CSES 1132 Tree Distances I - Walkthrough

Tree: edges ($1$,$2$), ($1$,$3$), ($3$,$4$), ($3$,$5$). BFS from $1$ gives farthest nodes $4$ and $5$ (distance $2$). Pick $4$.

BFS from $4$ gives farthest node $2$ (distance $3$). BFS from $2$ gives distances {$2$:$0$, $1$:$1$, $3$:$2$, $4$:$3$, $5$:$3$}.

From endpoint $4$: distances {$4$:$0$, $3$:$1$, $5$:$2$, $1$:$2$, $2$:$3$}. From endpoint $2$: distances {$2$:$0$, $1$:$1$, $3$:$2$, $4$:$3$, $5$:$3$}.

For node $3$: max(dist from $4$, dist from $2$) = max($1$, $2$) = $2$. That is node $3$'s answer.