Added tree height challenge.

graphs_trees/tree_height/height_solution.ipynb

@@ -0,0 +1,193 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<small><i>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).</i></small>"
+   ]
+  },
+  {
+   "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"
+   ]
+  },
+  {
+   "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(log n)"
+   ]
+  },
+  {
+   "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": [],
+   "source": [
+    "def height(node):\n",
+    "    if node is None:\n",
+    "        return 0\n",
+    "    return 1 + max(height(node.left), \n",
+    "                   height(node.right))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Unit Test"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Overwriting test_height.py\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%writefile test_height.py\n",
+    "from __future__ import print_function\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": 4,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Success: test_height\n"
+     ]
+    }
+   ],
+   "source": [
+    "%run -i test_height.py"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.10"
+  }
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+}