Distinct Colors - Walkthrough

Tree: node $1$ (color $1$) has children $2$ (color $2$) and $3$ (color $1$). Node $2$ has child $4$ (color $3$). Process leaf $4$: set = {$3$}, answer = $1$. Process node $2$: take set from child $4$ which is {$3$}, add color $2$. Set = {$3$, $2$}, answer = $2$.

Process leaf $3$: set = {$1$}, answer = $1$. Process node $1$: child $2$ has larger subtree (size $2$ vs $1$). Take set {$3$, $2$} from child $2$. Merge {$1$} from child $3$. Add color $1$. Final set = {$1$, $2$, $3$}, answer = $3$.