Comments on: New WordPress hotness http://www.kuliniewicz.org/blog/archives/2008/05/04/new-wordpress-hotness/ After all, it could only cost you your life, and you got that for free. Thu, 19 Jan 2012 00:09:18 +0000 hourly 1 http://wordpress.org/?v=3.1.4 By: Paul Kuliniewicz http://www.kuliniewicz.org/blog/archives/2008/05/04/new-wordpress-hotness/comment-page-1/#comment-1913 Paul Kuliniewicz Sat, 10 May 2008 03:50:55 +0000 http://www.kuliniewicz.org/blog/?p=776#comment-1913 How the Fibonacci function works? The invariant for the <code>for</code> loop is that, after each iteration, <code>b</code> is set to the <code>i</code>th Fibonacci number, and <code>a</code> is set to the (<code>i</code>-1)th Fibonacci number. The more obvious recursive definition is bad because you end up repeating a lot of work. For example, <code>fibonacci(10)</code> would need to compute <code>fibonacci(8)</code> and <code>fibonacci(9)</code>, but <code>fibonacci(9)</code> ends up calling <code>fibonacci(8)</code> as well. You end up running in <a href="http://en.wikipedia.org/wiki/Big_O_notation">O</a>(<a href="http://en.wikipedia.org/wiki/Golden_ratio">φ</a><sup><var>n</var></sup>) because of all the repeated work, instead of O(<var>n</var>) like the iterative implementation, which only computes each intermediate Fibonacci number once. How the Fibonacci function works? The invariant for the for loop is that, after each iteration, b is set to the ith Fibonacci number, and a is set to the (i-1)th Fibonacci number.

The more obvious recursive definition is bad because you end up repeating a lot of work. For example, fibonacci(10) would need to compute fibonacci(8) and fibonacci(9), but fibonacci(9) ends up calling fibonacci(8) as well. You end up running in O(φn) because of all the repeated work, instead of O(n) like the iterative implementation, which only computes each intermediate Fibonacci number once.

]]> By: Ryan http://www.kuliniewicz.org/blog/archives/2008/05/04/new-wordpress-hotness/comment-page-1/#comment-1911 Ryan Sat, 10 May 2008 03:30:17 +0000 http://www.kuliniewicz.org/blog/?p=776#comment-1911 As usual, explain? As usual, explain?

]]> By: Paul Kuliniewicz http://www.kuliniewicz.org/blog/archives/2008/05/04/new-wordpress-hotness/comment-page-1/#comment-1896 Paul Kuliniewicz Mon, 05 May 2008 00:53:28 +0000 http://www.kuliniewicz.org/blog/?p=776#comment-1896 Hmm, if you look at the post in the RSS feed, the colors don't show up, since the CSS doesn't get pulled in from there. Oh well. Hmm, if you look at the post in the RSS feed, the colors don’t show up, since the CSS doesn’t get pulled in from there. Oh well.

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