Height balanced means the height is O(log n). So if I don't use the [n/2] as a pivot (say I use [n/3]), it is still a height balanced tree. But the judge will say you are wrong.
I'm not 100% sure but I think what you're talking about is weight-balanced trees, not height-balanced trees. You can find the imho typical definition of height-balanced trees here: https://leetcode.com/problems/balanced-binary-tree/. Your tree probably violates that.
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