Solutions for prime and palindrome

README.md

@@ -1,3 +1,78 @@
-This is a test is intended to test your knowledge of basic programming, coding style, algorithms, django and javascript.
-You will be judged more on the style of the code, maintainibility and readability than how the UI looks.
+# Python Challenge
 
+
+## Overview
+
+Some programming exercises
+
+### Sieve / Primes
+
+Relied heavily on this [paper](http://www.cs.hmc.edu/~oneill/papers/Sieve-JFP.pdf). Executes in under 20 seconds on my machine when asking for the 1 millionth prime.
+
+ - Implemented the 'failful sieve' according to that paper in three incarnations
+   - Naive - tries all candidates (including evens) up to p^2
+   -  Used wheel skipping multiples of 2 & 3
+   -  Used wheel skipping multiples of 2, 3 & 5 (however, something did not perform well in this implementation)
+ - Other optimizations included
+   - Uses lazy iteration described in the paper. Does not generate all multiples of p up to limit but only as needed.
+ - Optimizations not attempted
+   - Composites managed with priority queue. The paper indicated that a priority queue yielded large performance increases. However, after reading [this answer](http://stackoverflow.com/questions/13463417/the-genuine-sieve-of-eratosthenes-in-python-why-is-heapq-slower-than-dict) on stackoverflow  it seems a plain dict is probably just as fast and possibly better.
+
+### Palindrome
+
+The approach taken avoids making a brute force attempt at combing all n-digit numbers and testing for palindrome. Instead, it first generates the list of all palindromes for the expected range and then tests for factors in the n-digit range. This seems like a good approach since the number of palindromes grows slowly in relation to the number of digits in the products.
+
+Other points of interest in the implementation:
+ - Implemented a function which takes the number of digits of the factors as a parameter. Tested for n=2 & 3. It should work for larger n without modification.
+ - Avoided testing for palindrome-ness or manipulating the data as strings
+ - Next optimization that I would address would be to avoid brute forcing the n-digit factor testing of palindromes. For large n this could be expensive. Going after prime factors might be a sensible next step.
+
+## Installation
+
+### Manual installation
+
+#### Virtualenv
+Recommended that you create a virtualenv to install this code and it's dependencies into.
+
+See [virtualenv docs](https://pypi.python.org/pypi/virtualenv)
+
+#### Run the install
+You can install the code simply by running
+
+`python setup.py test` 
+
+If the tests pass proceed with the intsall. Execute
+
+`python setup.py install` 
+
+from the project's root directory.
+
+## Usage
+
+After installation the following will be available on your path 
+
+`nth-prime.py n`
+
+You can run it without arguments to get a help message or specify an integer of reasonable size to see what the nth prime is.
+
+`palindrome-product.py`
+
+
+## Testing
+You can run the automated tests with
+
+`python setup.py test`
+
+If the package is already installed there might be some conflicts. You can usually clean these up by deleting the build directory
+
+`rm -rf build/`
+
+from the project's root directory.
+
+The run tests from setup.py or by `py.test`
+
+## Information
+
+Source: https://github.com/lakeslc/python_test
+
+Authors: [Jonathan Randall](https://github.com/lakeslc/)

bin/nth-prime.py

@@ -0,0 +1,38 @@
+#!/usr/bin/env python
+
+import argparse
+import sys
+import datetime
+from datetime import timedelta
+from primes.sieves import WheelSieve
+
+desc = '''Find the nth prime number using the sieve of Eratosthenes'''
+
+parser = argparse.ArgumentParser(description=desc)
+parser.add_argument('nth', metavar='n', type=int,
+                    help='\'n\' as in the nth prime number')
+args = parser.parse_args()
+
+
+if args.nth < 1:
+    msg = 'Must specify an number greater than 0'
+    raise argparse.ArgumentTypeError(msg)
+
+if args.nth > 1000000:
+    msg = 'Umm... that\'s a really big number... maybe try something smaller?'
+    raise argparse.ArgumentTypeError(msg)
+
+start = datetime.datetime.now()
+primes = WheelSieve().sieve()
+last_prime = 0
+for i in xrange(args.nth):
+    last_prime = primes.next()
+finish = datetime.datetime.now()
+delta = finish - start
+
+msg = '''The nth prime for n={0:,} is {1:,}
+Finished in {2} milliseconds'''
+
+print msg.format(args.nth,
+                 last_prime,
+                 (delta.seconds * 1000) + (delta.microseconds/1000.0))

bin/palindrome-product.py

@@ -0,0 +1,23 @@
+#!/usr/bin/env python
+
+import sys
+import datetime
+from datetime import timedelta
+from palindrome.products import largest_palindrome
+
+desc = '''Find the largest palindrome made from the\
+product of two 3-digit numbers.'''
+
+start = datetime.datetime.now()
+result = largest_palindrome(3)
+finish = datetime.datetime.now()
+
+msg = '''That largest palindrome with two 3-digit factors is {0:,}
+It's factors are {1} & {2}
+Finished in {3} milliseconds'''
+
+delta = finish - start
+print msg.format(result.palindrome,
+                 result.factor1,
+                 result.factor2,
+                 (delta.seconds * 1000) + (delta.microseconds/1000.0))