Ryan Bright - Latest Comments

Re: Algorithms Revisited: Fibonacci Sequence

Ryan Bright — Tue, 17 Aug 2010 21:49:02 -0000

Thanks for the insights! That's a much more efficient way of going about it than what I have listed above.

Re: Algorithms Revisited: Fibonacci Sequence

Kanak — Tue, 17 Aug 2010 19:41:51 -0000

As I explained in my reddit comment, the matrix version is logarithmic only if you perform exponentiation by repeated squarings. So, when you show M^4 being calculated by doing M * M^3, you are actually doing doing a linear time algorithm.

What you should instead be doing is: M^513 = M * M^512 = M * (M^256)^2 = M * ((M^128)^2)^2 = ... = M * ((((((((M^2)^2)^2)^2)^2)^2)^2)^2)^2

Notice how a total of 10 matrix multiplications are required.

Re: Algorithms Revisited: Fibonacci Sequence

Ryan Bright — Mon, 16 Aug 2010 19:20:36 -0000

Are you referring to the iterative solution or the matrix solution? The upper bound of the matrix solution will depend on the matrix multiplication algorithm used by the programming language, and all we're doing in our own algorithm is grabbing the lower right-hand value from the resulting matrix. Since we're not iterating, we won't need to know the values of previous Fibonacci numbers in the sequence.

If you're referring to the iterative solution, I might know what you're getting at. In most languages, we would need to store the value of f[0] + f[1] into a third variable before assigning new values to f[0] and f[1]. However, Ruby allows us to circumvent that redundancy through its parallel assignment operator. This operator will cause all right-hand values to be evaluated before assigning to the left-hand values, so the statement f[0] + f[1] will be evaluated with the original value of f[0] instead of the one being assigned by f[0] = f[1]. This might have nothing to do with your question, but I figured I'd clarify this for anyone that was curious!

Re: Algorithms Revisited: Fibonacci Sequence

josh — Mon, 16 Aug 2010 17:22:58 -0000

The matrix version is wasteful, unless you always also want the current plus the last 2 values of the sequence. fib (a, b, cur, n) = if cur == n then b else fib (b, a + b, cur + 1, n) should be better, shouldn't it? fib (1, 1, 1, 8) for the 8th number in the sequence.

Re: Algorithms Revisited: Fibonacci Sequence

John Tantalo — Mon, 16 Aug 2010 10:34:21 -0000

I think it might be fair to call it a dynamic programming algorithm.

Re: Algorithms Revisited: Fibonacci Sequence

Ryan Bright — Mon, 16 Aug 2010 10:16:23 -0000

I suppose referring to the algorithm as iterative instead of "memoization" would be more accurate. The main reason I used an array instead of two variables was purely for syntactic reasons rather than efficiency. I preferred to write f[0] and f[1] instead of fp and f when I threw the script together. :)

Re: Algorithms Revisited: Fibonacci Sequence

John Tantalo — Mon, 16 Aug 2010 10:01:43 -0000

That's not memoization between nothing is remembered between calls. Also, why do you use an array when two variables would suffice?

Re: Algorithms Revisited: Fibonacci Sequence

Renga — Mon, 16 Aug 2010 05:28:06 -0000

Very useful article

Re: 5 Resources for Refining Your Programming Skills

Kevin — Fri, 22 Jan 2010 22:12:39 -0000

This is a good list to practice our programming skills. I am a member of CodeChef and it has a good way of allowing programmers to choose the level of problems to solve.

Re: I’d Like Some Jelly with my Coworking

Ryan Bright — Mon, 14 Dec 2009 16:12:18 -0000

Yup, I'm looking forward to the meeting. I just recently began working with Flash and Flex, so I don't expect to be able to follow along quite yet. However, it will be interesting to see what everyone else is doing and also to derive some inspiration.

Re: I’d Like Some Jelly with my Coworking

@storypixel — Mon, 14 Dec 2009 15:13:14 -0000

Ryan! I've never met you I think but I hope to at the upcoming Flashcoders meet.

Re: 5 Resources for Refining Your Programming Skills

@codechef — Mon, 02 Nov 2009 08:14:32 -0000

Thanks for mentioning CodeChef, if you have any ways we can make the site better, please let us know :)

Re: 5 Resources for Refining Your Programming Skills

Lutz Hankewitz — Mon, 02 Nov 2009 07:45:27 -0000

Good List, maybe the code Kata by Chad Fowler may fit into this list.
See http://codekata.pragprog.com/ for details.

Re: 5 Resources for Refining Your Programming Skills

Daniel H — Fri, 30 Oct 2009 18:13:43 -0000

Good list. I will be bookmarking this for later.