Tree Diameter - State Design

$dp[v]$ = the length of the longest path starting at $v$ and going down into $v$'s subtree. For a leaf, $dp[\text{leaf}] = 0$ (no edges going down).

For internal nodes, $dp[v] = 1 + \max(dp[\text{child}])$ over all children. At each node $v$, the longest path through $v$ combines the two deepest downward paths: $dp[\text{child}_1] + dp[\text{child}_2] + 2$. Track this in a global variable as you go.