{
"cells": [
{
"cell_type": "markdown",
"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: Implement common bit manipulation operations: get_bit, set_bit, clear_bit, clear_bits_msb_to_index, clear_bits_msb_to_lsb, update_bit.\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",
"* Can we assume this fits memory?\n",
" * Yes"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Test Cases\n",
"\n",
"* None as a number input -> Exception\n",
"* Negative index -> Exception\n",
"\n",
"### get_bit\n",
" number = 0b10001110, index = 3\n",
" expected = True\n",
"### set_bit\n",
" number = 0b10001110, index = 4\n",
" expected = 0b10011110\n",
"### clear_bit\n",
" number = 0b10001110, index = 3\n",
" expected = 0b10000110\n",
"### clear_bits_msb_to_index\n",
" number = 0b10001110, index = 3\n",
" expected = 0b00000110\n",
"### clear_bits_index_to_lsb\n",
" number = 0b10001110, index = 3\n",
" expected = 0b10000000\n",
"### update_bit\n",
" number = 0b10001110, index = 3, value = 1\n",
" expected = 0b10001110\n",
" number = 0b10001110, index = 3, value = 0\n",
" expected = 0b10000110\n",
" number = 0b10001110, index = 0, value = 1\n",
" expected = 0b10001111"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Algorithm\n",
"\n",
"### get_bit\n",
"\n",
"\n",
"indices 7 6 5 4 3 2 1 0 index = 3\n",
"--------------------------------------------------\n",
"input 1 0 0 0 1 1 1 0 0b10001110\n",
"mask 0 0 0 0 1 0 0 0 1 << index\n",
"--------------------------------------------------\n",
"result 0 0 0 0 1 0 0 0 number & mask != 0\n",
"\n",
"\n",
"Complexity:\n",
"* Time: O(n)\n",
"* Space: O(n)\n",
"\n",
"### set_bit\n",
"\n",
"\n",
"indices 7 6 5 4 3 2 1 0 index = 4\n",
"--------------------------------------------------\n",
"input 1 0 0 0 1 1 1 0 0b10001110\n",
"mask 0 0 0 1 0 0 0 0 1 << index\n",
"--------------------------------------------------\n",
"result 1 0 0 1 1 1 1 0 number | mask\n",
"\n",
"\n",
"Complexity:\n",
"* Time: O(n)\n",
"* Space: O(n)\n",
"\n",
"### clear_bit\n",
"\n",
"\n",
"indices 7 6 5 4 3 2 1 0 index = 3\n",
"--------------------------------------------------\n",
"input 1 0 0 0 1 1 1 0 0b10001110\n",
"mask 0 0 0 0 1 0 0 0 1 << index\n",
"mask 1 1 1 1 0 1 1 1 ~(1 << index)\n",
"--------------------------------------------------\n",
"result 1 0 0 0 0 1 1 0 number & mask\n",
"\n",
"\n",
"Complexity:\n",
"* Time: O(n)\n",
"* Space: O(n)\n",
"\n",
"### clear_bits_msb_to_index\n",
"\n",
"\n",
"indices 7 6 5 4 3 2 1 0 index = 3\n",
"--------------------------------------------------\n",
"input 1 0 0 0 1 1 1 0 0b10001110\n",
"mask 0 0 0 0 1 0 0 0 1 << index\n",
"mask 0 0 0 0 0 1 1 1 (1 << index) - 1\n",
"--------------------------------------------------\n",
"result 0 0 0 0 0 1 1 1 number & mask\n",
"\n",
"\n",
"Complexity:\n",
"* Time: O(n)\n",
"* Space: O(n)\n",
"\n",
"### clear_bits_index_to_lsb\n",
"\n",
"\n",
"indices 7 6 5 4 3 2 1 0 index = 3\n",
"--------------------------------------------------\n",
"input 1 0 0 0 1 1 1 0 0b10001110\n",
"mask 0 0 0 1 0 0 0 0 1 << index + 1\n",
"mask 0 0 0 0 1 1 1 1 (1 << index + 1) - 1\n",
"mask 1 1 1 1 0 0 0 0 ~((1 << index + 1) - 1)\n",
"--------------------------------------------------\n",
"result 1 0 0 0 0 0 0 0 number & mask\n",
"\n",
"\n",
"Complexity:\n",
"* Time: O(n)\n",
"* Space: O(n)\n",
"\n",
"### update_bit\n",
"\n",
"* Use `get_bit` to see if the value is already set or cleared\n",
"* If not, use `set_bit` if setting the value or `clear_bit` if clearing the value\n",
"\n",
"Complexity:\n",
"* Time: O(n)\n",
"* Space: O(n)\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Code"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def validate_index(func):\n",
" def validate_index_wrapper(self, *args, **kwargs):\n",
" for arg in args:\n",
" if arg < 0:\n",
" raise IndexError('Invalid index')\n",
" return func(self, *args, **kwargs)\n",
" return validate_index_wrapper"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"class Bit(object):\n",
"\n",
" def __init__(self, number):\n",
" if number is None:\n",
" raise TypeError('number cannot be None')\n",
" self.number = number\n",
"\n",
" @validate_index\n",
" def get_bit(self, index):\n",
" mask = 1 << index\n",
" return self.number & mask != 0\n",
"\n",
" @validate_index\n",
" def set_bit(self, index):\n",
" mask = 1 << index\n",
" self.number |= mask\n",
" return self.number\n",
"\n",
" @validate_index\n",
" def clear_bit(self, index):\n",
" mask = ~(1 << index)\n",
" self.number &= mask\n",
" return self.number\n",
"\n",
" @validate_index\n",
" def clear_bits_msb_to_index(self, index):\n",
" mask = (1 << index) - 1\n",
" self.number &= mask\n",
" return self.number\n",
"\n",
" @validate_index\n",
" def clear_bits_index_to_lsb(self, index):\n",
" mask = ~((1 << index + 1) - 1)\n",
" self.number &= mask\n",
" return self.number\n",
"\n",
" @validate_index\n",
" def update_bit(self, index, value):\n",
" if value is None or value not in (0, 1):\n",
" raise Exception('Invalid value')\n",
" if self.get_bit(index) == value:\n",
" return self.number\n",
" if value:\n",
" self.set_bit(index)\n",
" else:\n",
" self.clear_bit(index)\n",
" return self.number"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Unit Test"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Overwriting test_bit.py\n"
]
}
],
"source": [
"%%writefile test_bit.py\n",
"from nose.tools import assert_equal\n",
"\n",
"\n",
"class TestBit(object):\n",
"\n",
" def test_bit(self):\n",
" number = int('10001110', base=2)\n",
" bit = Bit(number)\n",
" assert_equal(bit.get_bit(index=3), True)\n",
" expected = int('10011110', base=2)\n",
" assert_equal(bit.set_bit(index=4), expected)\n",
" bit = Bit(number)\n",
" expected = int('10000110', base=2)\n",
" assert_equal(bit.clear_bit(index=3), expected)\n",
" bit = Bit(number)\n",
" expected = int('00000110', base=2)\n",
" assert_equal(bit.clear_bits_msb_to_index(index=3), expected)\n",
" bit = Bit(number)\n",
" expected = int('10000000', base=2)\n",
" assert_equal(bit.clear_bits_index_to_lsb(index=3), expected)\n",
" bit = Bit(number)\n",
" assert_equal(bit.update_bit(index=3, value=1), number)\n",
" bit = Bit(number)\n",
" expected = int('10000110', base=2)\n",
" assert_equal(bit.update_bit(index=3, value=0), expected)\n",
" bit = Bit(number)\n",
" expected = int('10001111', base=2)\n",
" assert_equal(bit.update_bit(index=0, value=1), expected)\n",
" print('Success: test_bit')\n",
"\n",
"\n",
"def main():\n",
" test = TestBit()\n",
" test.test_bit()\n",
"\n",
"\n",
"if __name__ == '__main__':\n",
" main()"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Success: test_bit\n"
]
}
],
"source": [
"%run -i test_bit.py"
]
}
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