No, I guess you've misunderstood the logic.

See, the idea is to build a max balanced tree.
For which,  we need to check the height of the tree
only the first time, there after we know what
the lengths of the left and right chains are
going to be.

So, though your recursive formula looks right,

>>>T(N) = 2T(N/2) + O(N) which results T(N) = O(NlogN)

there is a subtle flaw in that, the O(N) isn't
performed for every call.
Hope this clears things out.


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