- As hash is so heavily used in Perl, it is worth to explain why hash search is O(n).
One runs into the worst case of a hash search when all the elements calculate to the same hash key. In this case, a hash becomes no more than a one-dimentional chain of elements.
Even worse, the element one trying to look up happens to be the last element in the sequence. Now the searching engine has to go throguh the entire chain, all n elements, to find what one wants.
- (In rest of the post, I will just use small o instead of big O, as now I am more focused on complexity, doesn't matter whether it is for worst case, best case or whatever. Big O is just a notion saying that it is for the worst case.)
In an average case, if n is the number of elements we have in a hash, and k is the number of all possible hash key values. Ideally all elements would spread nearly even among possible hash keys, so the chain length under each hash key is n/k. Averagely you need to go though half of the chain to get what you want, thus you need to go thru n/2k elements.
So averagely a hash search would close to o(n/2k) (be very careful, n is a variable when k is a constant, this is serious), which ~ o(n).
How come the average case is the same as the worst case, NO they are not the same, but they are ~.
- Some time it is seriously dangerous to casually simplify things that is seriously complex.
o(n) is not o(n/2k), but o(n) ~ o(n/2k) (again, n is variable, and k is constant, this is very serious), the easiest way to explain ~, yet does not lose seriousness too much is that: the speed o(n) and o(n/2k) approach infinite is the same.
Although o(n) ~ o(n/10^100), what takes o(n/10^100) algorithm 1 sec, might take a o(n) alogorithm 10^100 sec to finish. They are far from the same.
Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
Read Where should I post X? if you're not absolutely sure you're posting in the right place.
Please read these before you post! —
Posts may use any of the Perl Monks Approved HTML tags:
Outside of code tags, you may need to use entities for some characters:
- a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
Link using PerlMonks shortcuts! What shortcuts can I use for linking?
See Writeup Formatting Tips and other pages linked from there for more info.
| & || & |
| < || < |
| > || > |
| [ || [ |
| ] || ] ||