{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solution Notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem: Implement a binary search tree with an insert method.\n",
    "\n",
    "* [Constraints](#Constraints)\n",
    "* [Test Cases](#Test-Cases)\n",
    "* [Algorithm](#Algorithm)\n",
    "* [Code](#Code)\n",
    "* [Unit Test](#Unit-Test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constraints\n",
    "\n",
    "* Can we insert None values?\n",
    "    * No\n",
    "* Can we assume we are working with valid integers?\n",
    "    * Yes\n",
    "* Can we assume all left descendents <= n < all right descendents?\n",
    "    * Yes\n",
    "* For simplicity, can we use just a Node class without a wrapper Tree class?\n",
    "    * Yes\n",
    "* Do we have to keep track of the parent nodes?\n",
    "    * This is optional\n",
    "* Can we assume this fits in memory?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "### Insert\n",
    "\n",
    "Insert will be tested through the following traversal:\n",
    "\n",
    "### In-Order Traversal\n",
    "\n",
    "* 5, 2, 8, 1, 3 -> 1, 2, 3, 5, 8\n",
    "* 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.\n",
    "\n",
    "You do not have to code the in-order traversal, it is part of the unit test."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\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",
    "* Else\n",
    "    * If the current node's right child is None, set it to Node(data)\n",
    "    * Else, recursively call insert on the right child\n",
    "\n",
    "Complexity:\n",
    "\n",
    "* Time: O(h), where h is the height of the tree\n",
    "    * 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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting bst.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile bst.py\n",
    "class Node(object):\n",
    "\n",
    "    def __init__(self, data):\n",
    "        self.data = data\n",
    "        self.left = None\n",
    "        self.right = None\n",
    "        self.parent = None\n",
    "\n",
    "    def __repr__(self):\n",
    "        return str(self.data)\n",
    "\n",
    "\n",
    "class Bst(object):\n",
    "\n",
    "    def __init__(self, root=None):\n",
    "        self.root = root\n",
    "\n",
    "    def insert(self, data):\n",
    "        if data is None:\n",
    "            raise Exception('Data cannot be None')\n",
    "        if self.root is None:\n",
    "            self.root = Node(data)\n",
    "            return self.root\n",
    "        return self._insert(self.root, data)\n",
    "\n",
    "    def _insert(self, node, data):\n",
    "        # Constraint: Assume we are working with valid ints\n",
    "        if node is None:\n",
    "            return Node(data)\n",
    "        if data <= node.data:\n",
    "            if node.left is None:\n",
    "                node.left = self._insert(node.left, data)\n",
    "                node.left.parent = node\n",
    "                return node.left\n",
    "            else:\n",
    "                return self._insert(node.left, data)\n",
    "        else:\n",
    "            if node.right is None:\n",
    "                node.right = self._insert(node.right, data)\n",
    "                node.right.parent = node\n",
    "                return node.right\n",
    "            else:\n",
    "                return self._insert(node.right, data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%run bst.py"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%run dfs.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%run ../utils/results.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting test_bst.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile test_bst.py\n",
    "from nose.tools import assert_equal\n",
    "\n",
    "\n",
    "class TestTree(object):\n",
    "\n",
    "    def __init__(self):\n",
    "        self.results = Results()\n",
    "\n",
    "    def test_tree_one(self):\n",
    "        bst = Bst()\n",
    "        bst.insert(5)\n",
    "        bst.insert(2)\n",
    "        bst.insert(8)\n",
    "        bst.insert(1)\n",
    "        bst.insert(3)\n",
    "        in_order_traversal(bst.root, self.results.add_result)\n",
    "        assert_equal(str(self.results), '[1, 2, 3, 5, 8]')\n",
    "        self.results.clear_results()\n",
    "\n",
    "    def test_tree_two(self):\n",
    "        bst = Bst()\n",
    "        bst.insert(1)\n",
    "        bst.insert(2)\n",
    "        bst.insert(3)\n",
    "        bst.insert(4)\n",
    "        bst.insert(5)\n",
    "        in_order_traversal(bst.root, self.results.add_result)\n",
    "        assert_equal(str(self.results), '[1, 2, 3, 4, 5]')\n",
    "\n",
    "        print('Success: test_tree')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestTree()\n",
    "    test.test_tree_one()\n",
    "    test.test_tree_two()\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success: test_tree\n"
     ]
    }
   ],
   "source": [
    "%run -i test_bst.py"
   ]
  }
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