Concepts25
Category
Centroid Decomposition - Distance Queries
Centroid decomposition splits a tree into levels by repeatedly removing a centroid so that each remaining component is at most half the size.
Centroid Decomposition
Centroid decomposition splits a tree around a special node (centroid) so that every remaining component has at most half the nodes.
HLD - Path Queries and Updates
Heavy-Light Decomposition (HLD) breaks a tree into a small number of vertical chains so any path (u,v) becomes O(log n) contiguous segments in an array.
Wavelet Tree
A wavelet tree is a recursive data structure built over a sequenceβs alphabet that answers rank, select, and quantile (k-th smallest) queries in O(log Ο) time, where Ο is the number of distinct values.
Heavy-Light Decomposition
Heavy-Light Decomposition (HLD) breaks a tree into O(n) disjoint chains so that any root-to-node path crosses only O(log n) chains.
Persistent Array and Treap
Persistence lets you keep every past version of a data structure while making O(log n) updates and queries on any version.
Splay Tree
A splay tree is a self-adjusting binary search tree that moves the most recently accessed node to the root with rotations.
Implicit Treap
An implicit treap is a randomized balanced binary tree that treats array positions as keys without storing them explicitly.
Persistent Segment Tree
A persistent segment tree stores every historical version of an array-like data while supporting queries and updates in O(log n) time.
Treap
A treap is a binary search tree on keys combined with a heap on random priorities, which keeps the tree balanced in expectation.
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.