Static tree problems: Tree structure is fixed. Use HLD, Euler tour, or tree DP.
Dynamic tree problems: Edges are added/removed. Examples:
- Network design: connect/disconnect servers
- Game trees: add/remove moves
- Dynamic minimum spanning tree
Why Union-Find isn't enough: Union-Find tracks connectivity but can't:
- Answer path queries (sum, min, max)
- Support edge deletions (only additions)
- Find LCA or path length
Link-Cut trees solve all these with operations.