Concepts6
Think Backwards (Reverse Thinking)
Think Backwards is a problem‑solving pattern where you reverse time or direction so hard deletions become easy insertions and the final state becomes the starting point.
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.
Sqrt Decomposition on Queries
Sqrt decomposition on queries (time blocking) processes Q operations in blocks of size about \(\sqrt{Q}\) to balance per-query overhead and rebuild cost.
Parallel Binary Search
Parallel Binary Search (PBS) lets you binary-search the answers of many queries at once by batching them by their current mid value.
DSU on Tree (Sack)
DSU on Tree (also called the Sack technique) answers many subtree queries in O(n \log n) by keeping data from the heavy child and temporarily re-adding light subtrees.
Mo's Algorithm
Mo's algorithm answers many range queries offline by reordering them to minimize pointer movement along the array.