The Naive Approach

You could run BFS from every node, find the farthest distance from each, and take the maximum. That gives you the diameter but costs $O(n^2)$ time: $O(n)$ BFS calls, each taking $O(n)$.

For small trees this works. For $n = 10^5$, you would do $10^{10}$ operations, which is too slow. You need a smarter approach that finds the diameter without checking every starting point. The two-BFS method does exactly this in $O(n)$ total time. It exploits a property of trees that general graphs lack.

Space complexity is $O(n)$ for the data structures used.