Linear algorithm of finding tree diameter

Question

I have the following code to find the diameter of a tree:

ALGORITHM: TREE_DIAMETER (T)

maxlength ← 0
for s ← 0 to s < |V[T]|
      do temp ← BSF(T, S)
               


        

Answer 1

Here is a simple algorithm with linear time complexity:
1)Pick an arbitrary vertex v.
2)Find the furthest vertex from v using BFS(let's call it u).
3)Find the furthest vertex from u using BFS one more time(let's call it t).
Then distance(u, t) is the diameter.
BFS is called only twice, so the time complexity is linear.