Extracting the median of, say, 51 element, consists of splitting the 51 in a H(ead) group of 25, followed by the median, followed by a T(ail) of 25. All the algorithms that I know end up with the additional property that H and T are such that [min(H), max(H)[ and ]min(T), max(T)] do not overlap.
Is this additional property proven mandatory (I guess yes) ? where can I find the proof (I guess it have been done for long) ?
(This is only for the sake of love for algorithms)