High-performance specialized structures: Segment Trees with Lazy Propagation, Fenwick (BIT), Sparse Tables, Tarjan's SCC, KMP, and Tree Decompositions.
Segment Trees (point update, range query), Lazy Propagation for range updates, Binary Indexed Trees (Fenwick), and Sparse Tables for static RMQ.
Tarjan's and Kosaraju's Strongly Connected Components (SCC), Bridges & Articulation Points, KMP string prefix function, and Bitmask DP.
Heavy-Light Decomposition (HLD) mapping tree paths to Segment Tree intervals in O(log² n), Centroid Decomposition, and Link-Cut Trees.