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.
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If this sounds familiar to you, it’s because this method works very similarly to error-diffusion. Instead of letting adjacent pixels compensate for the error, we’re letting each successive candidate compensate for the combined error of all previous candidates.