Having a fast and responsive app is orthogonal to “knowing your big Os”. Unfortunately, most tech companies over-emphasize algorithms in interviews and downplay systems knowledge, and I believe that’s one reason behind sluggish apps and bloated systems.
I’ve seen this play out repeatedly. Interviewers ask a LeetCode-style coding question, which is then followed by the ritual of discussing time and memory complexity. Candidates ace the answers. But then… their “real” code suffers from subtle yet impactful performance problems.
Itcs a generalized method/notation of measuring how long a piece of code takes to run for a given input.
O(n2) 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. n2 comparisons.
There’s some rules about simplifying the result down to the most significant portion, so On+n would be simplified as On, but that’s the basics.
It’s a pretty important concept as you get into making larger projects.
this is really pedantic, but O(n2) is quadratic, not exponential. the exponential runtimes are things like O(2n). when n gets even modestly big (say n=100), youre looking at a difference of 2100 ≈ 1.26×1030 vs 1002 = 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