Will N^(1.5) give TLE for N=2e5 and time is 1 seconds? In genral how many operation can be executed in 1 seconds?
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With the CPP you can do 2*10^8 operations per second on average. So you can solve a question with a limit of 10^6 in nlogn time. But be careful, data structures with high constant (like std::set) may cause time limit error on such limit. If you optimize your code using pragma and etc. you can do up to 10^10 operations per second.
Optimizations don't affect the number of operations u can do per second. It only affects the number of operations that you have to do, so it takes less time in total.
If you are using the same processor, then number of operations per second (or clock speed) is always constant.
Yeah you are right, sorry for misinformation.