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Across all three versions, there’s a mockToString or spoof helper. But the V3 implementation is subtly more robust than the V2 one, and it’s worth examining why.
Notice how the highlighted region shrinks at each step. The algorithm never examines points outside the narrowing window. In a balanced tree with nnn points, this takes about log4(n)\log_4(n)log4(n) steps. For a million points, that's roughly 10 steps instead of a million comparisons.