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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第一百一十八条 公安机关办理治安案件的期限,自立案之日起不得超过三十日;案情重大、复杂的,经上一级公安机关批准,可以延长三十日。期限延长以二次为限。公安派出所办理的案件需要延长期限的,由所属公安机关批准。