How range of constraints given in problem help ?

I know complexity of algorithm is very important part and while developing solution for problem complexity plays an important role.
What I want to ask is that when you people are thinking for problem how you reject/select based you particular solution on basis of complexity .
Say 1sec is time limit . constraint n= 10^8 . no of computation in 1sec can be done ~= 10^7.
And algo you are thinking is linear .So , you reject your solution at that point only ?

And by seeing AC time of other contestants can we deduce complexity if solution like nlogN or not.
What I am asking is problem solving approach (I hope you are getting my point ) .
Please give some light about your techniques while thinking about solution .

A similar question has been answered in this quora link