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15 Mar 10 Project Euler : Problem 29 in Ruby

I spent some time playing around with a way to reduce calculations by constructing something akin to a sieve, (2^16 is the same as 4^8 and 16^4), but it turns out that the brute force solutions runs in under a second on my machine so it seemed silly to spend any more time with it.

Ruby even minds the big numbers for me, so the solution is quite trivial:

Problem #29

How many distinct terms are in the sequence generated by a^(b) for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?

MIN, MAX = 2,100
values = []

(MIN..MAX).each do |base|
  (MIN..MAX).each do |power|
    values << base**power
  end
end

puts values.uniq.length
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11 Mar 10 Project Euler : Problem 27 in Ruby

I've taken ill for the last two days, so I've been working on a couple Project Euler problems in between trips to the bathroom.

Problem #27

Find the product of the coefficients, a and b, for the quadratic expression that produces the maximum number of primes for consecutive values of n, starting with n = 0.

Since you start with n = 0, you know that b always has to be prime in order to satisfy n = 0.

Next, if b must be prime, and all primes greater than 2 are odd, and we don't care about expressions resulting in less than 3 consecutive primes (example expression has 40), then we know that all values of a must be odd in order to satisfy n = 1!

I also suspect that for the number of consecutive primes we need to 'win', that we only need to look at negative values of a, but I'm having a heck of a time trying to prove it.

027.rb

require 'prime_generator'

# pre-calculate primes
MAX     = 1_000
primer  = Prime_Generator.new MAX
primes  = primer.stack
product = 0
highest = 0

# a must be odd
(0..MAX).each do |i|
  next if i & 1 == 0

  # b must be prime
  primes.each do |b|

    # a can be positive or negative
    [i,-i].each do |a|
      n = 0
      while n += 1 do
        break unless primer.is_prime?(n ** 2 + a * n + b)
      end

      if highest < n
        highest = n
        product = a * b
      end

    end
  end
end

puts product

And here's the prime generator I'm using:

prime_generator.rb

class Prime_Generator

  attr_reader :stack

  def initialize max = 3
    @stack  = [1,2,3]
    fill_to max
  end

  def fill_to max
    n = 1
    while true do
      n += 4
      return @stack if n > max
      @stack << n if is_prime? n

      n += 2
      return @stack if n > max
      @stack << n if is_prime? n
    end
  end

  def is_prime? n
    return false if n <= 0
    max = Math.sqrt(n).floor
    fill_to(max + 1) if max > @stack.last

    @stack.each do |i|
      next if i == 1
      return true if i > max
      return false if n % i == 0
    end

    true
  end

end

You can find more Project Euler solutions here: https://svn2.assembla.com/svn/joe-zack-personal/projects/euler/ruby/

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09 Mar 10 The War of The Roosevelts – Part Deux

After spending a few dozen hours playing The War of the Roosevelts, I realized that there was a wee bit of room for improvement.

Now, there's like cards and stuff.

Enjoy.

THE WAR OF THE ROOSEVELTS!

Here's the source, but I still won't waste my time looking up the svn link. ;)

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02 Mar 10 The War of The Roosevelts

I've been tinkering around with C# and Flex a lot this year, but I haven't been posting much.

So in the interest of posting *something* I give you...

*drumroll*

THE WAR OF THE ROOSEVELTS!

You, standing in the (uneven?) shoes of Franklin D. Roosevelt, finally get a posthumous chance to stand up to your bullying older cousin Teddy in a game of WAR...well, at least the game of war as I knew it growing up. Wikipedia's got it's own ideas.

I lost interest in it by the time I got to the gui, so that aspects (aka as the part people actually see) is a bit...rough. Just a bit. ENJOY!

Here's the source, but I won't waste my time looking up the svn link. ;)

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07 Feb 10 ColdFusion CacheLocker

Pay Per Use Locker

Pay Per Use Locker

I ran into a problem the other day where I needed a way to temporarily store data between page requests. Typically I'm able to stash this sort of thing in the session scope, but these requests originated from different sources and I prefer to avoid (de)serializing when I can.

Instead I set up something akin to one of those pay-per-use lockers. You stick your items in the bin, drop in a few quarters, and take the newly unlocked key. Later you come back and use that key to retrieve your items. Your key is now 'locked' back into the starting position and the cycle begins anew.

Like one of those pay-per-use lockers you just stash your data, save they key, use the key, trash the data.

Simple as pie.

This isn't the sort of thing that comes up often, but should it arise I've got just the tool for the job!

Example Usage:

// initialize the locker
application.cacheLocker = CreateObject("component","cacheLocker").init();

// store some arbitrary data
key = application.cacheLocker.store([1,2,3,4]);

// then retrieve the data using the saved key
// throws a CacheException if the key doesn't 'fit'
arbitraryNumbers = application.cacheLocker.retrieve(key);

The data is destroyed after being retrieved; it's a one time only locker.

There are two important things to keep in mind when using this utility:

  1. There's currently no mechanism for cleaning out lockers, so if you're not regularly retrieving your data then this thing is just going to grow, and grow, and grow.
  2. The locker is not stored in any sort of persistent memory. If ColdFusion goes down, then the lockers are destroyed.

Enjoy!

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