent\n",
     "            parent = node.parent\n",
     "        if parent is None:\n",
-    "            return\n",
+    "            # We reached the root, the original input node\n",
+    "            # must be the largest element in the tree.\n",
+    "            return None\n",
     "        return parent.data"
    ]
   },
@@ -153,10 +161,15 @@
    "source": [
     "%%writefile test_bst_successor.py\n",
     "from nose.tools import assert_equal\n",
+    "from nose.tools import raises\n",
     "\n",
     "\n",
     "class TestBstSuccessor(object):\n",
     "\n",
+    "    @raises(Exception)\n",
+    "    def test_bst_successor_empty(self):\n",
+    "        bst_successor(None)\n",
+    "\n",
     "    def test_bst_successor(self):\n",
     "        nodes = {}\n",
     "        node = Node(5)\n",
@@ -184,6 +197,7 @@
     "def main():\n",
     "    test = TestBstSuccessor()\n",
     "    test.test_bst_successor()\n",
+    "    test.test_bst_successor_empty()\n",
     "\n",
     "\n",
     "if __name__ == '__main__':\n",
@@ -226,7 +240,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.4.3"
+   "version": "3.5.0"
   }
  },
  "nbformat": 4,

graphs_trees/bst_successor/test_bst_successor.py

@@ -1,8 +1,13 @@
 from nose.tools import assert_equal
+from nose.tools import raises
 
 
 class TestBstSuccessor(object):
 
+    @raises(Exception)
+    def test_bst_successor_empty(self):
+        bst_successor(None)
+
     def test_bst_successor(self):
         nodes = {}
         node = Node(5)
@@ -30,6 +35,7 @@ class TestBstSuccessor(object):
 def main():
     test = TestBstSuccessor()
     test.test_bst_successor()
+    test.test_bst_successor_empty()
 
 
 if __name__ == '__main__':