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Most often k is not a constant, but a function of n. If for example k would be ~ c * n then the average length of the lists of items in each bucket would be ~ n / (c * n) which is ~ 1 / c. Which is a constant.

Therefore the key lookup of the usual implementations of hashes has average complexity of o(1).

Of course this implementation forces you to recreate the hash when the number of keys grows over some limit which can be time consuming.


P.S.: I just looked at the number of buckets in the Perl hashes (I iteratively added elements, watched the number of buckets and printed the number of elements and buckets after every rehashing). This is the results:

1 => 8 9 => 16 18 => 32 34 => 64 70 => 128 130 => 256 258 => 512 514 => 1024 1024 => 2048 2052 => 4096 4098 => 8192 8193 => 16384 16386 => 32768 32768 => 65536 65538 => 131072 Perl 5.8.0 built for MSWin32-x86-multi-thread

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

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