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in reply to Re^6: Modified Binary Search
in thread Modified Binary Search

That doesn't change the complexity.

Rubbish!

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
"Science is about questioning the status quo. Questioning authority".
In the absence of evidence, opinion is indistinguishable from prejudice.

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Re^8: Modified Binary Search
by BrowserUk (Pope) on Jan 16, 2010 at 01:19 UTC

The point: A well implemented binary search is O(logN) worst case, but averages O(logN - 1).

But, in order to accommodate duplicates, you are forced to recind the possibility of early discovery, which forces the average case to the worst case. Eg. The complexity changes!

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
"Science is about questioning the status quo. Questioning authority".
In the absence of evidence, opinion is indistinguishable from prejudice.
In big O notation O(logN - 1) and O(log N) are equivalent. They denote the same complexity order.

Though, that does not mean that the two algorithms are equally efficient. Actually they are not: Re^3: Modified Binary Search.

I'm aware that the theorists will categorise them as having the same order of complexity, but when additional conditional checks are required, the complexity has increased.

And at some point it is necessary to decide whether you need to find the lowest value greater or equal to the search term or the highest value less than or equal to the search term. And that adds to the (actual, real-world), complexity of the code.

I know you know this--as your many Sort::* packages assert--in Perl, it is the number of source-level operations that is most relevant to efficiency:

```@a = 1 .. 1e6;
cmpthese -1, {
a=>q[ my \$total = sum @a; ],
b=>q[ my \$total = 0; \$total += \$_ for @a ],
};;
Rate    b    a
b 10.8/s   -- -73%
a 40.9/s 277%   --