Sorry IMHO O() is usually calculated for the worst case, otherwise "traveling salesman" and similar problems wouldn't be NP, even though there are well known algorithms which are "usually" polynomial!

You may want to calculate the complexity depending of what you called $factor, with $factor==1 its O(1) with $factor==1/2 it's O(n).

Anyway with binary search it's O(log n), which is the theoretical optimum for this class of problems. So O(1) would be considered a sensation in academic circles! IMHO binary search is mostly faster than your algorithm.

If you want to argue with something like average-case analysis you should indicate it clearly, since worst case is the usual approach.

The average case is much more complicated to define and to calculate. You have no clue what the average case really looks like, without far more input from the OP.

BTW: You can hardly compare collisions in hashes since they should be the exception not the rule.

Cheers Rolf

In reply to Re^4: Rapid text searches ( O(log n) time) by LanX
in thread Rapid text searches by joomanji

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