Yeah it helps make awful code decent, and some algorithms are better than others, but in terms of high performance code, locality, vectorization, and branching often matter much more big O.
That depends on what end ends. For a small N, very bad algorithms can still be plenty fast. Sometimes it can even be faster. Some of your lower O algorithms can have very terrible constant factors, which means they're terrible when N is small, but as N gets large.
Big and small N different for different algorithms and hardware both.
I've definitely had to change things into SOA in order to eke out performance. My coworkers aren't thrilled seeing `double[] x; double[] y;` but that really is about the only way to get the JVM to play nice.
