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It should be noted that many algorithm's O time can be reduced.
You may be getting "best case" and "worst case" mixed up. Clever short-circuits in implementations of algorithms often increase the best case, but only if the data behaves certain ways. There are usually mixes of data that defeat the short-cuts. O() is about worst-case behavior.
In reply to Re: Re: An informal introduction to O(N) notation
by dws
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