interactive-coding-challenges/hacker-rank/utopian-tree.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem: Utopian Tree\n",
    "\n",
    "From HackerRank: https://www.hackerrank.com/challenges/utopian-tree\n",
    "\n",
    "* [Algorithm](#Algorithm)\n",
    "* [Code](#Code)"
   ]
  },
  {
   "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": null,
   "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\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"
   ]
  }
 ],
 "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": "2.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}