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Maybe someone could clarify something for me here:

o(n) seems like a stronger statement to me than O(n), since all o(n) algorithms are O(n), but the reverse is not true.

Also if o(n) applies to all n, however small, whereas O(n) applies only when n -> inf,

(From the Wikipedia page example: 2n = O(n) but 2n != o(n))

Then doesn’t that means this algorithm should be applicable to even small n’s? Then it would be the opposite of a galactic algorithm, as someone above suggested, wouldn’t it?

Or am I missing something?


Little o is still an asymptotic statement: it doesn’t have to apply for small n. A definition of f(n) = o(g(n)) is something like

   lim (n -> infinity) f(n)/g(n) = 0
Or, in other words, for sufficiently large n, g grows faster than f.

For instance, this function is o(n), because 1e1000/n goes to 0 as n grows.

   f(n) = 10**n if n < 1000 else 1e1000
(Pseudo-Python for a piecewise function that grows exponentially to 10**1000 at n = 1000 and then remains constant after that.)


If the complexity of an algorithm is 3↑↑64*n^0.999, the algorithm is o(n) but can safely be said to be galactic.

* Ps, if memory serves me correct, 3↑↑64 is Graham's number.


Location: Switzerland

Remote: Yes

Willing to relocate: In Switzerland only

Technologies: Typescript, Python, C, Nextjs, TailwindCSS, Svelte

Résumé/CV: Upon request

Email: remimarche at gmail.com

----

Hey, I'm a friendly web developer, that likes say it's hard to make me lose my smile. I have several years of experience in the industry, mostly in C++ and Web (React), but I spent most of my free time with Svelte and Vue, have developed a music font, and studied Rust quite a good bit.

As I need a last internship to finish my engineering studies, I'll be willing to have a look at any interesting opportunity, and really, if anything, the fact that it's called internship is just because I need it to be so on papers. The only difference for you is that you may have to read a few pages explaining what I did during the last months of work. The internship should be from june to december.

Have the greatest day,

Remi Marche


Location: Switzerland

Remote: No

Willing to relocate: In Switzerland only

Technologies: Typescript, Python, C, Nextjs, TailwindCSS, Svelte

Résumé/CV: Upon request

Email: remimarche at gmail.com

----

Hey, I'm a friendly web developer, that likes say it's hard to make me lose my smile. I have several years of experience in the industry, mostly in C++ and Web (React), but I spent most of my free time with Svelte and Vue, have developed a music font, and studied Rust quite a good bit.

As I need a last internship to finish my engineering studies, I'll be willing to have a look at any interesting opportunity, and really, if anything, the fact that it's called internship is just because I need it to be so on papers. The only difference for you is that you may have to read a few pages explaining what I did during the last months of work. The internship should be from june to december.

Have the greatest day,

Remi Marche


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