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   "source": [
    "<small><i>This notebook was prepared by [Donne Martin](http://donnemartin.com). Source and license info is on [GitHub](https://bit.ly/code-notes).</i></small>"
   ]
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   "cell_type": "markdown",
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    "## Problem: Utopian Tree\n",
    "\n",
    "From HackerRank: https://www.hackerrank.com/challenges/utopian-tree\n",
    "\n",
    "* [Algorithm](#Algorithm)\n",
    "* [Code](#Code)"
   ]
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   "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"
   ]
  },
  {
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   "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\n",
    "\n",
    "num_lines = int(raw_input())\n",
    "for i in range(0, num_lines):\n",
    "    cycles = raw_input()\n",
    "    cycles = int(cycles)\n",
    "    res = calc_utopian_tree_height(cycles)\n",
    "    print res"
   ]
  }
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