CSES 1131 Tree Diameter - Core Idea

The core idea: start BFS from any node and find the farthest node $u$. Then run BFS from $u$ to find the farthest node $v$. The distance from $u$ to $v$ is the diameter.

Why does this work? The farthest node from any starting point must be a diameter endpoint. This is a property of trees that fails for general graphs. The proof involves showing that any path not ending at $u$ or $v$ cannot be longer than the $u$-$v$ path. You do not need to understand the proof to use the technique.