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You are given $n$ keys in array $X[ 1.. n ]$. We would like to determined the smallest, third smallest, and fifth smallest keys and
You are given $n$ keys in array $X[ 1.. n ]$. We would like to determined the smallest, third smallest, and fifth smallest keys and also the largest, third largest, and fifth largest keys in as few comparisons as possible. Design an algorithm to do so, count a tight upper bound on the number of comparisons performed, and state the a,b constants of that bound. A desirable comparison count/bound a * n * lgn + b*n + o(n) has constant a close to zero and b as small as possible and also smaller than 6.
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