interactive-coding-challenges/bit_manipulation/draw_line/draw_line_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)."
   ]
  },
  {
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   "source": [
    "# Solution Notebook"
   ]
  },
  {
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   "metadata": {},
   "source": [
    "## Problem: Implement the method draw_line(screen, width, x1, x2) where screen is a list of bytes, width is divisible by 8, and x1, x2 are absolute pixel positions.\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\n",
    "* For the output, do we set corresponding bits in screen?\n",
    "    * Yes\n",
    "* Can we assume this fits memory?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "* Invalid inputs -> Exception\n",
    "    * screen is empty\n",
    "    * width = 0\n",
    "    * any input param is None\n",
    "    * x1 or x2 is out of bounds\n",
    "* General case for len(screen) = 20, width = 32:\n",
    "    * x1 = 2, x2 = 6\n",
    "        * screen[0] = int('00111110', base=2)\n",
    "    * x1 = 68, x2 = 80\n",
    "        * screen[8], int('00001111', base=2)\n",
    "        * screen[9], int('11111111', base=2)\n",
    "        * screen[10], int('10000000', base=2)"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "* Set start offset to x1 % 8\n",
    "* Set end offset to x2 % 8\n",
    "* Determine where the first and last full bytes are\n",
    "    * First full byte = x1 // 8\n",
    "        * Increment by 1 if start offset != 0\n",
    "    * Last full byte = x2 // 8\n",
    "        * Decrement by 1 if end offset != 7\n",
    "    * Fill the bytes with 1111 1111\n",
    "* If x1 and x2 are in the same byte\n",
    "\n",
    "<pre>\n",
    "    x1 = 2\n",
    "    x2 = 6\n",
    "\n",
    "    index  0123 4567\n",
    "    byte   0011 1110\n",
    "\n",
    "    We want to build left and right masks such that:\n",
    "\n",
    "    left   0011 1111\n",
    "    right  1111 1110\n",
    "    ----------------\n",
    "           0011 1110  left & right\n",
    "\n",
    "    Build the left mask:\n",
    "\n",
    "    left   0000 0001  1\n",
    "           0100 0000  1 << (8 - x1)\n",
    "           0011 1111  (1 << (8 - x1)) - 1\n",
    "\n",
    "    Build the right mask:\n",
    "\n",
    "    right  0000 0000  1\n",
    "           0000 0010  1 << (8 - x2 - 1)\n",
    "           0000 0001  (1 << (8 - x2 - 1) - 1\n",
    "           1111 1110  ~((1 << (8 - x2 - 1) - 1)\n",
    "\n",
    "    Combine the left and right masks:\n",
    "\n",
    "    left   0011 1111\n",
    "    right  1111 1110\n",
    "    ----------------\n",
    "           0011 1110  left & right\n",
    "\n",
    "    Set screen[x1//8] or screen[x2//8] |= mask\n",
    "</pre>\n",
    "* Else\n",
    "<pre>\n",
    "    If our starting partial byte is:\n",
    "           0000 1111\n",
    "\n",
    "    Build start mask:\n",
    "    \n",
    "    start  0000 0001  1\n",
    "           0001 0000  1 << 1 << start offset\n",
    "           0000 1111  (1 << 1 << start offset) - 1\n",
    "\n",
    "    If our ending partial byte is:\n",
    "           1111 1100\n",
    "\n",
    "    Build end mask:\n",
    "    \n",
    "    end    1000 0000  0x10000000\n",
    "           1111 1100  0x10000000 >> end offset\n",
    "\n",
    "    Set screen[x1//8] |= start mask\n",
    "    Set screen[x2//8] |= end mask\n",
    "</pre>\n",
    "\n",
    "Complexity:\n",
    "* Time: O(length of screen)\n",
    "* Space: O(1)"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
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  {
   "cell_type": "code",
   "execution_count": 1,
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   "source": [
    "class BitsScreen(object):\n",
    "\n",
    "    def draw_line(self, screen, width, x1, x2):\n",
    "        if None in (screen, width, x1, x2):\n",
    "            raise TypeError('Invalid argument: None')\n",
    "        if not screen or not width:\n",
    "            raise ValueError('Invalid arg: Empty screen or width')\n",
    "        MAX_BIT_VALUE = len(screen) * 8\n",
    "        if x1 < 0 or x2 < 0 or x1 >= MAX_BIT_VALUE or x2 >= MAX_BIT_VALUE:\n",
    "            raise ValueError('Invalid arg: x1 or x2 out of bounds')\n",
    "        start_bit = x1 % 8\n",
    "        end_bit = x2 % 8\n",
    "        first_full_byte = x1 // 8\n",
    "        if start_bit != 0:\n",
    "            first_full_byte += 1\n",
    "        last_full_byte = x2 // 8\n",
    "        if end_bit != (8 - 1):\n",
    "            last_full_byte -= 1\n",
    "        for byte in range(first_full_byte, last_full_byte + 1):\n",
    "            screen[byte] = int('11111111', base=2)\n",
    "        start_byte = x1 // 8\n",
    "        end_byte = x2 // 8\n",
    "        if start_byte == end_byte:\n",
    "            left_mask = (1 << (8 - start_bit)) - 1\n",
    "            right_mask = ~((1 << (8 - end_bit - 1)) - 1)\n",
    "            mask = left_mask & right_mask\n",
    "            screen[start_byte] |= mask\n",
    "        else:\n",
    "            start_mask = (1 << (8 - start_bit)) - 1\n",
    "            end_mask = 1 << (8 - end_bit - 1)\n",
    "            screen[start_byte] |= start_mask\n",
    "            screen[end_byte] |= end_mask"
   ]
  },
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   "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_draw_line.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile test_draw_line.py\n",
    "from nose.tools import assert_equal\n",
    "\n",
    "\n",
    "class TestBitsScreen(object):\n",
    "\n",
    "    def test_draw_line(self):\n",
    "        bits_screen = BitsScreen()\n",
    "        screen = []\n",
    "        for _ in range(20):\n",
    "            screen.append(int('00000000', base=2))\n",
    "        bits_screen.draw_line(screen, width=32, x1=68, x2=80)\n",
    "        assert_equal(screen[8], int('00001111', base=2))\n",
    "        assert_equal(screen[9], int('11111111', base=2))\n",
    "        assert_equal(screen[10], int('10000000', base=2))\n",
    "        bits_screen.draw_line(screen, width=32, x1=2, x2=6)\n",
    "        assert_equal(screen[0], int('00111110', base=2))\n",
    "        bits_screen.draw_line(screen, width=32, x1=10, x2=13)\n",
    "        assert_equal(screen[1], int('00111100', base=2))\n",
    "        print('Success: test_draw_line')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestBitsScreen()\n",
    "    test.test_draw_line()\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
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  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success: test_draw_line\n"
     ]
    }
   ],
   "source": [
    "%run -i test_draw_line.py"
   ]
  }
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