Doubt on chances of TLE

Say the constraints for a question are a<=10^5 and b<=10^5 , what are the chances that a solution
with complexity = O(alog(a) + min(asqrt(b) , a/sqrt(b) ) will pass ?

time limit ?

1 second !

In one sec, approx. 10^7 to 10^8 operations can be excecuted. So, I think your solution would pass in 1 sec.

alog(a) can be maximum approx 2 * 10^6 and second term’s maximum value is 10^5.

what about O(min(a*b , a/b)) ? Chances of TLE ?
And is this realistic? I mean can best
solution for any question have this complexity?

O(min(a*b,a/b)) can be maximum 10^5. So the overall maximum operations are approx 2.1 * 10^6 and these number of operations can easily be executed in 1 sec. So there is no chance of getting of TLE. And yes, this is realistic.