Learning about trees

Computer Science Level pending

A program takes as input a balanced binary search tree with \(n\) leaf nodes and computes the value of a function \(g(x) \) for each node \(x\). If the cost of computing \(g(x)\) is the minimum value between the {number of leaf-nodes in left-subtree of \(x\), and the number of leaf-nodes in \(x\), then the worst-case time complexity of the program is \( \text{_____________}\).

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