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How to show that the median cannot be maintained in $O(1)$ time?

The question's title presupposes the wrong answer. Median can in fact be maintained in $O(1)$ time. Here is the counter example disproving the title's fallacious claim of “How to show that the ...
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How to show that the median cannot be maintained in $O(1)$ time?

If you can maintain the median of $n$ objects in $O(1)$, then you can sort a sequence $x_1, \dots, x_n$ in $O(n)$: first you compute a value $a$ smaller than all elements in the sequence and a value $...
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