From b4a64f78dceac82061c4929a869dc763c402cdd4 Mon Sep 17 00:00:00 2001 From: Donne Martin Date: Fri, 19 Jan 2018 19:14:17 -0800 Subject: [PATCH] Add check prime challenge (#226) --- math_probability/check_prime/__init__.py | 0 .../check_prime/check_prime_challenge.ipynb | 166 ++++++++++++++ .../check_prime/check_prime_solution.ipynb | 207 ++++++++++++++++++ .../check_prime/test_check_prime.py | 22 ++ 4 files changed, 395 insertions(+) create mode 100644 math_probability/check_prime/__init__.py create mode 100644 math_probability/check_prime/check_prime_challenge.ipynb create mode 100644 math_probability/check_prime/check_prime_solution.ipynb create mode 100644 math_probability/check_prime/test_check_prime.py diff --git a/math_probability/check_prime/__init__.py b/math_probability/check_prime/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/math_probability/check_prime/check_prime_challenge.ipynb b/math_probability/check_prime/check_prime_challenge.ipynb new file mode 100644 index 0000000..c7d4433 --- /dev/null +++ b/math_probability/check_prime/check_prime_challenge.ipynb @@ -0,0 +1,166 @@ +{ + "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": [ + "# Challenge Notebook" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Problem: Check if a number is prime.\n", + "\n", + "* [Constraints](#Constraints)\n", + "* [Test Cases](#Test-Cases)\n", + "* [Algorithm](#Algorithm)\n", + "* [Code](#Code)\n", + "* [Unit Test](#Unit-Test)\n", + "* [Solution Notebook](#Solution-Notebook)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Constraints\n", + "\n", + "* Is it correct that 1 is not considered a prime number?\n", + " * Yes\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 -> Exception\n", + "* Not an int -> Exception\n", + "* Less than 2 -> False\n", + "* General case" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Algorithm\n", + "\n", + "Refer to the [Solution Notebook](). If you are stuck and need a hint, the solution notebook's algorithm discussion might be a good place to start." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Code" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "class Math(object):\n", + "\n", + " def check_prime(self, num):\n", + " # TODO: Implement me\n", + " pass" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Unit Test" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**The following unit test is expected to fail until you solve the challenge.**" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# %load test_check_prime.py\n", + "from nose.tools import assert_equal, assert_raises\n", + "\n", + "\n", + "class TestMath(object):\n", + "\n", + " def test_check_prime(self):\n", + " math = Math()\n", + " assert_raises(TypeError, math.check_prime, None)\n", + " assert_raises(TypeError, math.check_prime, 98.6)\n", + " assert_equal(math.check_prime(0), False)\n", + " assert_equal(math.check_prime(1), False)\n", + " assert_equal(math.check_prime(97), True)\n", + " print('Success: test_check_prime')\n", + "\n", + "\n", + "def main():\n", + " test = TestMath()\n", + " test.test_check_prime()\n", + "\n", + "\n", + "if __name__ == '__main__':\n", + " main()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Solution Notebook\n", + "\n", + "Review the [Solution Notebook]() for a discussion on algorithms and code solutions." + ] + } + ], + "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": "3.5.0" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/math_probability/check_prime/check_prime_solution.ipynb b/math_probability/check_prime/check_prime_solution.ipynb new file mode 100644 index 0000000..858ca7a --- /dev/null +++ b/math_probability/check_prime/check_prime_solution.ipynb @@ -0,0 +1,207 @@ +{ + "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: Check if a number is prime.\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 it correct that 1 is not considered a prime number?\n", + " * Yes\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 -> Exception\n", + "* Not an int -> Exception\n", + "* Less than 2 -> False\n", + "* General case" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Algorithm\n", + "\n", + "For a number to be prime, it must be 2 or greater and cannot be divisible by another number other than itself (and 1).\n", + "\n", + "We'll check by dividing all numbers from 2 to the input number to determine if the number is prime.\n", + "\n", + "As an optimization, we can divide from 2 to the square root of the input number. For each value that divides the input number evenly, there is a complement b where a * b = n. If a > sqrt(n) then b < sqrt(n) because sqrt(n^2) = n.\n", + "\n", + "Complexity:\n", + "* Time: O(n) where n is the value of the input number\n", + "* Space: O(1)\n", + "\n", + "### Sieve of Eratosthenes\n", + "\n", + "The Sieve of Eratosthenes provides a more efficient way of computing and generating primes. See the challenge [\"Generate a list of primes\"]() for more details." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Code" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import math\n", + "\n", + "\n", + "class Math(object):\n", + "\n", + " def check_prime(self, num):\n", + " if num is None:\n", + " raise TypeError('num cannot be None')\n", + " if num < 2:\n", + " return False\n", + " for i in range(2, num):\n", + " if num % i == 0:\n", + " return False\n", + " return True\n", + "\n", + " def check_prime_optimized(self, num):\n", + " if num is None:\n", + " raise TypeError('num cannot be None')\n", + " if num < 2:\n", + " return False\n", + " for i in range(2, int(math.sqrt(num)+1)):\n", + " if num % i == 0:\n", + " return False\n", + " return True" + ] + }, + { + "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_check_prime.py\n" + ] + } + ], + "source": [ + "%%writefile test_check_prime.py\n", + "from nose.tools import assert_equal, assert_raises\n", + "\n", + "\n", + "class TestMath(object):\n", + "\n", + " def test_check_prime(self):\n", + " math = Math()\n", + " assert_raises(TypeError, math.check_prime, None)\n", + " assert_raises(TypeError, math.check_prime, 98.6)\n", + " assert_equal(math.check_prime(0), False)\n", + " assert_equal(math.check_prime(1), False)\n", + " assert_equal(math.check_prime(97), True)\n", + " print('Success: test_check_prime')\n", + "\n", + "\n", + "def main():\n", + " test = TestMath()\n", + " test.test_check_prime()\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_check_prime\n" + ] + } + ], + "source": [ + "%run -i test_check_prime.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": "3.5.0" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/math_probability/check_prime/test_check_prime.py b/math_probability/check_prime/test_check_prime.py new file mode 100644 index 0000000..83ad691 --- /dev/null +++ b/math_probability/check_prime/test_check_prime.py @@ -0,0 +1,22 @@ +from nose.tools import assert_equal, assert_raises + + +class TestMath(object): + + def test_check_prime(self): + math = Math() + assert_raises(TypeError, math.check_prime, None) + assert_raises(TypeError, math.check_prime, 98.6) + assert_equal(math.check_prime(0), False) + assert_equal(math.check_prime(1), False) + assert_equal(math.check_prime(97), True) + print('Success: test_check_prime') + + +def main(): + test = TestMath() + test.test_check_prime() + + +if __name__ == '__main__': + main() \ No newline at end of file