Concepts9
Sweepline Technique
The sweep line technique processes geometric or time-based events in sorted order and maintains an active set that reflects the current state at the sweep position.
State Space Reduction
State space reduction shrinks the number of dynamic programming or search states by keeping only the information that truly affects future decisions.
Offline Query Processing
Offline query processing means you collect all queries first and answer them later in a smart order that makes updates/queries cheap.
Mo's Algorithm
Mo's algorithm answers many range queries offline by reordering them to minimize pointer movement along the array.
Line Sweep
Line sweep (plane sweep) is a technique that processes geometric objects by moving an imaginary line and handling events in sorted order.
LIS Variants
LIS variants extend the classic longest increasing subsequence to handle non-decreasing sequences, counting how many LIS exist, and maximizing the sum of a subsequence.
Coordinate Compression
Coordinate compression replaces large, sparse, or arbitrary values with small consecutive integers while preserving relative order.
Merge Sort Tree
A Merge Sort Tree is a segment tree where every node stores the sorted list of values in its segment.
2D Fenwick Tree
A 2D Fenwick Tree (Binary Indexed Tree) supports point updates and rectangle sum queries in O(log n × log m) time.