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Good performance is not just big O
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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