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If the average depth of a node in an n-node binary search tree is O(lg n), then the height of the tree is

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If the average depth of a node in an $n$-node binary search tree is $O(\log{n})$, then the height of the tree is

  1. $O(n\log{n})$
  2. $O(n)$
  3. $O(\log{n})$
  4. $O(\sqrt(n\log{n}))$
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