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Good performance is not just big O
(jmmv.dev)
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this post was submitted on 09 Sep 2023
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Programming
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Itcs a generalized method/notation of measuring how long a piece of code takes to run for a given input.
O(n^2^) means that as the input n grows, it takes exponential time to process. Like if you were trying to find items that matched in an array by looping over every item in the array and then using a nested loop in the first one to compare against every other item in the array. You'd be doing (# of items) * (# of items) comparisons, or (# of items)^2^ comparisons. n^2^ comparisons.
There's some rules about simplifying the result down to the most significant portion, so O^n^+n would be simplified as O^n^, but that's the basics.
It's a pretty important concept as you get into making larger projects.
this is really pedantic, but O(n^2^) is quadratic, not exponential. the exponential runtimes are things like O(2^n^). when n gets even modestly big (say n=100), youre looking at a difference of 2^100^ ≈ 1.26×10^30^ vs 100^2^ = 10,000. this is just to say that exponential runtime is really in a class of its own.
but otherwise i think this was a pretty good explanation of the concept