Distinct Colors - Naive Approach

For each node, run a DFS to collect all colors in its subtree, then count distinct values. This is $O(n)$ per node, so $O(n^2)$ total. Too slow. Alternatively, maintain a set per node and merge child sets after processing them. If you merge in arbitrary order, you hit the $O(n^2)$ chain case.

Small-to-large merging fixes this. By always merging the smaller set into the larger one, you guarantee $O(n \log n)$ total operations across all merges in the tree.