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   "metadata": {},
   "source": [
    "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)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solution Notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem: Find the difference of two integers without using the + or - sign.\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",
    "* Can we assume the inputs are valid?\n",
    "    * No, check for None\n",
    "* Can we assume this fits memory?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "<pre>\n",
    "* None input -> TypeError\n",
    "* 7, 5 -> 2\n",
    "* -5, -7 -> 2\n",
    "* -5, 7 -> -12\n",
    "* 5, -7 -> 12\n",
    "</pre>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "We'll look at the following example, subtracting a and b:\n",
    "\n",
    "<pre>\n",
    "a 0110 = 6 \n",
    "b 0101 = 5\n",
    "</pre>\n",
    "\n",
    "First, subtract a and b, without worrying about the borrow (0-0=0, 0-1=1, 1-1=0):\n",
    "\n",
    "result = a ^ b = 0011\n",
    "\n",
    "Next, calculate the borrow (0-1=1).  We'll need to left shift one to prepare for the next iteration when we move to the next most significant bit:\n",
    "\n",
    "~a     = 1001\n",
    " b     = 0101\n",
    "~a & b = 0001\n",
    "\n",
    "borrow = (~a&b) << 1 = 0010\n",
    "\n",
    "If the borrow is not zero, we'll need to subtract the borrow from the result.  Recusively call the function, passing in result and borrow.\n",
    "\n",
    "Complexity:\n",
    "* Time: O(b), where b is the number of bits\n",
    "* Space: O(b), where b is the number of bits"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class Solution(object):\n",
    "\n",
    "    def sub_two(self, a, b):\n",
    "        if a is None or b is None:\n",
    "            raise TypeError('a or b cannot be None')\n",
    "        result = a ^ b;\n",
    "        borrow = (~a & b) << 1\n",
    "        if borrow != 0:\n",
    "            return self.sub_two(result, borrow)\n",
    "        return result;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting test_sub_two.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile test_sub_two.py\n",
    "from nose.tools import assert_equal, assert_raises\n",
    "\n",
    "\n",
    "class TestSubTwo(object):\n",
    "\n",
    "    def test_sub_two(self):\n",
    "        solution = Solution()\n",
    "        assert_raises(TypeError, solution.sub_two, None)\n",
    "        assert_equal(solution.sub_two(7, 5), 2)\n",
    "        assert_equal(solution.sub_two(-5, -7), 2)\n",
    "        assert_equal(solution.sub_two(-5, 7), -12)\n",
    "        assert_equal(solution.sub_two(5, -7), 12)\n",
    "        print('Success: test_sub_two')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestSubTwo()\n",
    "    test.test_sub_two()\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success: test_sub_two\n"
     ]
    }
   ],
   "source": [
    "%run -i test_sub_two.py"
   ]
  }
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