Also big O analysis IMO should just be the starting point of maximizing efficiency. Those coefficients that just get dropped can have a huge impact. For example, any algorithm written in JavaScript or visual basic will be of the same order as that same algorithm written in C/C++ or rust, but will likely perform much slower. And the exact manner of implementation could even result in the C version being slower than the VB one.
And on the other hand, I wouldn’t call a lot of big O analysis very advanced math. You might get a tighter bound with advanced math on some algorithms, but you can get a rough estimate just by multiplying and adding loops together. The harder question would be something like “does this early exit optimization result in an O(x³) algorithm becoming an O(log(x)*x²)?”
There’s a lot of software engineering that doesn’t require understanding Big O
Also big O analysis IMO should just be the starting point of maximizing efficiency. Those coefficients that just get dropped can have a huge impact. For example, any algorithm written in JavaScript or visual basic will be of the same order as that same algorithm written in C/C++ or rust, but will likely perform much slower. And the exact manner of implementation could even result in the C version being slower than the VB one.
And on the other hand, I wouldn’t call a lot of big O analysis very advanced math. You might get a tighter bound with advanced math on some algorithms, but you can get a rough estimate just by multiplying and adding loops together. The harder question would be something like “does this early exit optimization result in an O(x³) algorithm becoming an O(log(x)*x²)?”
I think the tldr; of what you said is that even when you have a theoretical handle on the growth function, you still need to actually benchmark anyway