Now that we can build the tree, let's use it to search. Finding a specific point means starting at the root and asking: which child quadrant contains this coordinate? Then you recurse into that child and ask again. Each level of the tree cuts the search space by roughly three-quarters.
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This month, OpenAI announced their Codex app and my coworkers were asking questions. So I downloaded it, and as a test case for the GPT-5.2-Codex (high) model, I asked it to reimplement the UMAP algorithm in Rust. UMAP is a dimensionality reduction technique that can take in a high-dimensional matrix of data and simultaneously cluster and visualize data in lower dimensions. However, it is a very computationally-intensive algorithm and the only tool that can do it quickly is NVIDIA’s cuML which requires CUDA dependency hell. If I can create a UMAP package in Rust that’s superfast with minimal dependencies, that is an massive productivity gain for the type of work I do and can enable fun applications if fast enough.
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