Groups
Category
Level
A Link-Cut Tree (LCT) maintains a dynamic forest and supports link, cut, and path queries in O(log n) amortized time.
A segment tree with lazy propagation supports fast range updates and range queries in O(\log n) time.
A Fenwick Tree (Binary Indexed Tree) maintains prefix sums so you can update a single position and query a prefix in O(\log n) time with a tiny constant factor.