Concepts22
Category
Merge Sort Tree
A Merge Sort Tree is a segment tree where every node stores the sorted list of values in its segment.
Sqrt Decomposition
Sqrt decomposition partitions an array into about \(\sqrt{n}\) blocks, each of size about \(\sqrt{n}\), to speed up range queries and updates.
Iterative Segment Tree
An iterative segment tree stores all leaves in tree[n..2n-1] and internal nodes in tree[1..n-1], enabling O(\log n) point updates and range queries without recursion.
Binary Trie for XOR
A binary trie (also called a bitwise trie) stores numbers by their binary bits, branching on 0/1 at each level.
Segment Tree with Lazy Propagation
A segment tree with lazy propagation supports fast range updates and range queries in O(\log n) time.
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.