One thing that you didn't actualy give is a defintion for "order of growth", which would explain why O(1)==O(2), and why O(2N+3) == O(N).

I'd try to give a defintion, but I'd most likely get it wrong... I almost quoted Knuth here, but then I realized that I didn't understand what he meant. (For those that care, see pg 107 of vol 1, 3rd ed, of TAoCP.)

Update: Everything below this point. (I kept reading that section, and didn't want to "waste" another node.)

In purticular, note that O(n) gives an /upper/ bound on the order of growth of a purticular algo, and is by no means exact. There's also Ω(N), which gives the lower-bound.

Additionaly, saying that one algo is O(1), whereas another is O(2^N) does mean that, for a large enough dataset, the first algo will be faster then the second. It does /not/ mean that it will be for any reasonable dataset. For example, if the first algo takes 1 year to complete, but the second takes 2^N nanoseconds, it will take... well, a huge dataset before the first becomes faster.

Warning: Unless otherwise stated, code is untested. Do not use without understanding. Code is posted in the hopes it is useful, but without warranty. All copyrights are relinquished into the public domain unless otherwise stated. I am not an angel. I am capable of error, and err on a fairly regular basis. If I made a mistake, please let me know (such as by replying to this node).

In reply to Re: An informal introduction to O(N) notation by theorbtwo
in thread An informal introduction to O(N) notation by dws

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