Concepts6
Sqrt Tree
A sqrt tree is a layered block-decomposition data structure that answers range queries in O(1) time after O(n \log \log n) preprocessing.
Segment Tree with Range Affine Transformation
A segment tree with lazy propagation can support range updates of the form x → a·x + b (affine transformations) and range-sum queries in O(log n) per operation.
Segment Tree Beats
Segment Tree Beats is a segment tree variant that supports range chmin/chmax (clamping) together with queries like range sum, min, and max in amortized logarithmic time.
Segment Tree - Handling Multiple Lazy Operations
When a segment tree supports multiple range updates, you must define how lazy tags compose, because the order of operations matters and composition is not commutative.
Segment Tree with Lazy Propagation
A segment tree with lazy propagation supports fast range updates and range queries in O(\log n) time.
Fenwick Tree - Range Update Range Query
A Fenwick Tree (Binary Indexed Tree) can support range additions and range sum queries by maintaining two trees, often called B1 and B2.