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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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   "source": [
    "## Problem: Maximizing XOR\n",
    "\n",
    "From HackerRank: https://www.hackerrank.com/challenges/maximizing-xor\n",
    "\n",
    "* [Algorithm](#Algorithm)\n",
    "* [Code](#Code)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "* Set max to 0\n",
    "* For i in the range (lower, upper) inclusive\n",
    "    * For j in the range (lower, upper) inclusive\n",
    "        * Compare i ^ j with max, update max if needed\n",
    "* return max\n",
    "\n",
    "Complexity:\n",
    "* Time: O(n^2)\n",
    "* Space: O(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
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   "outputs": [],
   "source": [
    "def max_xor(lower, upper):\n",
    "    result = 0\n",
    "    for l in xrange(lower, upper + 1):\n",
    "        for u in xrange(lower, upper + 1):\n",
    "            curr = l ^ u\n",
    "            if result < curr:\n",
    "                result = curr\n",
    "    return result\n",
    "\n",
    "lower = int(raw_input());\n",
    "upper = int(raw_input());\n",
    "\n",
    "result = max_xor(lower, upper);\n",
    "print(result)"
   ]
  }
 ],
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