Quadtrees are everywhere spatial data exists. Mapping services use quadtree-like tile pyramids to serve map tiles at different zoom levels (Bing's quadkey system, for example, addresses tiles as base-4 paths). Game engines use them for collision detection and visibility culling. Geographic information systems use spatial indexes to store and query spatial datasets. PostGIS uses GiST indexes (R-tree-style) for spatial queries on geometries, while PostgreSQL's core supports quadtree-like SP-GiST indexes for certain data types like points.
The algorithm maintains a running "best distance" that starts at infinity. As it walks the tree, it checks each visited point and updates the best distance if it finds something closer. Before recursing into a child node, it checks whether the closest possible point in that child's bounding box is farther than the current best. If so, the entire subtree gets pruned.
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