Are there any good rules of thumb on when a square root decomposition will be too slow? I suspect if we have an interval of length 105 and 3 × 105 queries a square root decomposition is too slow but this is only based on my attempts to solve http://codeforces.com/problemset/problem/765/F with a square root decomposition where I calculated the complexity of my algorithm to be 
and exceeding the time limit. In general if you are given an interval of length N and Q queries what sort of values of 
do you want in order to be confident that a square root decomposition will pass the time constraint? Also are there standard limits used in Codeforces deliberately set to prevent square root decomposition based approaches?
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Is it really ever possible to be confident in square root decomposition?
Probably as long as complexity yield less than 200m operations you are fine.
Thanks I will use 200m operations as a rule of thumb for future problems.