HOW TO SOLVE THE INEQUALITY i*(i + 1) <= n such that i is maximum possible in O(1) time complexity.is their exist any method.
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This is the one I can think of. Solve $$$i^{2}+i-n=0$$$
So just take floor(sol) from the previous equation.
The problem is that solution involves computing square root which is not O(1).
yeah that is the problem, i can find it in sqrt complexity but i guess constant complexity is not possible
Computing the square root of a number is actually very close close to O(1) !
I don't know the complexity exactly but it is described here : https://en.wikipedia.org/wiki/Computational_complexity_of_mathematical_operations