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.