Comments on: Top 25 Memes

By: Jason Adams

Jason Adams — Mon, 02 Mar 2009 00:39:02 +0000

And just noticed that wordpress mangled greater than and less than symbols in my first comment.

By: Jason Adams

Jason Adams — Mon, 02 Mar 2009 00:37:37 +0000

Ahh, ok, I was indeed making it too complicated. Thanks for clearing that up! :)

By: Jon Elsas

Jon Elsas — Sun, 01 Mar 2009 17:19:42 +0000

I think you’re making it too complicated. best case would be (N – K + K log K), as you pointed out. If we assume K is a constant, or much smaller than N, then both worst- and best-case are essentially the same, O(N). If K = O(N), then its basically a full sort algorithm.

By: Jason Adams

Jason Adams — Sun, 01 Mar 2009 14:30:52 +0000

Ah good point, but wouldn’t that just be worst case? In the best case, it’s in descending order already and you make K log K + N – K comparisons. I was thinking in the average case you’d have some probability that is decreasing as you progress through the list that the value would be propagated through the tree.

So building the first 25 items has K log K comparisons. Then for each remaining item the runtime would be O(1) if root. Maybe P(item > root) reduces to some constant value and the runtime is still O(N log K)?

By: Jon Elsas

Jon Elsas — Sat, 28 Feb 2009 13:42:54 +0000

Its O(N log K ) where K is the number of top items (25 in this case). you need to look at all N data points, but the insertion time is less (log(K)) since the size of the tree is at most K elements.