The dashed circle shows the current best distance. As the algorithm finds closer points, the circle shrinks, which causes more subtrees to fail the "could contain a closer point?" test and get pruned. The search usually gets cheaper as it progresses.
Old English is certainly its own language, with its own grammar, vocab, and idioms. And it does need to be studied as a different language - even now I feel like I have only scratched it's surface.
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