{ "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: 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" ] }, { "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 }, "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" ] } ], "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": "3.4.3" } }, "nbformat": 4, "nbformat_minor": 0 }