Link-Cut Trees support dynamic tree operations. Core Operations:
- Link: Connect two trees
- Cut: Disconnect edge
- Path queries: Aggregate on root-to-node path
Key Concept: Preferred paths decompose tree.
Splay trees represent preferred paths. Access Operation: Makes path to root preferred.
All other operations build on access. Applications:
- Dynamic connectivity
- Online LCA queries
- Path aggregates in changing trees
Time: amortized. Space: .