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In the linear time selection algorithm, what if we just take any n/5 elements, find the median of these elements recusrively, and use this element

In the linear time selection algorithm, what if we just take any n/5 elements, find the median of these elements recusrively, and use this element as a pivot to partition the input array. We can then recurse on a subproblem based on the rank of the pivot in the input array. Will this modification also run in linear time? If so, analyze. If not, justify why

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