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 with Lazy Propagation

A segment tree with lazy propagation supports fast range updates and range queries in O(\log n) time.

#segment tree#lazy propagation#range update+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

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).

#monotonic deque#sliding window maximum#sliding window minimum+12