After diving more and more into randomized algorithms(and teeny-weeny bit into the simulation of ray tracing) I have realised the unfathomable potential of Monte-Carlo methods (if used properly) . It can help break down extremely complex constructive algorithms into simple random sampling.

However, considering the time limit of 1-2 secs on most of the problems on CF and AtCoder it feels impossible to simulate Monte Carlo without facing a TLE or a WA (if the ans involves exact floating points).

Is there any way to implement a time bound randomised search and bypass the natural time based restrictions and is it feasible during official rounds?

To those who help, ありがとうございます in advance..