Concepts5

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.

#sqrt decomposition#block decomposition#bucket decomposition+11

🗂️Data StructureIntermediate

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.

#iterative segment tree#segment tree#non-recursive+12

🗂️Data StructureIntermediate

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).

#segment tree#range query#point update+11

🗂️Data StructureIntermediate

2D Fenwick Tree

A 2D Fenwick Tree (Binary Indexed Tree) supports point updates and rectangle sum queries in O(log n × log m) time.

#2d fenwick tree#binary indexed tree 2d#bit 2d+12

🗂️Data StructureIntermediate

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.

#fenwick tree#binary indexed tree#prefix sum+11