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The issue with that approach is that, the distribution would be skewed in favor of elements belonging to depths (/heights) which have lesser nodes. For e.g. at depth 0, we only have 1 element, i.e. root. At depth 1, we have 2. At depth N, say its a balanced BST, we'd have 2^N elements. If we're choosing equally among depth [0, N], individual element at depth N, would have a much smaller chance of being selected than anything above it.
- mrjn April 22, 2013This might or might not be a concern. But, if I was the interviewer, I'd definitely want to get a solution where there's an equal probability of selection for each element in the tree.