Tree Diameter - Walkthrough

Trace diameter on a tree: $1$-$2$-$3$-$4$ with $5$ attached to $2$. The diameter is the path $4$-$3$-$2$-$5$ or $4$-$3$-$2$-$1$ (length $3$). At each node, compute $depth1$ and $depth2$ = two longest paths going down.

The candidate diameter through this node is $depth1 + depth2$. At node $2$: paths down are to $1$ (length $1$), to $5$ (length $1$), and to $3$-$4$ (length $2$). Two longest: $2$ and $1$. Candidate: $2 + 1 = 3$. The global maximum of all candidates gives the diameter. Post-order traversal keeps children are processed before parents.