In a balanced binary search tree with $n$ elements, what is the worst case time complexity of reporting all elements in range $[a, b]$? Assume that the number of reported elements is $k$.

To perform a range query $[a, b]$ in a balanced binary search tree with $n$ elements:

1. Finding the range boundary: Searching for the first element $\ge a$ (or the lowest common ancestor / split node) takes time proportional to the height of the balanced BST, which is $\Theta(\log n)$.

2. Reporting elements: An in-order traversal is performed to collect all keys within $[a, b]$. Visiting each of the $k$ relevant nodes and traversing up to $O(\log n)$ boundary edges takes $\Theta(k)$ additional time.

Thus, the total worst-case time complexity is $\Theta(\log n + k)$.

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