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Re^3: beginner help

by moritz (Cardinal)
on Aug 03, 2010 at 07:44 UTC ( #852621=note: print w/ replies, xml ) Need Help??

in reply to Re^2: beginner help
in thread beginner help

(If you're not interested in computer science subtleties, please ignore this node - for normal programming tasks the O(1) estimate is good).

For big numbers the algorithm is slower than O(n), while the summing all the values is O(2^n).

In computer science, if you are talking about O(f(n)), n is the input length, not the number that the input presents.

So adding two numbers with length n is O(n), multiplying two numbers naively is O(n^2), there are a few more elaborate algorithms that do it a bit faster.

Summing all numbers from 1 to $number is O(2^n), because the length of $number is what we call n.

(This calculation kinda assumes use bigint;, because otherwise on the perl vm adding and multiplying is O(1) indeed)

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Re^4: beginner help
by Jenda (Abbot) on Aug 03, 2010 at 10:11 UTC

    What is the "n" depends. It could very well be the output length, if the task at hand was eg. to produce N random numbers where N is the number coming from the input. There the length of the input is not really interesting, the value is. (OK, the length and the value of the number is kinda related, but you know what I mean.

    Enoch was right!
    Enjoy the last years of Rome.

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