Transformers solve these using attention (for alignment), MLPs (for arithmetic), and autoregressive generation (for carry propagation). The question is how small the architecture can be while still implementing all three.
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.
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