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https://github.com/donnemartin/interactive-coding-challenges.git
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Add generate primes challenge
This commit is contained in:
Donne Martin
parent
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commit
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0
math_probability/generate_primes/__init__.py
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0
math_probability/generate_primes/__init__.py
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169
math_probability/generate_primes/check_prime_challenge.ipynb
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169
math_probability/generate_primes/check_prime_challenge.ipynb
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"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)."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Challenge Notebook"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Problem: Generate a list of primes.\n",
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"\n",
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"* [Constraints](#Constraints)\n",
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"* [Test Cases](#Test-Cases)\n",
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"* [Algorithm](#Algorithm)\n",
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"* [Code](#Code)\n",
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"* [Unit Test](#Unit-Test)\n",
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"* [Solution Notebook](#Solution-Notebook)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Constraints\n",
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"\n",
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"* Is it correct that 1 is not considered a prime number?\n",
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" * Yes\n",
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"* Can we assume the inputs are valid?\n",
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" * No\n",
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"* Can we assume this fits memory?\n",
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" * Yes"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Test Cases\n",
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"\n",
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"* None -> Exception\n",
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"* Not an int -> Exception\n",
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"* 20 -> 2, 3, 5, 7, 11, 13, 17, 19"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Algorithm\n",
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"\n",
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"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."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Code"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"class PrimeGenerator(object):\n",
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"\n",
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" def generate_primes(self, max_num):\n",
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" # TODO: Implement me\n",
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" pass"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Unit Test"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**The following unit test is expected to fail until you solve the challenge.**"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"# %load test_generate_primes.py\n",
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"from nose.tools import assert_equal, assert_raises\n",
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"\n",
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"\n",
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"class TestMath(object):\n",
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"\n",
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" def test_generate_primes(self):\n",
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" prime_generator = PrimeGenerator()\n",
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" assert_raises(TypeError, prime_generator.generate_primes, None)\n",
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" assert_raises(TypeError, prime_generator.generate_primes, 98.6)\n",
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" assert_equal(prime_generator.generate_primes(20), [False, False, True, \n",
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" True, False, True, \n",
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" False, True, False, \n",
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" False, False, True, \n",
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" False, True, False, \n",
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" False, False, True, \n",
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" False, True])\n",
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" print('Success: generate_primes')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestMath()\n",
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" test.test_generate_primes()\n",
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"\n",
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"\n",
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"if __name__ == '__main__':\n",
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" main()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Solution Notebook\n",
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"\n",
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"Review the [Solution Notebook]() for a discussion on algorithms and code solutions."
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.5.0"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 0
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}
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220
math_probability/generate_primes/check_prime_solution.ipynb
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math_probability/generate_primes/check_prime_solution.ipynb
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@ -0,0 +1,220 @@
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"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)."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Solution Notebook"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Problem: Generate a list of primes.\n",
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"\n",
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"* [Constraints](#Constraints)\n",
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"* [Test Cases](#Test-Cases)\n",
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"* [Algorithm](#Algorithm)\n",
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"* [Code](#Code)\n",
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"* [Unit Test](#Unit-Test)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Constraints\n",
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"\n",
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"* Is it correct that 1 is not considered a prime number?\n",
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" * Yes\n",
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"* Can we assume the inputs are valid?\n",
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" * No\n",
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"* Can we assume this fits memory?\n",
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" * Yes"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Test Cases\n",
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"\n",
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"* None -> Exception\n",
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"* Not an int -> Exception\n",
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"* 20 -> 2, 3, 5, 7, 11, 13, 17, 19"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Algorithm\n",
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"\n",
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"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",
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"\n",
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"We'll use the Sieve of Eratosthenes. All non-prime numbers are divisible by a prime number.\n",
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"\n",
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"* Use an array (or bit array, bit vector) to keep track of each integer up to the max\n",
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"* Start at 2, end at sqrt(max)\n",
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" * We can use sqrt(max) instead of max because:\n",
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" * For each value that divides the input number evenly, there is a complement b where a * b = n\n",
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" * If a > sqrt(n) then b < sqrt(n) because sqrt(n^2) = n\n",
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" * \"Cross off\" all numbers divisible by 2, 3, 5, 7, ... by setting array[index] to False\n",
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"\n",
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"Complexity:\n",
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"* Time: O(n log log n)\n",
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"* Space: O(n)\n",
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"\n",
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"Wikipedia's animation:\n",
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"\n",
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""
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Code"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"import math\n",
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"\n",
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"\n",
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"class PrimeGenerator(object):\n",
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"\n",
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" def generate_primes(self, max_num):\n",
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" if max_num is None:\n",
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" raise TypeError('max_num cannot be None')\n",
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" array = [True] * max_num\n",
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" array[0] = False\n",
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" array[1] = False\n",
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" prime = 2\n",
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" while prime <= math.sqrt(max_num):\n",
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" self._cross_off(array, prime)\n",
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" prime = self._next_prime(array, prime)\n",
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" return array\n",
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"\n",
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" def _cross_off(self, array, prime):\n",
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" for index in range(prime*prime, len(array), prime):\n",
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" # Start with prime*prime because if we have a k*prime\n",
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" # where k < prime, this value would have already been\n",
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" # previously crossed off\n",
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" array[index] = False\n",
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"\n",
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" def _next_prime(self, array, prime):\n",
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" next = prime + 1\n",
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" while next < len(array) and not array[next]:\n",
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" next += 1\n",
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" return next"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Unit Test"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Overwriting test_generate_primes.py\n"
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]
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}
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],
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"source": [
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"%%writefile test_generate_primes.py\n",
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"from nose.tools import assert_equal, assert_raises\n",
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"\n",
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"\n",
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"class TestMath(object):\n",
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"\n",
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" def test_generate_primes(self):\n",
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" prime_generator = PrimeGenerator()\n",
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" assert_raises(TypeError, prime_generator.generate_primes, None)\n",
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" assert_raises(TypeError, prime_generator.generate_primes, 98.6)\n",
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" assert_equal(prime_generator.generate_primes(20), [False, False, True, \n",
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" True, False, True, \n",
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" False, True, False, \n",
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" False, False, True, \n",
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" False, True, False, \n",
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" False, False, True, \n",
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" False, True])\n",
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" print('Success: generate_primes')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestMath()\n",
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" test.test_generate_primes()\n",
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"\n",
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"\n",
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"if __name__ == '__main__':\n",
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" main()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Success: generate_primes\n"
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]
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}
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],
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"source": [
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"%run -i test_generate_primes.py"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.5.0"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 0
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}
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26
math_probability/generate_primes/test_generate_primes.py
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26
math_probability/generate_primes/test_generate_primes.py
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@ -0,0 +1,26 @@
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from nose.tools import assert_equal, assert_raises
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class TestMath(object):
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def test_generate_primes(self):
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prime_generator = PrimeGenerator()
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assert_raises(TypeError, prime_generator.generate_primes, None)
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assert_raises(TypeError, prime_generator.generate_primes, 98.6)
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assert_equal(prime_generator.generate_primes(20), [False, False, True,
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True, False, True,
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False, True, False,
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False, False, True,
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False, True, False,
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False, False, True,
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False, True])
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print('Success: generate_primes')
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def main():
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test = TestMath()
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test.test_generate_primes()
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if __name__ == '__main__':
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main()
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