interactive-coding-challenges/bit_manipulation/flip_bit/flip_bit_solution.ipynb

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   "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: Flip one bit from 0 to 1 to maximize the longest sequence of 1s.\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",
    "* Is the input an int, base 2?\n",
    "    * Yes\n",
    "* Can we assume the input is a 32 bit number?\n",
    "    * Yes\n",
    "* Do we have to validate the length of the input?\n",
    "    * No\n",
    "* Is the output an int?\n",
    "    * Yes\n",
    "* Can we assume the inputs are valid?\n",
    "    * No\n",
    "* Can we assume we are using a positive number since Python doesn't have an >>> operator?\n",
    "    * Yes\n",
    "* Can we assume this fits memory?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "* None -> Exception\n",
    "* All 1's -> Count of 1s\n",
    "* All 0's -> 1\n",
    "* General case\n",
    "    * Trailing zeroes\n",
    "        * 0000 1111 1101 1101 1111 0011 1111 0000 -> 10 (ten)\n",
    "    * Trailing ones\n",
    "        * 0000 1001 1101 1101 1111 0001 1111 0111 -> 9"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "* seen = []\n",
    "* Build a list of sequence counts\n",
    "    * Look for 0's\n",
    "        * This will be 0 length if the input has trailing ones\n",
    "        * Add sequence length to seen\n",
    "    * Look for 1's\n",
    "        * Add sequence length to seen\n",
    "* Find the largest sequence of ones looking at seen\n",
    "    * Loop through seen\n",
    "        * On each iteration of the loop, flip what we are looking for from 0 to 1 and vice versa\n",
    "        * If seen[i] represents 1's, continue, we only want to process 0's\n",
    "        * If this is our first iteration:\n",
    "            * max_result = seen[i+1] + 1 if seen[i] > 0\n",
    "            * continue\n",
    "        * If we are looking at leading zeroes (i == len(seen)-1):\n",
    "            * result = seen[i-1] + 1\n",
    "        * If we are looking at one zero:\n",
    "            * result = seen[i+1] + seen[i-1] + 1\n",
    "        * If we are looking at multiple zeroes:\n",
    "            * result = max(seen[i+1], seen[i-1]) + 1\n",
    "        * Update max_result based on result\n",
    "\n",
    "We should make a note that Python does not have a logical right shift operator built in.  We can either use a positive number or implement one for a 32 bit number:\n",
    "\n",
    "    num % 0x100000000 >> n\n",
    "    \n",
    "Complexity:\n",
    "* Time: O(b)\n",
    "* Space: O(b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
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   "outputs": [],
   "source": [
    "class Bits(object):\n",
    "\n",
    "    MAX_BITS = 32\n",
    "    \n",
    "    def _build_seen_list(self, num):\n",
    "        seen = []\n",
    "        looking_for = 0\n",
    "        count = 0\n",
    "        for _ in range(self.MAX_BITS):\n",
    "            if num & 1 != looking_for:\n",
    "                seen.append(count)\n",
    "                looking_for = not looking_for\n",
    "                count = 0\n",
    "            count += 1\n",
    "            num >>= 1\n",
    "        seen.append(count)\n",
    "        return seen\n",
    "    \n",
    "    def flip_bit(self, num):\n",
    "        if num is None:\n",
    "            raise TypeError('num cannot be None')\n",
    "        if num == -1:\n",
    "            return self.MAX_BITS\n",
    "        if num == 0:\n",
    "            return 1\n",
    "        seen = self._build_seen_list(num)\n",
    "        max_result = 0\n",
    "        looking_for = 0\n",
    "        for index, count in enumerate(seen):\n",
    "            result = 0\n",
    "            # Only look for zeroes\n",
    "            if looking_for == 1:\n",
    "                looking_for = not looking_for\n",
    "                continue\n",
    "            # First iteration, take trailing zeroes\n",
    "            # or trailing ones into account\n",
    "            if index == 0:\n",
    "                if count != 0:\n",
    "                    # Trailing zeroes\n",
    "                    try:\n",
    "                        result = seen[index + 1] + 1\n",
    "                    except IndexError:\n",
    "                        result = 1\n",
    "            # Last iteration\n",
    "            elif index == len(seen) - 1:\n",
    "                result = 1 + seen[index - 1]\n",
    "            else:\n",
    "                # One zero\n",
    "                if count == 1:\n",
    "                    result = seen[index + 1] + seen[index - 1] + 1\n",
    "                # Multiple zeroes\n",
    "                else:\n",
    "                    result = max(seen[index + 1], seen[index - 1]) + 1\n",
    "            if result > max_result:\n",
    "                max_result = result\n",
    "            looking_for = not looking_for\n",
    "        return max_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_flip_bit.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile test_flip_bit.py\n",
    "from nose.tools import assert_equal, assert_raises\n",
    "\n",
    "\n",
    "class TestBits(object):\n",
    "\n",
    "    def test_flip_bit(self):\n",
    "        bits = Bits()\n",
    "        assert_raises(TypeError, bits.flip_bit, None)\n",
    "        assert_equal(bits.flip_bit(0), 1)\n",
    "        assert_equal(bits.flip_bit(-1), bits.MAX_BITS)\n",
    "        num = int('00001111110111011110001111110000', base=2)\n",
    "        expected = 10\n",
    "        assert_equal(bits.flip_bit(num), expected)\n",
    "        num = int('00000100111011101111100011111011', base=2)\n",
    "        expected = 9\n",
    "        assert_equal(bits.flip_bit(num), expected)\n",
    "        num = int('00010011101110111110001111101111', base=2)\n",
    "        expected = 10\n",
    "        assert_equal(bits.flip_bit(num), expected)\n",
    "        print('Success: test_print_binary')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestBits()\n",
    "    test.test_flip_bit()\n",
    "\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_print_binary\n"
     ]
    }
   ],
   "source": [
    "%run -i test_flip_bit.py"
   ]
  }
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