Should we really care about Branch Prediction while writing and submitting code on any online judge, as branch prediction drastically can increase or decrease a programs runtime?
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When it would actually affect your result (AC/TLE), then yes.
Most of the time, however, no.
Xellos have you ever got your code TLE due to branch prediction?
Yeah, but not often and mostly when using suboptimal algorithms. It's not something you should primarily worry about.