Comments on: Functions Order is No Laughing Matter

By: sal

sal — Thu, 04 Dec 2008 15:45:45 +0000

Okay, this comment has nothing to do with your post!
How come you didn’t link me to your blog!!! it looks great! nice new design :)

By: Maan

Maan — Fri, 14 Nov 2008 11:29:00 +0000

Oh, I see (I thought something was wrong when I started writing that simple math. I thought you were testing me or something :P).
Hmm, yeah, mostly I think he was talking about the 2nd case.
Thanks for a lot the explanation! :)
(Doh! *forehead smack*, 1024 is for bytes only)

By: benryves

benryves — Tue, 11 Nov 2008 13:05:56 +0000

I think that the problem is in the phrasing of the example problem. Saying that it takes 1 millionth of a second to process one pixel implies a pixel-processing algorithm that is O(1), ie constant time. If you then state the size of the image in linear terms (1, 2, 3 megapixel) then you are executing an O(1) algorithm n times, giving you an O(n) algorithm to process the entire image.

If, on the other hand, the algorithm for each pixel sampled the value of every other pixel in the image then that algorithm would be O(n), and running it n times would indeed result in an O(n²) algorithm to process the entire image.

PS 1 megapixel in digital cameras is 1 million pixels, not 1024*1024 pixels. :)

By: Maan

Maan — Mon, 10 Nov 2008 18:31:13 +0000

I am honored that you took the time to visit my little blog Ben :). Thank you.

With regards to the math, let me see if I can justify it correctly:
1 Mega pixel = 1024 Kilo pixel = 1048576 pixel. This is our N.
N * N = N^2 = 1099511627776 operation using an O(N^2) algorithm on 1048576 pixel.
With 1 microsecond for each pixel operation, we need 1099511.627776 Second = 18325.193796267 Minute = 305.419896604 Hour = 12.7258 Day.

As for the linearity, Check f(x) = x^2 in this image http://en.wikipedia.org/wiki/Image:Function_ax%5E2.jpg . Without using the image, f(1) = 1, f(2) = 4, f(3) = 9. If the function was linear, there would have been a constant increase in the result of the function as x in f(x) increases. As x increases by 1 each time, the increases in f(x) are 3 then 5.

As I’m still rediscovering the joy of math, please tell me if any of the above seems illogical.

By: benryves

benryves — Mon, 10 Nov 2008 15:18:08 +0000

Maybe I’m being an idiot, but if it takes 1 millionth of a second to process one pixel, surely it takes one second to process a one megapixel image and three seconds to process a three megapixel image? That’s definitely linear.