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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: 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)"
]
},
{
"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",
"\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",
"\n",
"* Else\n",
"\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",
"\n",
"\n",
"Complexity:\n",
"* Time: O(length of screen)\n",
"* Space: O(1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Code"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"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"
]
},
{
"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()"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Success: test_draw_line\n"
]
}
],
"source": [
"%run -i test_draw_line.py"
]
}
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