Extension - LCA

Binary lifting also solves the LCA problem: given two nodes $u$ and $v$, find their lowest common ancestor. The idea: bring $u$ and $v$ to the same depth using binary lifting.

Then jump both upward simultaneously until they meet. This takes $O(\log n)$ per query. You will implement this in the next problem. LCA is one of the most common tree queries in competitive programming, and binary lifting gives you a clean $O(\log n)$ solution.