diff --git a/math_probability/generate_primes/__init__.py b/math_probability/generate_primes/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/math_probability/generate_primes/check_prime_challenge.ipynb b/math_probability/generate_primes/check_prime_challenge.ipynb new file mode 100644 index 0000000..e2b748a --- /dev/null +++ b/math_probability/generate_primes/check_prime_challenge.ipynb @@ -0,0 +1,169 @@ +{ + "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: Generate a list of primes.\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", + "* 20 -> 2, 3, 5, 7, 11, 13, 17, 19" + ] + }, + { + "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": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "class PrimeGenerator(object):\n", + "\n", + " def generate_primes(self, max_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_generate_primes.py\n", + "from nose.tools import assert_equal, assert_raises\n", + "\n", + "\n", + "class TestMath(object):\n", + "\n", + " def test_generate_primes(self):\n", + " prime_generator = PrimeGenerator()\n", + " assert_raises(TypeError, prime_generator.generate_primes, None)\n", + " assert_raises(TypeError, prime_generator.generate_primes, 98.6)\n", + " assert_equal(prime_generator.generate_primes(20), [False, False, True, \n", + " True, False, True, \n", + " False, True, False, \n", + " False, False, True, \n", + " False, True, False, \n", + " False, False, True, \n", + " False, True])\n", + " print('Success: generate_primes')\n", + "\n", + "\n", + "def main():\n", + " test = TestMath()\n", + " test.test_generate_primes()\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/generate_primes/check_prime_solution.ipynb b/math_probability/generate_primes/check_prime_solution.ipynb new file mode 100644 index 0000000..6f7a58b --- /dev/null +++ b/math_probability/generate_primes/check_prime_solution.ipynb @@ -0,0 +1,220 @@ +{ + "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: Generate a list of primes.\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", + "* 20 -> 2, 3, 5, 7, 11, 13, 17, 19" + ] + }, + { + "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 use the Sieve of Eratosthenes. All non-prime numbers are divisible by a prime number.\n", + "\n", + "* Use an array (or bit array, bit vector) to keep track of each integer up to the max\n", + "* Start at 2, end at sqrt(max)\n", + " * We can use sqrt(max) instead of max because:\n", + " * For each value that divides the input number evenly, there is a complement b where a * b = n\n", + " * If a > sqrt(n) then b < sqrt(n) because sqrt(n^2) = n\n", + " * \"Cross off\" all numbers divisible by 2, 3, 5, 7, ... by setting array[index] to False\n", + "\n", + "Complexity:\n", + "* Time: O(n log log n)\n", + "* Space: O(n)\n", + "\n", + "Wikipedia's animation:\n", + "\n", + "![alt text](https://upload.wikimedia.org/wikipedia/commons/b/b9/Sieve_of_Eratosthenes_animation.gif)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Code" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import math\n", + "\n", + "\n", + "class PrimeGenerator(object):\n", + "\n", + " def generate_primes(self, max_num):\n", + " if max_num is None:\n", + " raise TypeError('max_num cannot be None')\n", + " array = [True] * max_num\n", + " array[0] = False\n", + " array[1] = False\n", + " prime = 2\n", + " while prime <= math.sqrt(max_num):\n", + " self._cross_off(array, prime)\n", + " prime = self._next_prime(array, prime)\n", + " return array\n", + "\n", + " def _cross_off(self, array, prime):\n", + " for index in range(prime*prime, len(array), prime):\n", + " # Start with prime*prime because if we have a k*prime\n", + " # where k < prime, this value would have already been\n", + " # previously crossed off\n", + " array[index] = False\n", + "\n", + " def _next_prime(self, array, prime):\n", + " next = prime + 1\n", + " while next < len(array) and not array[next]:\n", + " next += 1\n", + " return next" + ] + }, + { + "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_generate_primes.py\n" + ] + } + ], + "source": [ + "%%writefile test_generate_primes.py\n", + "from nose.tools import assert_equal, assert_raises\n", + "\n", + "\n", + "class TestMath(object):\n", + "\n", + " def test_generate_primes(self):\n", + " prime_generator = PrimeGenerator()\n", + " assert_raises(TypeError, prime_generator.generate_primes, None)\n", + " assert_raises(TypeError, prime_generator.generate_primes, 98.6)\n", + " assert_equal(prime_generator.generate_primes(20), [False, False, True, \n", + " True, False, True, \n", + " False, True, False, \n", + " False, False, True, \n", + " False, True, False, \n", + " False, False, True, \n", + " False, True])\n", + " print('Success: generate_primes')\n", + "\n", + "\n", + "def main():\n", + " test = TestMath()\n", + " test.test_generate_primes()\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: generate_primes\n" + ] + } + ], + "source": [ + "%run -i test_generate_primes.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/generate_primes/test_generate_primes.py b/math_probability/generate_primes/test_generate_primes.py new file mode 100644 index 0000000..85ed132 --- /dev/null +++ b/math_probability/generate_primes/test_generate_primes.py @@ -0,0 +1,26 @@ +from nose.tools import assert_equal, assert_raises + + +class TestMath(object): + + def test_generate_primes(self): + prime_generator = PrimeGenerator() + assert_raises(TypeError, prime_generator.generate_primes, None) + assert_raises(TypeError, prime_generator.generate_primes, 98.6) + assert_equal(prime_generator.generate_primes(20), [False, False, True, + True, False, True, + False, True, False, + False, False, True, + False, True, False, + False, False, True, + False, True]) + print('Success: generate_primes') + + +def main(): + test = TestMath() + test.test_generate_primes() + + +if __name__ == '__main__': + main() \ No newline at end of file