Concepts318
Category
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.
Hash Table
A hash table stores key–value pairs and finds items in expected O(1) time using a hash function to map keys to buckets.
Ordered Set and Map
std::set and std::map store elements in sorted order using a balanced binary search tree (typically a Red-Black Tree).
Priority Queue (Heap)
A priority queue returns the highest-priority element first and is efficiently implemented by a binary heap.
Queue and Deque
A queue is a First-In-First-Out (FIFO) line where you add at the back and remove from the front in O(1) time.
Monotonic Deque
A monotonic deque is a double-ended queue that keeps elements in increasing or decreasing order so that the front always holds the current optimum (min or max).