Concepts40
Segment Tree with Lazy Propagation
A segment tree with lazy propagation supports fast range updates and range queries in O(\log n) time.
Dynamic Segment Tree
A dynamic segment tree stores values over a huge coordinate range by creating nodes only when an operation touches their interval.
Trie (Prefix Tree)
A trie (prefix tree) stores strings or bit-sequences so that common prefixes share nodes, making operations depend on the key length L rather than the set size.
Segment Tree Basics
A segment tree is a complete binary tree that stores information about array intervals to answer range queries and support point updates in O(log n).
2D Fenwick Tree
A 2D Fenwick Tree (Binary Indexed Tree) supports point updates and rectangle sum queries in O(log n × log m) 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.
Fenwick Tree (Binary Indexed Tree)
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.
Sparse Table
A Sparse Table is a static range-query data structure that preprocesses an array in O(n \log n) time and answers many queries in O(1) time.
Rollback DSU
Rollback DSU (Disjoint Set Union with undo) lets you union sets and later revert to any previous state in LIFO order.
DSU with Weighted Edges
A DSU with weighted edges (also called a potential or difference-constraint union-find) maintains relative values between elements while still supporting near-constant-time merges and finds.
Disjoint Set Union (Union-Find)
Disjoint Set Union (Union-Find) maintains a collection of non-overlapping sets and supports fast merging and membership queries.
Policy-Based Data Structures
Policy-Based Data Structures (PBDS) are GNU C++ extensions that add advanced containers like an order-statistics tree, a fast hash table, and ropes for efficient string edits.