Challenge: Finding the Actual Path

The diameter DP gives the length, but what about the actual path? Track which children give the two longest depths. At the node where the maximum occurs, you have two endpoints.

From each, trace back through the tree. Alternative: run BFS from any node to find the farthest node $u$. Then BFS from $u$ to find the farthest node $v$. The path $u \to v$ is the diameter. The two-BFS approach is simpler to implement when you need the actual path, not just the length.