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You know QI-based optimizations. Now meet recurrences as lines and query minimum/maximum with CHT.
Covered with full walkthrough in this section.
The canonical CHT problem. Optimal substructure where cost depends linearly on previous state, perfect for convex hull optimization.
The transformation
Requires CHT in both directions. Tests understanding of when slopes are monotonic vs need Li Chao tree.
Elegant geometry problem reducible to CHT. Requires insight to transform rectangle selection into linear DP.
CHT on trees with small-to-large merging. Combines convex hull with tree DP and DSU-on-tree.
Multi-dimensional DP with CHT optimization. Teaches how to reduce O(n²k) to O(nk log n).
Geometry + CHT combination. Requires translating projection constraints into convex hull queries.
Dijkstra + CHT combination. Models flight costs as linear functions requiring convex hull queries.
Classic DP with quadratic cost. Natural introduction to CHT before harder variants.
Simpler jump optimization. Good warmup for understanding optimal substructure in CHT problems.
DP with binary search. Understanding interval DP optimization leads naturally to CHT ideas.
Frog jumping with quadratic cost - the canonical convex hull trick problem.
