{
 "cells": [
  {
   "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: Determine the height of a tree.\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",
    "* Is this a binary tree?\n",
    "    * Yes\n",
    "* Can we assume we already have a Node class with an insert method?\n",
    "    * Yes\n",
    "* Can we assume this fits memory?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "* 5 -> 1\n",
    "* 5, 2, 8, 1, 3 -> 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "We'll use a recursive algorithm.\n",
    "\n",
    "* If the current node is None, return 0\n",
    "* Else, return 1 + the maximum height of the left or right children\n",
    "    \n",
    "Complexity:\n",
    "* Time: O(n)\n",
    "* Space: O(h), where h is the height of the tree"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%run ../bst/bst.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting height.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile height.py\n",
    "def height(node):\n",
    "    if node is None:\n",
    "        return 0\n",
    "    return 1 + max(height(node.left), \n",
    "                   height(node.right))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%run height.py"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting test_height.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile test_height.py\n",
    "from nose.tools import assert_equal\n",
    "\n",
    "\n",
    "class TestHeight(object):\n",
    "\n",
    "    def test_height(self):\n",
    "        root = Node(5)\n",
    "        assert_equal(height(root), 1)\n",
    "        insert(root, 2)\n",
    "        insert(root, 8)\n",
    "        insert(root, 1)\n",
    "        insert(root, 3)\n",
    "        assert_equal(height(root), 3)\n",
    "\n",
    "        print('Success: test_height')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestHeight()\n",
    "    test.test_height()\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success: test_height\n"
     ]
    }
   ],
   "source": [
    "%run -i test_height.py"
   ]
  }
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