Consider how a bitonic path can be constructed by combining two monotonic paths (one increasing, one decreasing) in a sorted point set.

Explore dynamic programming where the state tracks the last point added to each of the two paths and the current "frontier" of unprocessed points.

Investigate how to efficiently compute the optimal split point where the two paths merge by leveraging geometric properties (e.g., nearest neighbors or convex hull edges) to reduce the search space.