The topics below are not exhaustive for this division.
Contest problems may contain topics not covered in the guide, or topics listed under different divisions!
Some lower-frequency topics are included in "Advanced."
It seems that no Platinum contest is complete without a segment tree ...
More Applications of Segment Tree
Walking on a Segment Tree, Non-Commutative Combiner Functions
Range Queries with Sweep Line
Solving 2D grid problems using 1D range queries.
Range Update Range Query
Lazy updates on segment trees and two binary indexed trees in conjunction.
Sparse Segment Trees
Querying big ranges.
2D Range Queries
Extending Range Queries to 2D (and beyond).
Divide & Conquer - SRQ
Using Divide & Conquer to answer offline or online range queries on a static array.
Square Root Decomposition
Splitting up data into smaller chunks to speed up processing.
... or a tree!
Introduces the problems of finding level ancestors in a tree and computing the lowest common ancestors.
A way to merge two sets efficiently.
Path and subtree updates and queries.
Decomposing a tree to facilitate path computations.
More advanced concepts in computational geometry.
Basic setup for geometry problems.
Introduction to line sweep.
Smallest convex polygon containing a set of points on a grid.
Convex Hull Trick
A way to find the maximum or minimum value of several convex functions at given points.