Solve k-Nearest Places by Latitude/Longitude

Given a set of geographic coordinates and a query point, return the k nearest locations. Describe how you compute great-circle distance (e.g., Haversine), choose data structures or indexes (e.g., k-d tree variants, geohash bucketing, or R-tree), and bound runtime and memory complexity. Discuss handling of Earth curvature, antimeridian crossings, and performance at scale, including approximate search and batching.