{ "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: Determine the number of bits to flip to convert int a to int b.\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 A and B are always ints?\n", " * Yes\n", "* Is the output an int?\n", " * Yes\n", "* Can we assume A and B are always the same number of bits?\n", " * Yes\n", "* Can we assume the inputs are valid (not None)?\n", " * No\n", "* Can we assume this fits memory?\n", " * Yes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Test Cases\n", "\n", "* A or B is None -> Exception\n", "* General case\n", "
\n", " A = 11101\n", " B = 01111\n", " Result: 2\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Algorithm\n", "\n", "We can use the xor operator to determine the bit differences between a and b\n", "\n", "* Set count to 0\n", "* Set c to a xor b\n", "* Loop while c != 0:\n", " * Increment count if the LSB in c is a 1\n", " * We can check this by using a mask of 1\n", " * Right shift c by 1\n", "* Return the count\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": {}, "outputs": [], "source": [ "class Bits(object):\n", "\n", " def bits_to_flip(self, a, b):\n", " if a is None or b is None:\n", " raise TypeError('a or b cannot be None')\n", " count = 0\n", " c = a ^ b\n", " while c:\n", " count += c & 1\n", " c >>= 1\n", " return count" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Unit Test" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Overwriting test_bits_to_flip.py\n" ] } ], "source": [ "%%writefile test_bits_to_flip.py\n", "import unittest\n", "\n", "\n", "class TestBits(unittest.TestCase):\n", "\n", " def test_bits_to_flip(self):\n", " bits = Bits()\n", " a = int('11101', base=2)\n", " b = int('01111', base=2)\n", " expected = 2\n", " self.assertEqual(bits.bits_to_flip(a, b), expected)\n", " print('Success: test_bits_to_flip')\n", "\n", "\n", "def main():\n", " test = TestBits()\n", " test.test_bits_to_flip()\n", "\n", "\n", "if __name__ == '__main__':\n", " main()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Success: test_bits_to_flip\n" ] } ], "source": [ "%run -i test_bits_to_flip.py" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.2" } }, "nbformat": 4, "nbformat_minor": 1 }