{
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   "metadata": {},
   "source": [
    "<small><i>This notebook was prepared by [Donne Martin](http://donnemartin.com). 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: Utopian Tree\n",
    "\n",
    "See the [HackerRank problem page](https://www.hackerrank.com/challenges/utopian-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",
    "*Problem statements are sometimes ambiguous.  Identifying constraints and stating assumptions can help to ensure you code the intended solution.*\n",
    "\n",
    "See the [HackerRank problem page](https://www.hackerrank.com/challenges/utopian-tree)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "See the [HackerRank problem page](https://www.hackerrank.com/challenges/utopian-tree)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "* If cycles is 0, return height of 1\n",
    "* For 1 to cycles:\n",
    "    * If cycle is odd, double height\n",
    "    * Else, increment height\n",
    "* Return height\n",
    "\n",
    "Complexity:\n",
    "* Time: O(n), where n is the number of cycles, for each cycle we perform a calculation\n",
    "* Space: O(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# cycles = 0, print 1: base case\n",
    "# cycles = 1, print 2: i = 1: 1 * 2\n",
    "# cycles = 4, print 7: i = 1: 1 * 2, i = 2: 2 + 1, i = 3: 3 * 2, i = 4: 6 + 1\n",
    "def calc_utopian_tree_height(cycles):\n",
    "    height = 1\n",
    "    if cycles == 0:\n",
    "        return height\n",
    "    for i in xrange(1, cycles+1):\n",
    "        if i % 2 == 1:\n",
    "            height *= 2\n",
    "        else:\n",
    "            height += 1\n",
    "    return height"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit Test\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting test_utopian_tree.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile test_utopian_tree.py\n",
    "from nose.tools import assert_equal\n",
    "\n",
    "\n",
    "class TestUtopianTree(object):\n",
    "\n",
    "    def test_utopian_tree(self):\n",
    "        assert_equal(calc_utopian_tree_height(0), 1)\n",
    "        assert_equal(calc_utopian_tree_height(1), 2)\n",
    "        assert_equal(calc_utopian_tree_height(4), 7)\n",
    "        print('Success: test_utopian_tree')\n",
    "\n",
    "def main():\n",
    "    test = TestUtopianTree()\n",
    "    test.test_utopian_tree()\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success: test_utopian_tree\n"
     ]
    }
   ],
   "source": [
    "run -i test_utopian_tree.py"
   ]
  }
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