Recall that Tarjan's off-line LCA algorithm uses Union-Find (Disjoint Set Union) to efficiently answer multiple LCA queries after a single DFS traversal.

Focus on how the algorithm maintains two key pieces of information during the DFS: the ancestor of each node in the current DFS path and the set of nodes in the subtree rooted at that node.

Analyze the time complexity of the algorithm by considering the operations performed on the Union-Find data structure and the DFS traversal, and how they contribute to the overall efficiency.